![Types of Searching Algorithms · The Number of Objectives: Depending on the nature of the problem, some problems have a single-objective function while there are many others that have goals with multi-objective functions, referred to as multi-objective optimization. In reality, the latter case requires to be incorporated with a weighted average to reflect the nature of the several objectives' existence. So, a multi-parameter vector is used for their fitness functions. [6]](http://web-wp.archive.org/web/20230308211349/https://www.researchgate.net/profile/Nidhal-El-Omari/publication/344324283/figure/fig2/AS:941224244551690@1601416755408/Types-of-Searching-Algorithms-The-Number-of-Objectives-Depending-on-the-nature-of-the_Q320.jpg)
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IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
30
Manuscript received January 3, 2020
Manuscript revised August 25, 2020
DOI: 10.22937/IJCSNS.2020.20.08.5
Sea Lion Optimization Algorithm for Solving the Maximum
Flow Problem
Dr. Nidhal Kamel Taha El-Omari
Department of Software Engineering, Faculty of Information Technology,
The World Islamic Sciences and Education (WISE) University, Amman – Jordan
Summary
There is a shred of ample evidence that optimization is an enormous
field that pervades essentially every aspect of our day-to-day life
ranging from academic and engineering fields, going to industrial and
agricultural segments, passing through social domains, and ending
with commercial and business sectors. Evidently, the philosophy of
optimization has emerged out of the utmost need for finding the best
available solution among a set of candidate ones, without which our
life will lose its vitality.
Over the last few decades, a worthy amount of interest has been
focused on finding solutions for a wide range of intractable
optimization problems by scientists and researchers from diversified
domains not only for academic and research objectives but also due
to the existence of a wide variety of real-life applications. They
indeed see the remarkable resemblance between the swarms, for
instance, and the behavior of a human in solving problems and trying
to come up with new goal-oriented operating methods to tackle many
important real-world problems. Nature Inspired Computing (NIC), as
its name implies, is the fusion of nature, by itself, and Artificial
Intelligence (AI) to solve various global optimization problems.
Furthermore, swarm optimization is considered as the most
representative of these nature-inspired algorithms. Motivated by
applying natural phenomena to metaheuristics and trying to simulate
the harmonious behaviors of creatures in solving problems
particularly the joint hunting behavior of the sea lions, the aim of the
research work reported in this paper is twofold. On the one hand,
many theoretical and practical aspects of heuristic and metaheuristic
approaches, from classical to novel approaches, are discussed and
covered. On the other hand, this nature-inspired paper addresses a
pioneer metaheuristic optimization algorithm in the context of
finding the optimal solution for the Maximum Flow Problem (MFP).
To be more precise, this paper elaborates on using the Sea Lion
Optimization (SLnO) Algorithm for solving the Maximum Flow
Problem (MFP), hence the name “SLnO-MFP”.
After the proposed solution SLnO-MFP algorithm is analyzed and
the experimental tests are conducted on various real-case datasets, the
reported practical results are represented, discussed, and compared
using the same datasets with other algorithms, including the Whale
Optimization Algorithm (WOA) and Ford-Fulkerson (FF) algorithm,
which have been used to solve the same problem of interest. As the
accomplishment achieved in this valuable research is efficient and
robust, the proposed algorithm is proved to be a senior-level
alternative to the optimization problem and, in turn, can be efficiently
used to solve various optimization problems having a fairly large-
scale data such as the underlying problem (i.e. MFP).
Keywords:
Artificial Intelligence (AI), Artificial Neural Network (ANN), Global
optimization, Maximum Flow Problem (MFP), Metaheuristic
Algorithms, Optimization, Sea Lion Optimization (SLnO) Algorithm,
Swarm Intelligence.
1. Introduction
Every aspect, visible or invisible, of our life, encompasses
inside its folds a wide range of optimization problems. Not just
that, every real-world system, or even a portion of a system,
can be abstracted as an optimization system and encapsulates
internally one or more optimization problems. In the most
basic sense, the primary interests of optimization algorithms
(OAs) are pivoting around making something more and more
effective to the greatest possible extent by recursively
searching to provide more refined and scalable solutions for the
problem of interest [1][2][3]. This implies that there is an
ultimate need for reformulating the considered problems in
terms of optimization which, in turn, has two faces of the same
coin: first, generating a set of candidate solutions for the
desired problem which is referred to as the “search space”,
second and more importantly, assessing the achieved
performance of these available solutions based on some quality
measures which should be previously defined [4][3][5]. These
quality-measures or as so-called fitness functions, objective
functions, or goodness levels are quantifiable and revolve
around maximizing some desired features and/or minimizing
the undesirable ones until a predefined optimization goal is
achieved [6]. Generally speaking, neither generating these
solutions from the search pool nor devising their objective
functions is a simple task to do; hence, most real-life
optimization problems are too challenging to solve [4].
Inevitably, there is a pressing necessity for a search
methodology that is used to get in-depth information that
originally exists in one way or another within the promising
search space of the problem domain. In terms of this, there are
broad ranges of searching algorithms and a number of features
for which to categorize them. Some are classified according to
the searching strategies, some are classified by the searching
scope and area, some are classified upon the optimality of their
output, some are classified by their ways in generating
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
31
solutions, and so forth. Each of them is inspired, implicitly or
explicitly, by an existing natural world phenomenon or a
certain sort of metaphor [6]. Nonetheless, all of them seek
around the same goal of improving effectiveness.
Broadly speaking, there are actually many types of networks
that are routinely faced through daily life-cycle. These various
types, which have enormous practical importance in our life,
include the following real-life examples: Internet, telephone,
cell, highways, rail, water, sewer, electrical power, oil, and gas,
to name just a few. Depending on each one, every network has
a material flowing from point to point [7][8]. While each point
is referred to as a node, each connected path between any two
nodes is called a route or an arc [7][8]. In analogous to its type,
each material has a corresponding unit to measure the flowing
capacity such as time, price, distance, quantity, and other units
[7][9]. Based on this, optimization is a solution procedure in
which one aims to systematically enhance the material flowing
through a given network [4]. From a different perspective, this
enhancement can be either maximize the goodness or minimize
the badness of a stated solution [4]. Without loss of generality,
the maximization problems are considered instead of the
minimization throughout this paper. In case of the need for
considering minimization problems, the same methodology is
simply used after reversing the sign of calculation. To this
objective, this paper is trying to reach the maximum flow
capacity of the network at which the flow can be transmitted
more reliably from the starting source node “s” to the target
node “t”. This rate is greatly related to the same network “G”,
which, undoubtedly, depends heavily on both the number of
nodes “n” and the number of edges “m” [7][8]. Going forward,
this problem itself is known as the Maximum Flow Problem
(MFP) where the search space is actually represented by a
graph, an example of which is shown in Fig. 1 where the first
value that is associated with every edge represents the actual
flow value and the second value represents the maximum
capacity value; this will be explained later. The comparison of
these networks are often defined by the amount of flow, the
number of edges and vertices they have, as well as whether
their flows are bidirectional or not. The values of “n” and “m”
of this example are equal to seven and ten, respectively. It is
worth remarking that neither side of “m” and “n” is dominant
over the other, both are important in driving the size of the
problem. In this regard, both the number of nodes “n” and the
number of edges “m” with their capacities determine the
complexity of the network “G” and, for that the runtime
complexity associated with any instance generated from “G”
increases rapidly with the dimension of the network graph, i.e.
the numbers of vertices and edges [10][7].
Fig. 1. An example of MFP, having seven nodes and ten edges
As shown in Fig. 1, MFP is much related to the essence of the
objects' movement through the desired network where four
milestones are there: source place called a source or a start
node “s”, a destination node called “t”, one or more connected
routes between the source and the target, and an associated
positive number to represent the flow between every directed
route that connects any two nodes [11][8]. In order to simplify
the problem of interest, one can think of this problem as using
pipes of different sizes for carrying liquid from a source node
to a destination one. Or, one can think of this problem as using
conduits to link between the start and the destination nodes.
Anyway, the important thing is the availability of several
intermediate connecting paths, called by routes or tracks,
which can be followed in carrying the flow between “s” and “t”.
It is vitally important to mention that MFPs are part of the
graph paradigm that doesn't require capturing every low detail
of the problem under discussion. The rationale behind this
relates to the fact that they are mainly based on
abstract concepts where deep knowledge of the problem at
hand is no longer required. And so, the ordinary user can use
the metaheuristic optimization algorithm in solving many
optimization problems without having to have an in-depth
exhaustive understanding of the same algorithms.
The critical thing to keep an eye on is that nodes can't transfer
any matter more than their previously defined capacity value
[11][7]. This term might be generalized in the long-run as that
any network can't transfer more than its computed capacity
value. Whenever there is more than one feasible track to be
chosen between the source and the destination nodes, the MFP
is regarded as a player with a considerable role in enabling a
greater movement of these objects or matters. And so, the
intended objective is to choose the most optimal route between
the source “s” and the destination “t” that has the maximum
throughput, i.e. flow [7]. Even though the focus view varied
depending on each network, one fundamental three-sided
cornerstone remained fairly viewed in a broad sense: speed up
the flow to the looked-for value and reduce the time and cost.
Simply, this objective can be redefined as the more flow the
network has, the more efficient and effective it will be.
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IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
32
To this aim, the core motivation behind this research article is
to get the maximum flow capacity at which this flow might be
transferred reliably between the two special extremes: the
source node “s” and the destination node “t”. However, this
amount is closely associated to the same network “G”, which,
in turn, rely upon the various intermediate paths between these
two extremes and on both the number of nodes “n” and the
number of edges “m” by which the size of the network is
defined accordingly.
This research is concerned with solving optimization problems
and describes a new metaheuristic optimization algorithm
(namely, Sea Lion Optimization Algorithm for Solving the
Maximum Flow Problem, SLnO-MFP) which, as a member of
the swarm-intelligence family, mimicking the hunting behavior
of the sea lions. According to the acquaintance of the author of
this research, there is no previous literature on the usage of
SLnO for solving the MFP and this finding has not been
reported yet in the optimization literature.
In line with the said objectives and in order to lay the
foundation of this paper, an outline of this paper is structured
as follows. After this section justifies the importance of this
research and provides background knowledge on the maximum
flow problem for the novice readers, Section 2 explores the
depth of literature to introduce both the heuristic and the
metaheuristic optimization paradigm. Section 3 surveys the
literature within the research area to gain a concise overview of
the other related work and, moreover, it ferrets out the
objectives of the underlying problem and discusses some of the
different algorithms which are proposed to solve this problem
intelligently. The model formulation and the different
assumptions related to the problem of interest are provided and
discussed in Section 4. In order to build an authentic depiction
of the considered problem, the formulation of the theoretical
and mathematical foundation of this proposed solution is
introduced in Section 5. Section 6 is where the real work
begins; it takes a closer look at the current algorithm developed
in this contribution and then walks through all the various
stages which would be required to implement. While the
conducted experiments and their detailed intensive analysis are
discussed in Section 7, Section 8 concludes the project work of
this research. Lastly, to close the discussion of this research
article, Section 9 offers some ample research scopes and
introduces a fairly wide range of promising research
opportunities in furthering the aims and objectives of the
research.
2. Background of Metaheuristic Optimization
Algorithms
With the purpose of providing a self-explanatory paper, this
section establishes preliminary knowledge of the background
pertaining to the concepts of the optimization paradigm and
draws an inclusive image for both the current and future status
of metaheuristic research. Therefore, the following subsections
discuss the different categories of optimization algorithms.
2.1 Types of Searching Algorithms
As such, there is definitely a broad range of techniques
proposed in today’s progressive and growing arena of
optimization; each of which has its own capability, strength,
weakness, objective space, detailed specifications, constraints,
requirements, and other fundamental relevant features of
searching. Since most of them claim a progressive style to
implement, the right decision for the most reliable algorithm to
encompass a given problem selection is no longer a simple
mission to be carried out. Bearing in mind that most of the
complicated hard problems can be framed within the
optimization borders in which one strives harder in an effort to
either minimize or maximize the achieved results within
limited resources [12][13], Fig. 2 is directly interrelated to the
question of which algorithm to choose and which notions to
implement for a given problem of interest. In terms of reaching
the most right one of the optimization algorithms, this figure
deliberate and then formulates the different critical factors
which influence people’s decisions in picking up one of them.
However, there are various distinct elements between them
which overlap with each other. Viewed in a broad sense, the
classification of these algorithms encloses, but is not limited to,
the following overlapped categories:
· Problem Functionality: In terms of functionality,
algorithms can be classified into two major types: problem-
specific and problem-independent. While the former
provides that the algorithm, as well as the code, is just
tailor-made for a specific type of problems, the latter
assures that the same code is used for various varieties of
problems, namely it is a generic-implementation code.
While the focus of the latter search strategies is mainly
concentrated on using the algorithms without any problem-
dependent knowledge, the former look as if they were
tailor-made for a narrow range of problems. [14]
· Searching Scope: From a classification point of view, the
searching scope is used as well. Different than the global
ones that are commonly used in finding the global optimum
quality solutions, local search techniques might become
stuck in the so-called local-optimum values of the solution
space when no better solution is observed in the present
existing neighborhoods. Even though both techniques are
striving to find a solution that more optimizes the cost
criterion among a set of candidate ones, the distinction
between them is that the global search looks at the entire
problem space as a single entity when trying to find the best
possible candidate solution [15]. Despite that all of the
global optimum solutions are never guaranteed concerning
solution level of quality, finding global optimums in global
search ones could be more counted on.
In the pursuit of being on the best of what it has already
been achieved so far, most current-state-of-the-art
optimization algorithms fall within the realm of iteratively
improving the outcomes in the course of the search
process. Thus, by considering their ways of generating
solutions, further additional taxonomy can be possible for
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
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the exploration of the solution space effectively. Fig. 2
exhibits that the searching process falls into quadruple
pivot points: stochastic, exploration versus exploitation,
iterated (i.e. iterative), and guided:
- The searching has a stochastic nature when the set of
random variables is employed in extracting a new
generation, called a potential solution [9][16]. Each
generation's new values of these variables are chosen
stochastically in harmony with the general paradigm.
On the other side, some problems are evolving
stochastically at different points in time which makes
the optimization hard to grasp and solve. For instance,
the passengers' numbers of airlines occur stochastically
which calls the airlines for implementing the statistical
theories, including stochastic analysis and probability
distributions, in forecasting the numbers of passengers.
- Exploration and exploitation are two supplementary
activities used to explore the search space. The first one
is the activity through which the search algorithm tries
to explore as much broad search space as possible to
evade falling in the local-optima traps. Whereas the
second one is representing the activity in which the
searching algorithm tries to develop the finest
discovered solutions through some targeted
approaches. While exploitation is the optimized
outcome derived out of exploration, the progress of the
search for more solutions continues in both cases to
find more-optimal ones. [10][17][18]
- For highly efficient exploiting the former iteration (also
called trial or time-step) to the greatest possible extent,
the outcomes in the guided search are frequently
improved over the course of the iteration steps where
the newly generated trials are influenced by the older
ones. The basic idea of that is wrapping around
deliberating knowledge and extracting patterns from
the former good-quality searching iterations in an effort
to harmony guide the searching process in the
subsequent iteration steps hoping to be in the optimal
solution direction, hence the notion of “guided” is used
to continuously approximate the goal based on
replacing the old solutions with the new successful
ones. From a more general angle, the useful
information related to the optimas of the preceding
iteration steps is stored on to get benefit from them in
the succeeding ones. That is, the key philosophy of
deriving more successful trials is coupled with building
up a well-stocked knowledge store containing the past
trials. [10][17][16]
Unlike the conventional local search that stops when it
gets stuck by any local optima, the guided local search
makes the best use of the available features of the
current optima to escape away and then form another
more optimum feasible solution. In the guided search
absence, an optimization algorithm (OA) inevitably
takes on a longer exploratory time range that is mainly
driven by the trial-and-error aspects. [10][17][18]
- The progress of the searching process will be
continuing iteratively with the same searching
procedure until one or more of the predefined
evaluation functions, called termination conditions or
stopping criteria, imposed by the user are reached, and
accordingly, the best possible candidate solution is
produced. Without that, the progress of the searching
mechanism will obviously be in an infinite loop
[10][17]. The followings are some of the possible
termination conditions that may be imposed by the user
to terminate the series of iterations: the maximum
number of iterations steps previously defined (i.e. no.
of runs) is reached, the maximum allowable CPU
computational run-time (i.e. max-CPU-time), coming
across some significant evidence that an optimal
solution has been achieved, the maximum number of
iteration attempts that comes amid two successive
developments is reached, the maximum number of
iteration attempts has reached without noticing any
difference or making any forward positive progress for
the problem of interest, or there is no way to get more
developments for the problem of interest (i.e. there is
no progress) [10][17]. Related to the first termination
condition, the applications of the Artificial Neural
Networks (ANNs) use the name “epoch” to represent
an iteration step (i.e. time-step) [10][18]. In-line with
the second termination condition, it's very crucial to
balance between the quality of given feasible solutions
and the overall computation time frame that is utilized
in generating these solutions and decide accordingly
how to set up the timeout bound [10][18]. On the other
hand, the last termination condition represents the case
that after many generations, the solutions start
approaching each other in the hope that this
approaching is a good indicator that the final achieved
solution is closer to the ideal solution of the problem
under research [10][18]. In the report of this, there is an
essential need for suitable criteria to define the quality
of the acceptable solution and to decide according to
that whether to stop the searching activity or not
[10][17][18]. If the procedure fails to reach a visible
solution or a practical compromise within the timeout
bound, it is inevitably stopped [10][18].
· Output Optimality: The problems are basically
categorized into two different types of models:
Deterministic (i.e. exact) and Stochastic [9]. While the first
one is directly associated with the problems in which the
different-used variables are known in advance with
certainty and before solving them, the second model is
indicating to the cases where the associated variables
involved a degree of uncertainty [9][18]. Upon the
optimality of their output through the different runs,
algorithms are generally categorized into two fields:
deterministic and nondeterministic. Within this context, the
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
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“Deterministic Algorithm”, also known as exact algorithms,
describes the cases where the same algorithm at all times of
the repeated runs will definitely produce one and only one
same output, called solution, for the given particular input
data. As this grip on the reality of a single certain outcome,
it is obvious that their exclusive orphan solution is the
provably optimal one, and nothing else. Furthermore, since
such solutions can be extracted within a fair rational time,
they are used only for problems of small-scale instances as
they defined under the term “Deterministic”. Conversely,
complex large-scale instances can't be generally resolved
within a rational time by using these classical exact
approaches. This is caused by the fact that proceeding
ahead in the real-world with all possible solutions, as is the
case of exact or precise approaches, is sometimes time-
consuming and hard to sustain in terms of resource
availability and utilization. From a computational aspect,
enumerating and checking all potential candidate solutions
for optimality satisfaction is systematically impossible for
the majority of large-scale optimization problems
especially those involve hundreds and even thousands of
variables. [19][20]
Going forward, the “non-deterministic algorithm”, by
contrast, means that the same algorithm may show some
alternative behaviors from run to run even though the input
data are the same. Form another perspective, this
discrepancy in the behavior is attributed to the fact that the
calculation is subject to some norm of randomization and,
for that, the outputs have a fluctuating-stochastically
behavior and may vary from one run to another. With
regard to this norm of uncertainly, all the generated
behaviors are considered as valid outcomes and every one
of them may be the optimal solution or close to the sole
optimal one. And so, every execution for any algorithm
belonged to this type hides a degree of “uncertainty” or
“randomness” behind its output. Definitely, this extent of
“uncertainty” is only limited to agreed sets of rules that
should be defined before. [9][17][21][5]
Beyond that, this category is commonly used when the
tackled problem tolerates multiple possible outcomes
where all of them are considered as valid ones through the
solution space without providing proof of optimality.
Within the fact that they may perform differently within
various routes, the non-deterministic algorithms are
extensively used in finding estimated solutions; this is
specifically true when we coming across credible evidence
that revealing the optimal solution among a set of possible
candidate ones is beyond the capability of exact algorithms
and, perhaps more importantly, an optimal solution is too
costly to be attained especially in terms of time function.
[14][5]
· Time complexity: By considering their time-growth
complexity, a further taxonomy can be possible for these
algorithms; Fig. 2 illustrates that algorithms can be forked
into two subfields: polynomial and non-polynomial.
Polynomial, as the name implies, means that the tackled
problem can be initially solved from scratch in polynomial
run-time by not less than one algorithm [10]. However, in
the other case, the problem at hand needs non-polynomial
time to be solved which often means too long
computational time to be tolerated [10]. If the processing
time is narrow and usually it is that, there is a sorely need to
sacrifice the seeking of the solution optimality at the
expense of near-optimal solutions [20].
· Problem Hardness: When the last two categorizations are
integrated together, another categorization is emerged out
of them. In view of this, the problems themselves can be
categorized according to their complexity: Polynomial
problems and NP-hard problems. Even though the former
one is directly related to the problems whose computational
time is growing polynomially with the problem size, the
latter is relevant to the problems whose time-growth rates
are often growing exponentially with the size of the
problem. Notwithstanding that the computational time of
the NP-hard problems might not strictly with exponential
increases in all cases, but they are definitely not
polynomially. As opposite to NP-hard problems, the time
of the former category is firmly constrained by a
polynomial function based mainly on the problem size. For
instance, suppose that “q” is the problem size, then all the
followings are polynomial functions “q2”, “q3”, “q4”, “q5”,
etc. Quite the opposite, there isn't any known polynomial
algorithm that is capable to solve the problems that lie
under the latter category. As a matter of fact, most
optimization problems are classified under the second
category and they are describable as non-deterministic
polynomial-time hardness (NP-hard) problems which
address the case that a solution for the problem under
consideration can be achieved within a polynomial time by
using a nondeterministic computer without providing proof
of optimality. [22][23][13][10]
The followings are some of the key factors that are related
to NP-hard problems [22][10]:
- It is often the case that most of the NP-Hard problems
are very easy to define and described but so hard to be
framed or/and solved as optimization problems.
- Searching space: These problems are usually of huge
dimensions, namely, they involve a fairly wide range of
possible solutions so that they are usually very hard to
be tackled.
- Solution's quality level: The good-quality assurance or
excellence of the calculated results is not guaranteed.
But, if the optimal solution has not been reached, it
doesn’t mean that a “good” one isn't achieved. All in
all, this is much related to the nature of the underlying
problem. In terms of time-growth complexity, the
perceived relationship between the optimal solution
(i.e. the best candidate solution) and the size of the
problem under consideration is exponential. As soon as
the problem size begins to mount, the computational
time needed for further refining the candidate solutions
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
35
is growing at an exponential pace. In such scenarios,
these algorithms need a relatively long processing time
for driving the optimal solution and, as a result, these
problems are generally not resolvable within a rational
amount of computational time. In a variety of cases,
extracting an approximation to the optimal solution is
also hard to be achieved within a rational period.
- Exhaustive search: In practice, brute-force examining
of all candidate solutions may be placed into the realm
of the sheer impossibility.
- Time-growth complexity: Since this norm of problems
is ordinarily large-scale and, as a result, demanding
some “expensive” time computations, they are often
difficult to solve. To this end, these problems are
generally calling for exponential resources to reach the
optimum quality solution or the near-optimum one.
- Despite the fact that some of these problems are said to
as having a polynomial-time algorithm to solve but as a
matter of fact, no anyone at all sets apart what the
algorithm is!
In all these contexts, these problems are also referred to
as long-term problems. To state a truth, the largest
fraction of real-world optimization problems falls into
the NP-hard class or at least in the sense of NP-hard.
[22][10]
Fig. 2. Types of Searching Algorithms
· The Number of Objectives: Depending on the nature of
the problem, some problems have a single-objective
function while there are many others that have goals with
multi-objective functions, referred to as multi-objective
optimization. In reality, the latter case requires to be
incorporated with a weighted average to reflect the nature
of the several objectives' existence. So, a multi-parameter
vector is used for their fitness functions. [6]
· The Number of Starting Solutions: On conformity with
the problem domain and in order to come up with these
classifications, single-solution (also referred to as trajectory)
versus population-based searches may be considered as an
additional alternative classification element. The following
core points are listed here to compare and contrast the two
searching strategies:
Categories of Algorithms
Time Complexity
Polynomial
Nonpolynomial
Searching Scope
Local Search based
Iterated (Iterative)
Stochastic Nature
Guided Nature
Global Search
Population Based
Number of Starting Solutions
single-solution methods
population-based methods
Number of Objectives
single-objective
multi-objectives
Otput Optimality
Deterministic (exact)
Nondeterministic
Approximation Methods
Heuristic Techniques
Problem Functionality
Problem-Specific
Generic implementation
Problem Hardness
Polynomial Problems
Discrete domain
Continuous domain
NP-hard Problems
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
36
- The single-solution category contains methods that
start by choosing one solution randomly and then
enhanced it in the course of the search process. Since
these methods contain only one solution in every one
of the iterations, they are also called single-point or
trajectory methods. Simulated Annealing (SA) and
Tabu Search (TS) methods are the most leading
examples of this category On the contrary of starting
with a single nominal solution, the population-based
category starts initially by generating a set of multiple
random solutions, and then these solutions are
enhanced extensively towards more superior search
areas throughout the series of iteration steps. The
enhancement of the population-based strategy is
emanated either by recombination of more than one
solution into a single one or reforming each solution by
the use of a given strategy adopted especially to impose
exploration and exploitation of the search space. [10]
[20][24][16][18]
- A higher exploration power is attained in the
population-based towards finding out the overall global
solution rather than staying on local ones. On the other
hand, the nature of the single-solution category is
considered as more exploitation oriented. [20][24][16]
- Since the abstracted knowledge about the search space
in the population-based approaches is shared between
many possible solutions, there may a sudden and
widespread shift in the direction of the optimal solution
[16].
- The recombined solutions of the population-based
methods are normally based on big-guided steps while
these steps in the single-solution methods are
commonly smaller-guided and, of course, the
movement of each of the two alternatives for more
productive solutions and bettered outcomes is only
within its corresponding own search space. Despite
these solutions' improvements, these big and small
guided steps are at the expense of the danger of being
close to or missing good solutions where this danger is
higher in the population-based approaches of that of
the single-solution approaches.[10][16]
- By the population-based methods, multiple possible
solutions collaborate with one another to go beyond
local-optima traps [16]. Namely, all new solutions are
built on previous ones and provide inspiration for
future ones.
With respect to the fact that there are no clear-cut boundaries
that are determining where the above-named categories start
and stop, there might be many varieties of hybridized
categories. For instance, a further forked group may compose
of some approaches which deal directly or implicitly with the
graphs. From a different point of view, the positive capabilities
of two or more approaches may be fused together to form a
new hybrid technique that can be used to solve problems from
the same domains or the others.
2.2 Approximation and heuristic approaches
Due to the stated limitations of the classical exact approaches
in supporting most complex optimization problems, scientists
and experts from both research and industrial communities
think intensely for finding possible alternative approaches that
are developed to support and capture efficiently the solution of
the optimization problems within a fully acceptable time
border even if there aren't some high levels of certainty. To this
end, approximation and heuristic approaches are eventually
evolved for finding the optimum or at least close-to-optimum
solutions regardless that these approaches have no assurance
for the computational time or the accuracy of the in reaching
the optimal solution. Ground truth, the quality level of the
approximated methods is ordinarily under the terms of
predefined boundaries that are not far off the exact solutions. In
contrast to this, the quality level of the heuristics methods is
not guaranteed in exploring the global optimum solutions or to
be within these predefined boundaries; however, the exact
results might be caught in some exceptional situations. Unlike
the approximate ones, heuristic approaches may have included
some chancy errors that are incapable of being anticipated. [25]
[1][14][10][20]
To further control optimization problems, there is an utmost
need for a higher-level of heuristic especially when one be
faced with some extensive searches that have one or more of
the following feasible constraints and obstacles: [14][26][13]
[9][27]
· Information constraint: Incomplete, limited, imperfect, or
conflicted pieces of information upcoming from different
causes and sources.
· Resources constraints: Restricted by limited computation
capacity or with resource availability and utilization.
· Time constraint: Guaranteeing the computational time to
be within the stipulated time is an ever-growing concern for
the decision-makers and all the stakeholders in both the
industry and academia communities.
· Problem difficulty: The tackling problem is, to some
extent, a difficult optimization one that is comparatively
hard to solve.
· Quality constraints: In some occasional cases, the search
process may be caught by some local-optima traps without
having the ability to bypass them. However, it is an
important issue to look beyond these local optimas in the
hoping of finding the global optima.
· Knowledge constraint: A shortage of sufficient
knowledge to design the equivalent well-organized solving
methods.
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37
Crucially, all of the above-stated critical issues are worthy
enough to address the necessity for “high-level heuristics”
especially for the cases where capturing every low-level detail
of the considered problem is hard to attain in a reasonable
amount of time. Due to these challenges and with the
advancement in alternative modeling, scientists over the past
few years are constantly trying their best to come up with new
goal-oriented operating methods to solve these important real-
world issues. They find their enlightenment and guidance by
abstracting the structure and function of nature's laws, by itself,
and the so remarkable behaviors of the different creatures in
solving problems; hence, “metaheuristic” algorithms arose into
the vision among which nature-inspired algorithms are actually
the largest fraction of them. The next subsection introduces the
basic concepts of metaheuristic algorithms. [10][2][28][16]
2.3 Metaheuristic
Fig. 3 illustrates the most ten leading areas that are imitated by
most metaheuristic algorithms. It is obvious from this figure
that insects are the most popular imitated area among these
areas where (23%) of the total publishing metaheuristic
literature are concentrated on mimicking the living ways and
the survival systems of insects. The next area has (17%) which
is inspired by the natural evolution of Darwin's theory of
evolution and survival (i.e. survival-of-the fittest). Then, the
next one is with animals (whales, wolves, fish, cats, monkeys,
bats, and many others) which has (16%), and so on up to the
percentage (4%). To state a relevant truth, the social behavior
of bees followed by ants are the most top favorite insects that
are foremost imitated and reported while searching the related
metaheuristic literature. [20][27][29]
Fig. 3. The top ten leading metaheuristic areas
On the other hand, the drawing of Fig. 4 states that (93%) of
the available reported metaheuristics are distributed among six
disciplines where more than half of them are classified as
nature-inspired optimization algorithms; they are also termed
as bio-inspired or bio-based metaheuristic [20][27][29].
Fig. 4. The top six leading metaheuristics disciplines
In addition to that these nature-inspired optimization
algorithms are relatively easier to implement as compared to
the conventional optimization techniques used earlier, they can
be adopted and implemented in widely varied fields of
problems covering multidisciplinary fields and objectives.
Above and beyond that these optimization algorithms have
more abstract concepts and relying on the usage of simple
concepts of the higher-level strategies (hence the term “meta”),
they are heuristic, stochastic in their nature, and, perhaps more
importantly, they are categorized under the iterative
optimization techniques. Besides that they encompass highly-
scalable intelligent methodologies and problem-independent
algorithmic frameworks, they normally revolve around adding
flexibility to the ways of utilizing control parameters that can
be customized and tuned to well suit the nature of the problem
under consideration. It is worthwhile considering that these
techniques can eventually be implemented so that the complex
working details are simply abstracted away from the end-users
[21]. This high reliability and simplicity that metaheuristics
offer are the principle behind their broad diffusion and finding
them in numerous successful applications. [10][28][16]
Even though the global optimality of the final metaheuristic
solutions among the multiple possible alternatives is not
guaranteed or proven to be optimal, these techniques may be at
least worthy enough to be trusted in extracting the
approximated solutions within reasonable computational time.
In its absence, many problems that may be solved with
metaheuristics will be inevitably unsolvable. This is especially
true for the hard problems in which their exact solutions are too
hard to be achieved within rational computation time. As a
matter of fact, the price to be paid for the time complexity or as
so-named scalability improvement is mainly at the expense of
approximation of the optimal matching and, therefore, a fair
balancing as empirical as possible between time and quality is
definitely a determining factor and a radical issue. [10][20]
[28]
23%
17% 16%
9% 8% 8% 7%
4% 4% 4%
0%
5%
10%
15%
20%
25%
54%
14% 11%
7% 5% 2%
7%
0%
10%
20%
30%
40%
50%
60%
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
38
Table I highlight the abovementioned notions related to
metaheuristic optimization techniques. As they are coined to
utilize the power of nature, the source of inspiration for every
metaheuristic algorithm has an attractive story behind.
Motivated by this and as shown in Fig. 5, they can be
categorized upon their common features into at least nine basic
categories: [14][15][20][27][2][28][30][17][31][26]
· Evolution-inspired algorithms: These algorithms attempt
to imitate the rules and laws of the natural evolution of the
biological world. Regardless of their nature, these
evolutionary-based optimization algorithms are regarded as
generic population-based metaheuristic algorithms. The
search process of this norm of algorithms has two focal
stages; exploration and exploitation. The exploration phase
precedes the exploitation phase which can be regarded as
the process of exploring in detail the search space. At the
exploration stage, the progress of the search process is
launched with a randomly generated population which is
then evolved over a number of subsequent generations. The
most applicable point of these heuristics is that the next
generation of individuals is shaped by collecting the best
individuals and then integrating them together. Through this
integration, the population is enhanced over the succeeding
generations. On the basis of this, the optimizer of the
exploration stage includes some design parameters that
have to be randomized as much as possible to globally
explore the promising solution search space. [17][18][32]
Because of the stochastic-based nature included in the
optimization process, picking up the right parameters for an
adequate balancing between the exploration-exploitation
dilemmas is a serious challenge and perhaps the most
critical challenge facing the development stages of any
metaheuristic algorithm [33]. The most popular leading
examples of this category are Genetic Algorithms (GA),
Genetic Programming (GP), Biogeography-Based
Optimizer (BBO). [17][18][32][28]
To sum up, it is vitally important to realize that decision
making by using metaheuristics implicit involves a
fundamental selection between “Exploration” by which
more information is assembled that might direct us to more
superior forthcoming decisions or “Exploitation” by which
the finest decision is made in the light of the existing
knowledge.
· Swarm Intelligence (SI) algorithms: These optimization
algorithms are evolved out from the collective intelligence
and the communication channels that can be observed in the
social behavior of the biological populations in nature. They
are used to solve most of the optimization problems that
arose on the metaheuristics' horizon over recent years. A
typical example of this category is the Sea Lion
Optimization (SLnO) algorithm that imitates the hunting
activities of the sea lions. Artificial Bee Colony (ABC), Ant
Colony Optimization (ACO), and Particle Swarm
Optimization (PSO) algorithms are considered as other
common examples. [17][18][32]
Furthermore, these algorithms remain the most fertile
research area in the field of metaheuristics. In comparison
swarm-based with evolution-based algorithms, the former
has some more advantages over the latter. Since
evolutionary approaches have relatively more operators
than swarm-based, they are more difficult to apply.
Different than evolution-based approaches that immediately
discard any obtained piece of information related to the old
iteration once a new population is generated, swarm-based
algorithms normally keep these valuable pieces
of information over the subsequent iterations. [17][28][32]
· Physics-based algorithms: These algorithms are mainly
coined to simulate the physical phenomena in the world.
Gravitational Search Algorithm (GSA) is one of the best-
known examples of this category. GSA is formulated on
both the law of gravity and the law of motion. Harmony
Search (HS), and Simulated Annealing (SA) are other
dominant examples of this category. [18][28]
· Chemical-based mechanisms (CBM): The natural process
that involves transforming unstable ingredients into stable
ones is named as a chemical reaction. During these
interactive operations, excrescent energy exists due to the
sequence of elementary interactions between these
molecules. But at the end of these transformations, the
unstable molecules are converted to stable ones and,
naturally, with low energy stability. In this regard, scientists
focus their efforts on trying to find algorithms that imitate
the chemical interactions among molecules that happen
during the chemical reactions and usually lead to chemical
changes. Chemical Reaction Optimization (CRO) proposed
by Lam and Li (2010) is one of the best-known examples of
this category of algorithms. [11][21][34][29]
· Stochastic optimization (SO) Algorithms: The
formulation of these optimization algorithms includes not
only generating random variables to be used in the progress
of the searching process but also using methods that have
arbitrary (i.e. random) iterate steps. However, the outcome
success of the iteration steps couldn't be guaranteed. The
followings include broad examples of these algorithms:
stochastic hill-climbing, swarm algorithms, evolutionary
algorithms, genetic algorithms, simulated annealing, to
mention but a few. [29][10]
· Probabilistic-based Algorithms (PA): These algorithms
are so named because the probabilities play a significant
role in making decisions within the different runs (i.e.
iteration steps). Simulated Annealing (SA) is mostly the
oldest example of this type of algorithms. [10][18][35][32]
· Artificial Immune Systems (AIS): As a sub-field of
biologically-inspired computing, these artificial intelligence
algorithms are mainly concerned with imitating the
biological immune processes of the human immune system
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
39
towards solving a broad category of different optimization
problems from engineering, information technology, and
mathematics. [10][28]
· Artificial neural networks (ANNs): These algorithms are
one of the information processing paradigms and a subfield
of biologically-inspired computational intelligence family.
Inspired by the manner that biological neural systems
process data and based on the principle that self-learning is
acquired from experience, these artificial networks need to
be trained enough by using a set of examples to create
adequate knowledge that can be used later for solving a
wide variety of optimization problems in real life. [36][18]
[37][29]
· Human-based algorithms: Because there are laws
governing all the internal operations of the human being, all
the contained internal activities of these complicated
systems operate functionally without any problems.
Attractive by this motivation, scientists from all domains try
to simulate the ways in which these subsystems work and
come up with new goal-oriented operating methods to solve
many important real-world problems. Thus, the algorithms
of this category emulate the intelligence and the social
behaviors of the human being and their associated activities.
Teaching Learning Based Optimization (TLBO) [2][29],
Interior Search Algorithm (ISA)[2][29], Colliding Bodies
Optimization (CBO)[2][29], and Harmony Search
Algorithm (HSA) [30][3][38][29] are broad examples that
are classified under this category.
From a broader perspective and under one scheme, these
optimization techniques can also be categorized by some wider
classifications as the followings:
· They can be categorized as being either exact (i.e.
enumerative) or approximated methods [2][10].
· Under another scheme, they can be also categorized
according to whether they are used in forming other hybrid
metaheuristics or not [29]. Regarding this hybridization,
evolutionary and nature-inspired algorithms are the most
algorithms that have been extensively hybridized with each
other over the last few years to solve a wide variety of
optimization problems [10].
· Another further broader categorization can be as
conventional metaheuristics, like Genetic Algorithms (GA)
which is the most famous and prevalent one, and the new
generation ones, such as the proposed algorithm of this
paper [29][27]. Compared to the classical ones, these
modern algorithms usually require lower computational
time and memory, fewer setting parameters to fit the
problem, and moreover easier to implement [10][20].
· Another completely different but it is a common
classification scheme is the availability or not of local
search mechanisms within their stages. Since local searches
usually give the best chances for approaching the best
candidate solution, this facility gives more feasible chances
for the candidate solutions improvement during the course
of successive iterations [29][32].
Yet, regardless of the fact that there is a fairly wide range of
heuristic and metaheuristic approaches that were proposed so
far in the spectrum of the optimization paradigm, there is still
immense room for improving and/or investing the available
ones or at least coming up with new viable algorithms and
techniques like the one described in this paper. This is
especially true if the following silent points are under the
vision: [13][12][9][4][21][20]
· Most optimization problems that arose on the horizon over
recent years are often very hard to be tackled by the
conventional models and, hence, they require new ways of
thinking to be solved. Anyway, creativity comes from the
well recognizing of the problems that require further
innovative usages of the optimization algorithms.
· As the scope of the optimization problems is growing
extremely in size and heterogeneity, the number of
optimization problems residing on diversified domains of
our life is exponentially larger than most scientists and
researchers have ever proposed.
· Since not all metaheuristics are reported as being successful
ones, there remains a relatively substantial research gap that
needs to be filled between the small number of accepted
metaheuristic methods, from classical to novel approaches,
and the vast number of day-to-day optimization problems
that are increasingly duplicated.
· Since many of the conventional optimization algorithms
used earlier may no longer be sufficient to upkeep the new
needs of today’s attitudes, it is vitally important to
reengineer them or make a permutation for them with new
applicable and practical alternatives.
· In the optimization paradigm, it seems so strange and
somehow unfamiliar to find a single algorithm that
performs well on most optimization problems, especially
that a large fraction of them have their own circumstances,
requirements, constraints, and implementations scenarios.
· It is regarded as axiomatic that the system that has been
constructed to meet the high needs of scalability and
reliability has more opportunities to stay functional for a
longer time. So, there may be counterintuitive variations in
the solution quality between the algorithms that had been
implemented and evaluated only on just small or medium
benchmark instances of the problem and the algorithms that
had been tested on all benchmark instances of various sizes
including complex large-scale ones.
· There is a clear and distinguishable variance between both
theorizing that is largely based on the theoretical-academic
world and the implementation that is conducted upon real-
world cases. An analogy with this, there may be some
considerable gaps between the metaheuristic theories and
their corresponding real-world implementation. This
mismatch between both of them is, of course, caused by the
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
40
fact that some metaheuristics are relying on just theoretical
or abstract possibilities without applying them viably with
the real-world applications or that some of them have been
tested and then evaluated using only low-to-mid-range data
without exposing them hard on large-range data. Close
related to this, a considerable fraction of these researches
have been originally initiated for only research purposes
without being for real-life applications.
More importantly, some metaheuristics are just carried out
inside research labs where some of them have been
constructed based on hypothetical projections with only an
academic or theoretical vision that may be far away from
the factual situations. That is, carrying out lab-problems
merely without being exposed to diverse real and hard tests
is subject to guesswork and experimentation may lead to
unexpected results. On top of all that, nearly the majority
of these labs are subject to some financial constraints with
rare to no external support available. Inevitably, this lack
of certainty may rarely lead to unfaithful decisions and
hence far-reaching problems.
· Some metaheuristics were conducted upon simulated data
that are nearly different from the relevant real-life ones and
they may not initially design for fully exploiting the real
environment. Since they are firmly governed by purely
theoretical standpoints without having a strong empirical
base or practical evidence, they could be as a matter of
theoretical tests and, for that reason, building knowledge
about simulated data could be neither viable nor feasible.
This, in a way or another, maybe behind finding some
missing environments to conduct experiments on.
Apart from the foregoing mentioned discussion, all
metaheuristic optimization approaches are alike on average in
terms of their performance. The extensive research studies in
this field show that an algorithm may be the topmost choice for
some norms of problems, but at the same, it may become to be
the inferior selection for other types of problems. On the other
hand, since most real-world optimization problems have
different needs and requirements that vary from industry to
industry, there is no universal algorithm or approach that can
be applied to every circumstance, and, therefore, it becomes a
challenge to pick up the right algorithm that sufficiently suits
these essentials [21][29][12].
What's more, the metaheuristic research community frequently
uses the two terms “Heuristics” and “heuristic methods”
interchangeably to simply give the same meaning. Like so, the
two terms “metaheuristics” and “metaheuristic methods” are
also used interchangeably. Furthermore, it is recalled that the
following optimization terms will be used to refer to the same
metaphor: algorithm, method, and technique.
Table I. Local search heuristic vs metaheuristic strategies
Feature
Heuristics
Metaheuristics
Heuristics level
· Low-level heuristics
· High-level heuristics
Evolution level
· Low
· High
Performance
level
· Low
· Generally, they have better performance, but it is not
guaranteed.
Domain
· Because they are tailor-made for specific
problems, they have a narrower and less generic
domain relevant to the problem type.
· A large fraction of them is proposed by and for
specialists in the same domain.
· They are problem-dependent & special-purpose
methods. Since they are usually created to solve
problems of a particular type (i.e. problem-
specific), they are more related to the problem
that needs to be solved. Therefore, they usually
work poorly when they are applied to solve other
problems.
· They are applicable in solving real-life problems that are
complex, nonlinear, high dimensional, and multimodal.
Moreover, these problems are usually having unknown
search space and a massive number of local-optima traps.
These problems can be easily seen in many aspects and
extents of our day-to-day life, like industry, agriculture,
engineering, business, social, and many other fields.
· So, these algorithms might be used to solve those problems
which are unsolvable.
· Since metaheuristics are based on novel and abstract
concepts, they allow designing versatile software that can be
applied to a broad range of optimization problems covering
various domains and disciplines. Hence, they are
categorized under the general-purpose methods.
· Wider and more generic domain, in relevant to the problem
type.
· They can be adopted to solve NP-hard problems that can’t
be unraveled by utilizing ordinary heuristic methods.
· They have multidisciplinary domains and objectives.
· Problem-independent & general-purpose heuristics
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41
Feature
Heuristics
Metaheuristics
Searching
space
· They have a narrower search criterion.
· They are applicable to solve optimization
problems whose search landscapes are well-
formalized.
· They are mostly more exploitative approaches.
· They have a wider search criterion and a broad range of
possible scales. So, they are primarily prepared to process
instances of large-scale problems.
· These algorithms are mainly suitable for solving
optimization problems for which the search space isn't well-
formalized.
· They are mostly more exploratory in nature.
Searching
process &
Local optima
trap
· A local search: The searching process is no more
than within the neighborhood surrounding.
· They have only one searching rule for guiding the
progress of the search process in the search-
space.
· Thus, they are more prone to stagnation in local
optimas. They might get trapped in some local
solutions (i.e. local optimums) without making
some progress in bypassing them.
· A global and widespread search: Since it is important to
look beyond local optimas to find the global optima that any
algorithm is ultimately looking for, the searching is relying
on the context of generalized searching hoping to be as near
as possible to the most optimal solution.
· As they have multiple abstract rules and higher-level
computational strategies, they are always exploring the
search space thoroughly under many highly intelligent
scenarios.
· They have some mechanisms to evade being stuck in some
local optimas traps and in forcing the algorithms to escape
away from them. Most of these mechanisms have a
stochastic nature to widely search the entire space.
The overall
searching
behavior
· Single behavior: They have just one and only one
behavior in achieving the most optimum solution.
· Multi behaviors: Based on self-adaptive computing, they
have multi behaviors that keep changing according to the
status of the problem.
· They are quite smart to tune their parameters in the direction
of finding the most optimum solution with the least possible
computational cost.
Abstraction
level
· The abstraction level is low and more specific in
relevant to the problem type.
· They take local views of the considered
problems.
· The abstraction level is high and more generic in relevant to
the problem type.
· Goal-oriented operating methods
· Bedside that they are based on abstract concepts, they
encompass highly-scalable methodologies.
· They take global views for the considered problems.
· Complex working details are simply abstracted away from
the end-users.
Simplicity
· They are relatively difficult to implement and
required more setting parameters to fit the
considered problems as it should be.
· a far less attractive
· They need fewer control parameters to fit the considered
problems.
· Since they are based on the usage of simpler concepts and
the utilizing of the setting parameters that can be adjusted
and tuned to match the problem nature, they are relatively
far more attractive and easier to implement.
Reliability and
Flexibility
· Capturing every detail of the problem under
consideration is always fundamental.
· less practical solutions
· Most of them look to the considered problem as a black box
that has an easily-known group of input and output as if
capturing every low-level detail is not always essential.
· Many diverse problems can be solved without much
changing in the original algorithm structure.
Other core
properties
· Approximated
· They require detailed knowledge of the
considered problem.
· Approximated, Heuristics & Stochastic & Iterative.
· Most of them are nature-inspired.
· They can be used in a broad array of problems without any
problem-dependent knowledge.
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42
Fig. 5. The various strategies for solving optimization problems and some of their main representatives.
3. Related Work
Related to its importance, researchers, experts, and
practitioners all over the globe increasingly extend their
literature towards solving the Maximum Flow Problem (MFP)
using different methods and techniques. In the course of that,
they made every effort in every way they could to propose new
potential solutions or modifying the already available ones.
Along this way, the first notable solution was presented by
Ford and Fulkerson in (1956) by using the augmenting path
algorithm which is later known as FF [39][8]. Their algorithm
is all about solving a problem that is described as the
followings: [39]
“Consider a rail network connecting two cities by way of a
number of intermediate cities, where each link of the network
has a number assigned to it representing its capacity.
Assuming a steady-state condition, find a maximal flow from
one given city to the other.”
Although the FF algorithm is the most popular one in this
paradigm, its overall complexity is comparatively high, which
is O(mn). Nonetheless, they remain the founders and the great
pioneers of MFP even with that aforesaid complexity, and
moreover, their research and standard results remain a
benchmark for excellence by which many other researchers
compare theirs. [39][8]
Optimization
Algorithms
Exact (i.e.
Enumerative)
Methods
Approximated
Methods
Heuristic
Techniques
Metaheuristics
(NP-hard
problems)
Human-based
algorithms (HBA)
Harmony Search Algorithm
(HSA)
Interior Search Algorithm (ISA)
Chemical-based
mechanisms (CBM)
Chemical Reaction Optimization
(CRO)
Adaptive Chemical Reaction
Algorithm (ACRO)
Physics-based
mechanisms (PBM)
Simulated Annealing (SA)
Harmony Search
Evolutionary
algorithms (EA)
Genetic Algorithms (GA)
Evolution Strategies Algorithm
Swarm-intelligence
algorithms (SIB)
Whale optimization algorithm
(WOA)
Ant Colony Optimization (ACO)
Stochastic
Algorithms (SA)
Tabu Search
Stochastic Hill Climbing
Probabilistic
Algorithms (PA)
Compact Genetic Algorithm
Bayesian Optimization Algorithm
Artificial Immune
Systems (AIS)
Clonal Selection Algorithm
Artificial Immune Recognition0
Neural Algorithms
(NA)
Artificial Neural Network (ANN)
Hopfield Network
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Since the seminal paper of FF and throughout the years,
researchers and scientists continue their goal-oriented research
toward finding various techniques and methods that are
revolved around the mission of capturing more optimal
solutions for the considered problem. Based on that, the lines
of advances have been initiated and a sequence of numerous
algorithms was suggested, presented, and released. Because
there's a large body of research studies on this line of research
and to offer a coherent narrative as an alternative of annotated
bibliography, this section is inherently selective to a certain
extent, and so there are some of a fair-bit less relevant topics
that haven't been presented. Some of these salient studies are,
therefore, presented in the following subsections.
3.1 Chemical Reaction Optimization (CRO)
In a broad sense, scientists frequently noted that the nature of
both chemical interactions, named as Chemical Reactions
(CRs), and optimization paradigms have high-level common
attributes and details. At the starting point, the following
noteworthy points highlight the common phenomena in
between: [13]
· Elements are substances, also better-known as materials,
which cannot be reduced to be simpler by the usual
chemical means.
· In its simplest terms, the basic unit in any CR is the
molecule.
· When a substance is transformed from an unstable case to a
more stable one, a chemical change will occur to this
substance which is referred to as chemical reaction (CR). In
fairness, this chemical process is considered as a natural
process and nothing else.
· A collision is the exact cause of any CR. In this regard, the
molecules are considered as being the manipulated agents
and, therefore, CR is a multi-agent paradigm. Each agent
has a number of features, some of which are fundamental to
the CR operations. However, other features may be easily
attributed to the agent.
· Taking for granted that the CR event is only triggered by
the sequence series of collisions in-between molecules (i.e.
agents) and nothing else, some rhythmic interactions
between these agents may occur that lead to some changes
upon these agents themselves. On the other hand, CRs can
be commonly categorized into four elementary schemes
that are viewed in Table II. Additionally, stability is the
primary objective of any CR in which involves changes in
the molecules.
· The following triple rules are directly related to energy.
First, energy already presents and can't be made. Second,
energy may inter-change from one shape to one or more
other. Third, energy can't be smashed. Related to the
second rule, collisions usually lead to the rearranging of
energies among molecules, but there may be a collision in
which no energy is transferred.
· Both CRs and optimization undergo a sequence of step-by-
step events. They both strive in finding the optimal solution
or at least the near-optimal one.
Table II. The four major types of chemical reactions
Name
General Reaction Pattern
A chemical formula example
Combination or synthesis reactions
A + B ð AB
S + O2 ð SO2
Decomposition reactions
AB ð A + B
CaCO3 ð CaO + CO2
Substitution or single replacement reactions
A + BC ð B + AC
H2 + 2 AgNO3 ð 2 Ag + 2 HNO3
Metathesis or double displacement reactions
AB + CD ð AD + CB
HCl + NaOH ð NaCl + HOH
Based on manipulating the above-mentioned observations,
especially the step-wise process of searching, many researchers
aim to relate the chemical reactions with the optimization
paradigm and, as a result, try to embed all the common
concepts and properties between them in new optimization
algorithms. Consequently, they proposed many general-
purpose metaheuristic potential algorithms that emulate by the
natural process of chemical reactions. Then, they successfully
utilized these algorithms with the intention of resolving a broad
range of both discrete and continuous engineering problems
which cannot be underestimated. In all cases, it is important to
take into account that these chemical-reaction-inspired
algorithms are often population-based and have a high ability
to be adapted to cover other problems. They are commonly
referred to as Chemical Reaction Optimization (CRO)
algorithms. [13]
For satisfiability, the core of the overall CRO-based algorithms
is primarily all about the followings [13]:
· Compared with the other classical algorithms, CRO offers
some flexibility to be customized and controlled by the
users themselves to fine suit their specific needs or to be
easily adapted to address particular problems.
· In order to reach or at least approach the global optima,
CRO-based algorithms are a self-adapted to reflect the
problem domain.
· In reality, CRO has the ability to solve some optimization
problems which have not earlier been successfully tackled
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
44
by other metaheuristic algorithms or that have been
classified as having some run-time complicity issues.
· Including C++ and Java, CROs can be easily coded using
object-oriented programming (OOP) languages. In this
context, the molecules are defined as classes and the
elementary reaction types are defined by the methods.
· For solving a particular problem, multiple CROs can be
implemented simultaneously without any trouble.
· Since each CRO keeps up its particular relevant population
size, it will not have to remain pending at any certain
instant until any other CRO accomplishing its certain tasks.
To be truthful, the CRO algorithm was originally devised up by
Lam and Li (2010) for the purpose of fixing the combinatorial
optimization problems [21]. Just within less than two years,
CRO was applied successfully to resolve a considerable
number of optimization problems, outperforming several other
existing algorithms in the majority of the experimental results
[13]. Through the said research, they put the generic
formulation for any optimization problem. In terms of this,
they mathematically define the minimization objective function
“f ” by utilizing Equation 1: [21]
subject to
(1)
Where the following points analyze the elements of this
equation:
· “R”, “E”, and “I” represent the real number set, the index
set for equalities, and the index set for inequalities,
respectively.
· and are the
vectors of variables and constraints, respectively. “n” and
“m” are the problem dimension and the total number of
constraints, respectively.
· If a negative sign is added to “f”, then it will be the
maximization objective function.
In order to evaluate the performance of the proposed solution,
the simulation code has been implemented using the Microsoft
Visual C++ programming language. The algorithm has been
applied successfully in solving 23 large-scale instances in
which their considered datasets were categorized as being NP-
hard of the type Quadratic Assignment Problem (QAP). They
observed that the proposed algorithm achieved the objective
drastically. Then, an ample computational investigation was
carried out in which the simulation results of the proposed
algorithm were evaluated and compared to the best performing
three metaheuristics recommended in the literature at that time,
relating to the solutions' quality level and their computational
execution times. These three competitors are: Fast Ant System
(FANT), an Improved Annealing Scheme (ISA), and Robust
Taboo Search procedure (TABU). Moreover and to offer more
objective among the other three compared metaheuristics and
to eliminate any issues related to the variations in the execution
environment, the same implementation environment was used
related to the computer type and model, operating system, the
function evaluation limit of the stopping criterion, and all the
other standard measures. In most of the cases, their pilot
experiments gained the best result and that is why this
proposed algorithm is among the current best algorithms which
can be used to solve QAP. Because it can be used as a generic
searching algorithm to formulate several NP-hard problems,
their algorithm is part of importance and remarkableness.[21]
After the antecedent algorithm successfully solves a variety of
optimization problems, Lam and Victor (2012) presented
another expanded research for solving a wide variety of
engineering problems, such as the quadratic assignment
problem, multimodal continuous problems, ANN training, and
other optimization problems. During their notable research,
they build a roadmap framework and theoretical guidelines
recommending other users on how to customize and tune the
CRO's setting parameters to match the nature of the other
problems. Besides that, their effective research is considered as
a tutorial and practical procedure that encourages other
researchers in exploiting CRO in solving their research
problems. In other words, their research study is
an inspiration for every optimization research which comes
along. [13]
The study by Barham et al. (2016) introduced another
noteworthy CRO algorithm which is conducted using JAVA
programming language. This CRO achieves an overall
complexity of “O(I E2)”, where “I” and “E” indicate the
number of iterations and arcs of the directed-weighted graph,
respectively. They prove that the number of iterations has
assured evidence towards capturing additional optimal
solutions and approaching the most optimal ones. [34]
3.1 Whale Optimization Algorithm (WOA)
On the relatively species-rich sea, humpback whales need a
developed strategy in their hunting for together. These whales
types actively hunt small fish or krill, following them
according to tight enough coherent strategy. This foraging
social process for self-maintaining is a unique interaction that
hasn't been detected in other creatures yet. It is interesting to
note that this type of social creature has no teeth and above that,
it has a very narrow throat and so, this is the rationale behind
that it couldn't swallow large prey as a whole. However, this
type of whales has an amazing policy in attacking a great group
of small prey and catching them, the studies find. This unique
to the concept foraging policy is called “bubble-net feeding”
and it is based upon a multi-stage coordinated mechanism for
capturing as much as possible fish at once. Once they are
teaming up together, they dive brilliantly beneath a large group
of prey and then all begin cleverly in bubbling out to produce a
net made of bubbles and forcing prey to be inside. To make
sure that the net of bubbles surrounds all the prey, they should
reinforce all the net’s weak points and, accordingly, they splash
their flippers (i.e. fins) at these weak parts. By this witty tactic,
a large group of prey is trapped tightly inside a well-organized
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45
fence isolated from outside, and so the only remaining event to
do is swallowing all of them by the helping of their flippers
that swiftly direct fish headed for their mouths. [26][40][29]
Whale Optimization Algorithm (WOA) is proposed by
Mirjalili and Lewis (2016) [26] which is considered as a new
competitive swarm-based optimization algorithm that evolved
mainly out of abstracting the fascinating hunting behavior of
the humpback whales. With this article, the researchers have
successfully created a mathematical model to match the
humpback whales' feeding strategy upon which many NP-Hard
optimization problems have been solved. This mathematical
model begins initially with a population of various stochastic
solutions, each of which is generated by a search agent (i.e. a
humpback whale). Whenever the best solution is determined
among the other ones, all the other search agents should
arrange their current locations accordingly. On the other hand,
this research also addresses the case where these animals may
make a random search moving towards finding other better
positions instead of remaining stuck with one of the current
search solutions. [26][29]
In order to test and evaluate the algorithm, WOA was
implemented empirically by solving 35 real-life optimization
problems of practical importance, 29 of them are mathematical
and the remainders are structural design. Furthermore, WOA
was verified to evaluate its performance using classical
benchmark functions that are usually utilized in the
optimization literature. Each one of the considered experiments
was iterated thirty times. After WOA is compared with other
conventional techniques, the gaining results were relatively
competitive. Due to its considerable success, this algorithm
becomes popular from then on. Day by day, a sequence of
similar research was conducted based on WOA. [26]
Any electric power system has been considered to entail three
functional zones. First of all, the electricity generation by
which the energy is transformed from the available resources
into electric power. Secondly, the transmission of bulk electric
power over long distances by using high-voltage networks.
Thirdly, the distribution which is related to providing the end
consumers' low-voltage service points from the high-voltage
networks. On the condition that the energy is consumed
directly by those end consumers as soon as it is changed into
electric power in the first functional stage, the important point
related to the entire system is that there is an electrical power
loss and the largest portion of this is routinely occurring at the
distribution level; it is about 70% of the total circuit loss. Due
to this, increasing the overall energy efficiency of any
distribution path is the hardest part of setting up any electric
power system. The study by Reddy et al. (2107) is based on
WOA by clearly decreasing the generating plants' losing power
during this distribution. In the long run, this study can be used
not only in reducing the voltage and the high power loss but
also in lowering the cost and producing stable, efficient
voltages by optimizing the placement and sizing the distributed
generators (DGs). [38]
Back-and-forth, Masadeh et al. (2018) suggested the
“MaxFlow-WOA” algorithm that is based mainly on the Whale
Optimization Algorithm (WOA). The proposed solution was
compared to Ford-Fulkerson's MF with respect to the accuracy
of the results and the average computational run-time where it
acquired “O (E2)” as the overall time complexity. According to
the authors’ experimental analysis, the impressive experimental
results give sufficient sound evidence and reinforce the
conclusion that “MaxFlow-WOA” is an effective metaheuristic
for solving the Maximum Flow Problem (MFP). [1]
Combining the WOA and the rapid and the big advances in the
distributed parallel applications of metaheuristics, a parallel
whale optimization (Parallel-MaxFlow-WOA) algorithm is
developed by Masadeh et al. (2020) to solve the MFP. But the
truth, this algorithm is considered as a more powerful and an
expanded version of the sequential MaxFlow-WOA. It works
by segmenting the search space (i.e. the network graph) into
four segments, all of which are computed in conjunction with
each other. Then, the best maximum flow of these segments is
selected. The algorithm was tested on different datasets that
have between 50 to 1000 vertices and the number of edges
between 502498 to 50024998. Then, the algorithm's solution
quality was evaluated for each dataset. Compared to the FF
sequential algorithm, the proposed algorithm achieved a
tangible (3.79) reduction in the overall computational running
time by running the segments on four-independent-parallel
processors. As this result is a great enhancement of the
computing time, the first noticeable impression of this four-part
segmentation stimulates the authors to strongly recommend
applying this proposed algorithm using the distributed systems
architectures, at least to gain their parallelism powerful benefits.
Table III shows a computational complexity comparison
between the FF, Sequential-MaxFlow-WOA, and Parallel-
MaxFlow-WOA. [40]
Table III. Complexity comparison between FF, Sequential-MaxFlow-WOA, and Parallel-MaxFlow-WOA
Complexity type
FF
Sequential MaxFlow-WOA
Parallel MaxFlow-WOA
Note
Augmenting path cost
O (mV)
O (|E|)
O (|E|)
· “m” denotes the number of the
arcs.
· “N” denotes the number of
clusters.
· “V” is the number of humpback
whales (i.e. vertices or nodes).
· “E” is the number of edges in the
directed-weighted flow graph.
Run-time complexity
O (|V| + |E|2)
O (|V| + |E|2)
O (|V| + |E|2)
The overall computational
running time
O (|V| + |E|2)
N * O (|V| + |E|2)
Max (O (|V| + |E|2)N)
The maximum flow
|E|
|E|
|E|
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3.2 Grey Wolf Optimization (GWO)
Within the animal kingdom, an animal itself may be the
predator and/or the eaten prey of the others. Grey wolves as
predators are mostly known to prey on a variety of large,
hoofed animals such as bison, mountain goats, moose, and
other different kinds of deer. These wolves, also formerly
known as “Canis Lupus”, are living in packs with an average
size between five and twelve; they have a very strict leadership
hierarchy or perhaps not surprisingly, one of the most
fascinating social behaviors one has ever seen. Mirjalili et al.
(2014) tried to mathematically simulate this dominance
hierarchy structure and the sovereignty levels during the social
hunting practice and, for that, a going-on-down-hierarchy
algorithm is designed that is closely related to this. This
algorithm is called Grey Wolf Optimization (GWO). As
illustrated in both Fig. 6 and Table IV, the dominance level in
this suggested tactic reclines from the top towards the bottom
and can be carried out at four-hierarchical commanding levels:
Alpha which is the dominant leader the one with the topmost
liability, Beta which is Alpha's assistance for decision-making,
Delta which controls Omega, and Omega which are under the
domination of the other wolves. Granted, each team member is
classified as being one of these four levels. [16]
Fig. 6. Pyramid of the leadership hierarchy for the grey wolves
Since catching and killing the prey should be simulated with a
particular interest, a three-stage algorithm that matches up to
their hunting plan of action is proposed in this research paper.
First, the exploration stage when these predators are searching
the area (i.e. the search space) in pursuit of prey. Second, what
they are doing when they are finding certain prey attain their
request; they pursue and then try to harass it to encircle. This
stage ends when the prey is encircled and stops moving to
escape. Third, the exploitation stage which represents the
scenario where the actual attack process will be launched on.
At this stage, Alpha begins a sheer attack on the prey.
Whenever Alpha needs assistance, Beta and Delta help in the
attacking process, but under the control of alpha. In short,
every wolf is part of a one-team attack that organized and
carried out the execution. [16]
Table IV. Grey wolves' dominance structure
Name
General
Reaction Pattern
Duties
Solution
Hierarchy
Alpha
The dominant
leader, i.e. the
one with the
highest liability.
Design the hunting
plan, the place to
sleep, the time to
sleep or wake up, and
so on.
The best
solution
Beta
The deputy
leader and the
commander
alternative.
The Alpha's decision-
making assistance
that rules the other
lower-level members.
Besides it is the
pack's educator, it
supplies alpha with
any constructive
feedbacks rendered to
carry out and support
the Liability. Since it
is the commander
alternative, it will be
appointed as a leader
in the case of Alpha's
dysfunctionality.
The second
best
candidate
solution (i.e.
the second
level in the
hierarchy).
Delta
They lead
omega, i.e.
members of
omega are
dominated by
delta.
The general care and
safeguard
responsibilities are
attached to them.
Hunters, scouts,
experts, ex-alphas,
ex-betas, and
caretakers are
belonging to this
category.
The third
best
candidate
solutions
Omega
The working class which is under the
domination of the other wolves (i.e.
Subordinates).
The
underneath
level in the
hierarchy.
To ensure that the algorithm' efficacy standard is of a high
level, the following investigations were applied in [16]:
· To benchmark its performance, the GWO algorithm was
evaluated against a comparison group containing twenty-
nine prominent test functions which were categorized as
benchmark tests. The algorithm was executed and iterated
thirty times on every one of these benchmark functions.
· The quality of the proposed algorithm was also compared
with the other five well-known metaheuristics
recommended in the literature which are Differential
Evolution (DE), Evolution Strategy (ES), Particle Swarm
Optimization (PSO), Evolutionary Programming (EP), and
Gravitational Search Algorithm (GSA).
· To further properly teste and extensively investigate its
behavior, all the aforesaid benchmark functions are
Alpha
Beta
Alpha's assistance for
decision-making
Omega
which controls Delta
Delta Subordinates
These subordinates are under the
domination of the other wolves.
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47
employed in testing the algorithm in terms of the
followings:
- Exploration: in relevant to this point, the algorithm
provides either a merit result when it has provided very
competitive outcomes compare to FEP and DE or a
distinction grade when it has outperformed GSA and
PSO, as well.
- Exploitation: the algorithm provided outstanding
performance and presented highly competitive
outcomes in the matter of exploiting the optimum
solution with the least possible computational cost.
- Local optima avoidance: At this point, the algorithm
extremely has outperforms the others in at least half of
the benchmark functions and has also provided
successful competitive results in the second half.
- Convergence: the behavior of the algorithm proves
that it has the ability to eventually convergences at a
point in the search space.
To tell the whole truth, the ability of the algorithm in
making and controlling a fair balancing between the two
cornerstones of any metaheuristic algorithm, exploration
and exploitation, has resulted in successfully going
beyond most local-optima traps.
· An important step forward was to proceed in evaluating the
algorithm on a wide range of three large and difficult
instances of engineering design problems that are quite
popular among researchers around the world. These
challenging problems are tension/compression spring,
welded beam, and pressure vessel designs. The algorithm
indicated a high-performance capability in solving these
problems.
· The said authors also took into account proving the
performance of the algorithm in an authentic application
and, in turn, the algorithm was inspected in an optical
engineering problem which is referred to as optical buffer
design. This problem is directly related to one of the
internal key elements of the optical CPUs. All over again,
the algorithm is also able to solve this real-world
application and can be widely adopted by the optical CPU
industry
To put it in a nutshell, all the above-mentioned experimental
analyses and the comparisons that have been made with the
other approaches have guaranteed that the GWO algorithm is
able to offer more competitive results and it is applicable in
many challenging problems, especially those that have
unknown search spaces.
Since then, the pyramid of the grey wolves' commanding levels
has garnered a lot of attention from the researchers and, so,
another GWO-based research has been held by Masadeh et al.
(2017) for solving the maximum flow problem (MFP), named
MaxFlow-GWO. The authors utilized the K-means technique
to divide the grey wolves into groups, called clusters, each has
its leadership and encloses by five-to-twelve wolfs.
Accordingly, the graph is segmented into clusters and each
five-to-twelve vertices are grouped together as one cluster.
Then, they proposed a three-stage algorithm that matched up
with their corresponding fishing scenario: searching for prey,
encircling prey, and attacking prey. The time-growth
complexity of this proposed algorithm is “O(|n| + |E|2)”, where
“E” indicates the number of arcs (i.e. the number of edges
between wolves) and “n” stands to the number of vertices (i.e.
wolves). After the computational run time of this algorithm
was compared with the well-known Ford-Fulkerson' algorithm
by using the same datasets, the achieved outstanding results
were significantly more optimal. [24]
3.3 Metaheuristics' Parallelism
As the systems of the clustered parallel data processing can be
employed for producing high-quality results and, at the same
time, surpassing the calculation speed, the artificial intelligence
(AI) specialists and other interrelated participants exploited this
distributed architecture in carrying out their High-Performance
Computing (HPC) codes to process large-scale problems. To
address this, the same network graph is divided into a number
of subgraphs based on the existing number of processors. Each
subgraph contains a number of augmenting paths. Then the
calculation of the whole network graph is distributed among a
number of processors where each subgraph is computed alone
by a single processor. On the grounds of this, all the processors
cooperate together to solve the problem simultaneously. [11]
[12][41]
In this context, some Jordanian researchers use IMAN1
supercomputer which is located in Jordan to conduct their
experiments. It was assembled using 2260 Sony PlayStation3
(PS3) devices that are linked together via a fiber-based network.
Combined, this supercomputer provides multiple resources,
high-end integrated clusters, and an open parallel and
distributed computing environment. Besides that this
supercomputer has an extraordinary efficiency such as its
capability in driving 25 trillion operations per second and
serving thousands of concurrent clients with sub-millisecond
latency, it has also many supporting powerful tools meeting
both industrial and academic computing needs performing
millions of simultaneous input/output actions. [42]
With the intention of solving the MFP by utilizing the modern
technology of IMAN1, a parallel genetic algorithm (PGA) is
suggested by Surakhi et al. (2017) which is an extension to the
serial version of the algorithm [41]. Based on a real distributed
system, they exploited the HPC cluster architecture in
designing the stages for each one of the iterations to work
simultaneously in conjunction with the others. After the
network's directed-weighted graph is segmented into a set of
subgraphs, all the different augmenting routes from the start
node “s” going to the target node “t” are altogether computed
concurrently through the using of the so-popular message
passing interface (MPI) library which is a standard library used
for multi-core multi-thread parallel execution development. As
each subgraph has its own local Maximum Flow (MF) solution,
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48
all the local MFs contribute together in generating the overall
global MFP solution. And so, the total maximum flow value
for every one of the iterations can be produced by the simple
summation of these augmenting routes. Consequently, this
value is subject to be enhanced from iteration to another one.
Compared with the sequential version of this algorithm, the
needed time was rationed by 50% and they have achieved more
worthy results in terms of accuracy, speed, and time efficiency.
In their ways of seeking high-level computation with respect to
the quality of the solutions and the response time, IMAN1 as a
supercomputing center is used yet again by Alkhanafseh et al.
(2017) in solving some of the chemical reactions problems. As
an improvement of the standard Chemical Reaction
Optimization (CRO) algorithm, the authors proposed a
modified version of the serial CRO algorithm where the main
problem graph was segmented into a set of subgraphs
distributed on multiple processors; each one was responsible
for computing one augmenting path. In comparison with the
sequential CRO, good enhancement was significantly achieved
by applying the parallel version in terms of the quality of
solutions and the overall computational running times. The
time needed (i.e. time complexity ) to solve the maximum flow
instance for the parallel implementation of the algorithm is
“O(NEF * P)” where “N”, “E”, “F”, and “P” are the count of
vertices (i.e. nodes) for each subgraph of the flow network, the
count of edges for each augmenting path between the source
and the sink vertices, the maximum flow value from the source
vertex to the sink vertex, and the number of concurrent
processors that are used in execution the algorithm,
respectively. [11]
Going with the new vision of the smart digital world, El-Omari
within two research articles, (2019) and (2020), ends up that
the CC digital-priceless environment is truly the most tolerable
place for hosting many complicated algorithms especially that
it has actually emanated out from unlimited and never-dying
diverse resources for ever-sooner and inexpensive calculation
and, moreover, it has the world's best price-per-performance
ratios for the HPC operations. The author also pointed out that
there are genuinely thousands to millions of virtual machines
(VMs) that are dynamically generated and demolished to serve
numerous customers in easily ending their very sophisticated
or even unmanageable tasks. Accordingly, the author pointed,
at least implicitly, to another further step forward by building
the needed optimization algorithms remotely as web-based
innovative services within the CC environments. From over
here, it is foreseen in the next few coming years that global
solving for the optimization problems based on utilizing CC
might become a wildly-popular simple practice among
ordinary users. [12][43]
3.4 Artificial Neural Network (ANN)
ANNs are a family of computational intelligent models that
strive to simulate the process of exchanging messages among
neural networks' biological systems that especially exist inside
the human and the animals' brains. In analogy to the brains'
working process when catching information, these artificial
nervous models are used particularly to solve the optimization
problems that have an extreme number of inputs in which
most of them are usually unknown. The neurons are imitated
in these artificial models as nodes connected with each other
to form an artificial model viewed as a network of nodes. The
important point is that every connection connects two nodes is
associated with a given numerical value that represents its
weight, called the neuron's activation value. These connection
weights are determined by feeding the training data set to the
input layer and adjusting these weights recursively over the
course of the training process' iterations. Since the acquired
knowledge is learned accumulatively from the collected data,
these neural networks need to be trained sufficiently on a
fairly large set of data that is relevant to the problem domain.
During the training process or as a so-called learning process,
these weights are fine-tuned based on the extracted
knowledge; this step is regarded as the most crucial one to
accomplish high recognition accuracy. From a purely practical
standpoint, the training process should be repeated until the
network is capable of learning and adaptive to the different
inputs. [36][18]
The objective of the learning process is to analyze,
summarize, extract, and elicit the associated knowledge from
the training data set. All these foregoing errands entail a deep
understanding of the basic structures of the training data set.
Even though exploring great amounts of data with the purpose
of retrieving some relevant knowledge could be a frustrating
and complicated task, the acquired knowledge could be latter
used successfully in detecting patterns and trends for the sake
of classifying information.
Since ANNs were introduced in the pattern recognition field
and optimizing nonlinear functions that work recursively, El-
Omari (2008) developed a new robust technique that intends
to optimize the segmentation of the compound images based
on modeling the solution sample space using the ANN
paradigm. By building prior knowledge utilizing four
interconnected ANN's as a one-model component, an image
can be segmented by this brilliant approach into labeled and
coherent regions of four classes: pictures, graphics, texts, and
backgrounds. Then each region is manipulated individually
according to its characteristics with the most effective
compression method that either a new one or one off-the-shelf.
In that research work, there were another three proposed
techniques to meet the preceding stated segmentation
objective; all of them revolve around a vivid central point by
modeling the ANN but each one has its own layered-structure
topology and characteristics related to the applied evaluation
criteria (i.e. activation function), the number of the hidden
layers and the number of nodes (i.e. neurons) in each one of
the hidden layers.
A fifth hybrid approach is further proposed in that research
work as a result of hybridizing these four stated approaches.
However, each of these proposed approaches has it is certain
trade-offs such as speed, reliability, accuracy, efficiency, and
ease of use. In fairness, the main concern of these proposed
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
49
models, particularly the last approach, is related to the high-
level computational power and the time complicity where the
author of the said study suggested two highly efficient
strategies to this end. The first one is by building the
segmentation methodology as utility software that may be
considered as part of any operating system. The second
strategy is by building the data segmentation mechanism
internally as a special-purpose built-in chip. Within these two
strategies, every image is right away encoded when it is stored
and, vice versa, decoded when it is retrieved back. [18][43]
Another relevant ANN research was developed by El-Omari et
al. (2012) for optimizing the segmentation process of the
compound images by using both the multilayer feed-forward
Artificial Neural Network (FF-ANN) and the Back-
Propagation (BP) learning methodology to feed-backward the
losses. BP, also called the error-BP method, is so named
because of the difference (i.e. error) between the desired
outcome of the current neural network iteration step, “Od”,
and the preceding one, “Oa” is fed back to the same neural
network, namely from the output units to the input ones. The
mathematical construction of this main difference can be
modeled as in Equation 2: [36]
E = 0.5 * (Od - Oa)2 (2)
In the course of this added-value work, the proposed algorithm
breaks down any compound image into equal-size-square
blocks. The network was designed and modeled to discover
and identify patterns that are relevant to the set of the various
components of the block. Since the right training of the neural
network is the most critical side of building a reliable model,
the neural network was modeled and implemented using
MATLAB® and trained empirically upon a collected database
containing 2987 24-bit-RGB-bitmap images of different
resolutions, each has its own features. After the necessary
proper-sufficient training of this neural network to ensure
lower error rates, the neural network weights were tuned
properly many times and then each block was evaluated to
determine its type and then classified accordingly. Once the
blocks are been classified as it’s intended to, all adjacent
blocks having alike features and classes are fused together to
form a single and coherent whole region. From the
observation of actual practices, the nuanced outcomes indicate
that the proposed model is successfully capable to define the
types of each block with an average accuracy of 89% and
broadly applicable. [36]
Despite its low error rates, the noteworthy issue of the
proposed solution of [36] is that the training process of ANN,
especially over big data, is seemed somewhat computationally
expensive and depends on a large number of hard-headed
setting parameters that demand extra steering effort to fit the
considered problem. So there is a necessity to enhance the
overall performance by speeding up the ANN's learning
activity. To make things most sense, substituting the training
functions of the learning process by more-advanced
metaheuristic algorithms may accelerate the ANN model and,
in turn, better performance may be achieved by solving this
drawback.
Since, utilizing the advantage of metaheuristic in hybridization
ANN with another metaheuristic may solve the
abovementioned performance weakness of this algorithm, the
first author of that study (i.e. [36]) is currently in the process
of implementing this proposed algorithm, namely SLnO-MFP,
as an alternative to the Back-Propagation (BP) function. By
this inclusion and integration, the suggested algorithm works
as an effective tool within the ANN's training. This may have
a strong probability in raising the outcomes' efficiency and in
reducing the maximum number of generations that are
necessary for the elicitation process of the final solution which
as an axiomatic in-line with reducing the time needed to
implement them. Furthermore, this may theoretically make the
probability of the optimal solution arrival even greater. For a
more detailed explanation and illustration of this algorithm,
the interested reader can refer to the mentioned paper.
3.5 Artificial Bee Colony (ABC)
The differentiation between honeybees’ behavior and computer
also attracted hundreds of researchers in proposing some
artificial intelligence algorithms used to solve many real-life
problems. The researchers found these bees live in groups
called colonies where each bee colony, also referred to as hive,
has at least three well-known subgroups of bees: scout bees
that responsible for searching for the new food sources (i.e.
solutions) which are the flower nectar, onlooker bees which
knew the amounts and determine the exact places of any food
source by watching the dancing ways of the scout bees, and the
employed bees which are responsible for gathering the food
from the resources' places that are defined by the scouts. They
also found the members of each group (i.e. colony), as well as
the subgroups, have their own structure for the working tasks
and dominance hierarchy. [31][29]
By studying the behaviors of these colonies especially how all
the bees contribute together in generating the optimal solution
of the nectar harvest, the research work held by Saab et al.
(2009) introduced a novel and valuable optimization algorithm
based on using the Artificial Bee Colony (ABC) optimization.
With the condition that the probability of choosing any
candidate solutions (i.e. flower nectar as the food source) is
directly connected with the fitness function (i.e. nectar's
amount, nectar's quality, and the distance between the colony
and the food’s source), the importance of their algorithm in the
real-world is its ability to balance between the two searching
phases exploration and exploitation in the searching iteration
steps around finding and reaping the flower nectar. For a more
detailed explanation and illustration of this algorithm, the
interested reader can refer to the mentioned paper. According
to the real implementations of the two scenarios of scouting
and forging processes, this algorithm can be used to employ
many real-life optimization problems that don't demand
supervision which includes, but are not limited to, the
following examples: combinatorial optimization problems,
stochastic problems, multi-targets, data-mining-search-engine
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crawling, parallel implementation, multi-targets, and parallel
implementations. [31]
3.6 Hyper-heuristic Framework
A number of researches have been made in an effort to find
solutions related to the optimization of the execution time
issues. In this regard, the study by Welch and Miller (2014)
offered a two-level model for optimization algorithms
turnaround. The primary premise of this much-appreciated
model is to separate the functionalities of the metaheuristic
optimization algorithm from the functionalities of the problem
itself. Broadly, this is the notion of the hyper-heuristic
framework where a set of intelligent metaheuristics can be
classified upon their shared common features into different
types of hyper-heuristics and then combined together through
the hybridization of the hyper-heuristics framework. Then,
rather than exploring the search space of the candidate possible
solutions for a given problem, the framework of the hyper-
heuristics automatically fabricates an algorithm that could
professionally find a better solution by one or more of the
already metaheuristics that have been classified and stored.
Besides that this hybridization leads to new approaches to
emerge, this combining of the positive capabilities of the
different metaheuristics gives more chances for capturing
better solutions. While two or more approaches that
participated in this hybridization can be fused together to form
one model, each one of them remains functioning as an
individual one. [5][29]
From a broader standpoint, hyper-heuristic frameworks can be
understood in such a way as if there were two abstracted parts
associated with each other and maintaining a high degree of
correlations: a top-level frontend and a lower-level backend.
While the metaheuristics themselves are encapsulated to form
the backend, the frontend which involves different types of
hyper-heuristics is the visible part that the optimization handler
sees and interacts with. By this easy-to-implement way of
using the hyper-heuristic frameworks, a higher level of
abstraction is provided where the backend complexity is
shielded from the frontend and so some unwanted details are
eliminated or hidden. This architecture allows those handlers
their selves to focus their effort on solving the problems rather
than concentrating on the minutiae of the underlying details
related to how the metaheuristics should be implemented for
solving the considered problem. In all sincerity, hyper-heuristic
does not revolutionize the field of metaheuristics, but it adds a
new easier and quicker face in dealing with them.[5]
3.7 The new-generation metaheuristics
Finally, to conclude the discussion of this section, the study by
Dokeroglu et al. (2019) introduced a considerable selective
survey to compare the most popular metaheuristic algorithms
that have been proposed in the last twenty years, namely
between the years 2000 and 2020. This distinguishable survey
reviewed and then analyzed the new-generation metaheuristics
in such a way that it can be considered as an excellent
benchmark for the metaheuristics comparison in the
optimization area. On part of comparative performance
measurement in that 20-year span, this prominent study drew
an objective comparison between the metaheuristics according
to the following five critical issues: [29]
· How many setting parameters are required to go efficiently
with the optimization task of the compared algorithm?
Since setting every input parameter requests more time and
effort to be adjusted and tuned to go with the problem
nature, the algorithm with the lesser parameters is, without
a doubt, the better choice to use. From a deeper viewpoint,
the number of parameters in any metaheuristic is directly
proportional to its complexity where the algorithm with
fewer parameters needs slighter variations to work well in
solving other problems and, as a result, to dominate over a
larger variety of applications.
· Which are the stages of the metaheuristic algorithm that
have the ability to balance properly between the exploration
and exploitation strategies? As a consequence of the
metaheuristics' stochastic nature, optimal balancing
between these two stages becomes unquestionably a
challenge to meet.
· Has the metaheuristic been used in developing other
hybridized approaches? There is no question that the
algorithm that is used much in other hybridized approaches
is credible evidence of its well-built organized structure
efficiency.
· Does the metaheuristic algorithm contain some local-search
mechanisms? Since local searches usually give the best
chances to keep approaching the best solutions, the
presence of this facility has a considerable influence on the
candidate solutions improvement during the course of the
successive iterations.
· Does the metaheuristic algorithm search the solution space
globally for catching the optimal solution or just within the
local solution space?
Granted, any metaheuristic algorithm satisfying the above
features will have more stability to be staying used in the
upcoming years. From another point of view, this analytical
study could highlight some clues as to how to screen and select
the most adequate metaheuristic for a given optimization
problem. [29]
Furthermore, this research study drew attention to two other
important issues that may prevent some metaheuristics from
being utilized. One is related to the lack of a solid analytical
foundation for validating many metaheuristics in which their
performance evaluations are measured only by carrying out the
classical ad-hoc statistical analysis without being based on real
theoretical or mathematical foundations. Then the said study
also pointed out how it is difficult to find clear guidance or
robust frameworks to recommend anyone interested in how to
adapt many metaheuristics to the considered problems. [29]
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Related to the previously mentioned setting parameters issue
debated in [29], the authors in the study by Lam and Li (2010)
emphasized that the adjustments of many metaheuristics are
just relying on the experience and prioritize of the researchers
themselves without applying clear conceptual structures and
theoretical guidelines for how to set and tune their input
parameters according to a problem domain [21].
4. Maximum Flow Problem (MFP)
Since the efficient flow supplying should be guaranteed by a
well-defined distribution system, MFP is one of the pillars of
computer engineering, mathematics, and computer science that
has been deeply studied [22]. From a conceptual standpoint,
MFP as a research area is indeed classified as being based on
the fusion of three-well-known-overlapped branches that are
directly interrelated with both Artificial Intelligence (AI) and
Operations Research (OR). First, Computational Complexity
Analysis (CCA) which is pertaining to the cost of solving
computational problems [22]. Second, Nature Inspired
Computing (NIC) which is an emerging research area that
mainly concentrates its focus on solving various global
optimization problems based on exploiting efficiently
Chemistry, Physics, and Biology approaches [3][20]. Third,
Combinatorial Optimization Problem (COP) that tries to make
every great effort into achieving an “optimal” solution among a
set of possible candidate ones [34].
Before describing how the proposed algorithm solves the
problem under consideration, it may be well to first consider
the matters of some notations and fundamental features. First
of all, any type of these problems (i.e. MFPs) considerably
includes the following common components:
· : This combination of variables is
formally referred to as the set of the initialization
parameters and so the problem dimension is represented by
“n”. It also indicates the vector of variables that are used to
frame the designed methodology of the proposed algorithm.
For its time convergence and to explore a much broader
diversity inside the candidate solutions, the impressive
achieved results of any algorithm are highly interrelated
with the choice of this set.
· represents the vector of constraints
(i.e. criterions or rules ) that are used to restrict the progress
of the searching process. From another perspective, this
vector is used for the purpose of limiting the various values
that are assigned to the vector “X”. On the assumption that
the total number of constraints is defined by “m”, all these
constraints are so sacred not to be violated while
discovering the optimized solution. It is vitally important
for any solution to have complied with this vector of
constraints. Prompted by this, a feasible solution is
considered as a potential one if it certainly satisfies all the
indicated constraints along.
· “S” represents the solution space. This vector represents the
set of all possible candidate solutions for a given problem.
[5][4]
· “s” indicates the set of values that are assigned to the vector
“X” and restricted by the vector of constraints “C”.
· “F” represents the objective function (i.e. objective
criterion) that is used to assess the quality level of a stated
solution. It represents the criteria used to pick out the
optimal solution among the possible candidate ones. [4][7]
Second, with the aim of using SLnO in solving the problem of
interest, the input of the maximum flow problem (MFP)
should be adapted into a layout format that can be understood
by SLnO. Thus, the input should be converted into a graph.
Broadly and from a mathematical modeling part, this can be
understood in an abstracted aspect by using the following
bullet points that represent the problem instance:
· The shape of the flow network is called “network
connectivity”. This network is a directed graph, “” that
has a finite set of directed weighted arcs (i.e. edges), “”,
and a non-empty finite set of vertices (i.e. nodes), “”. That
is to say, the MFP can be defined as “G = (V, E)” where the
following points clarify this: [40][7][8][44]
- “” indicates the weighted directed network graph,
called a digraph.
- “” denotes the group of nodes, also named vertices,
which are inside “”; their count is “n”. In an analogy
with Fig. 1, and n=7.
- In order to carry flow, nodes are combined together by
the set of arcs “E”, also referred to as edges. The
behavior of the network “G” is defined by the way that
the set of nodes “V” are connected via this set “E” and
by the strength of these connections, called weights or
capacities (i.e. flow). All edges' weights are assumed to
have strictly positive values and, conventionally, these
weights are set to be small numbers [29][2].
- A variable for each edge of the graph is introduced in
the graph of MFPs. For instance, the edge between the
two nodes “” and “” of Fig. 1 is represented by using
the variable “” where “ ”.
- The representation of the weights inside the set “E” is
used to represent the search agents. Every edge “ ”
that is directed from a given node “i” towards another
node “j” has a maximum of non-negative capacity “cij”.
The total number of edges inside the network “G” is
“m”. By looking at Fig. 1, the total number of edges is
10, hence m=10.
· Two special nodes in “G” are distinguishable and
designated in advance as follows: [44]
- A source or a start node “s” in which flow is arriving.
Unlike the other nodes, the node distributes flow to the
other nodes. It has only an incoming flow without
outgoing flow.
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· Related to the network graph, it is easy to see that Equation
2 holds: [44]
That is the flow value of a network “” is the sum of all
flows that get formed in the source node, “s”, or
equivalently of the flows that are used up in the sink node,
“t” [44]. By looking at Fig. 1, for instance, it can be seen
that both the incoming flow at the target node “t” and the
leaving flow at the starting node, “s” are equal to fifteen.
· Augmenting path: The set of all the arcs emanating from
node “i” is denoted by “E(i)”. From another standpoint,
“E(i)” refers to the all edges that are connected with “i”. In
relevant to this, a track (i.e. a path or a route) with available
capacity is referred to as an augmenting path.
· The conservation constraint: Assume that there are many
routes joining between the beginning node, “s”, and the
corresponding destination sink node, “t”, the maximum
flow capacity is defined as the maximum total value of
flow that can be moved where satisfying the following
constraints is definitely a must by any possible candidate
solution [7][8]:
- Every arc “ ” must satisfy all the mass balanced
constraints along.
- Since the graph of interest can be represented and used
as a basis to generate the flow, the total arriving flow
and the total leaving flow for every node “i”, other than
“s” and “t”, should be absolutely equal to each other.
This can be mathematically expressed as it can be
shown in Equation 3:
(3)
In other words, for every other node “i”, other than the
source or a start node “s” and the sink or a target node
“t”, both values of the incoming (i.e. arriving) flow and
the departing (i.e. leaving) flow must be equal.
Otherwise, the network “G” couldn't accurately map
the input flow into the output flow which means that
some given capacities values, “uij” are possibly missed
or incorrect.
- The total entire flow leaving “s” is equal to the total
incoming flow arriving in “t”. The value of the flow is
defined by using the formulas described in Equation 4
and Equation 5:
(4)
That is,
(5)
Where it is easy to see that the followings hold:
(6)
(7)
(8)
5. Sea Lion Optimization (SLnO) Algorithm
The term flock or flocking can be used to refer in particular to
the group of birds. On the other hand, swarm behavior or
swarming, as a term, is originally applied to insects but it can
also be used interchangeably to refer to any other collection of
interacting creatures or entities that in their normal lives
aggregate together in swarms and interact harmoniously with
each other according to two norms of interaction that are
mainly governed by laws of nature. The first norm is related to
the local interaction between each other, and the second one is
their collective interaction with their environment in which
joint hunting is the most distinguishable one among these core
activities. This collective behavior or as called collective
intelligence or global behavior, of these groups of creatures has
recently gained significant attention from scientists and
researchers from different research institutes and universities
around the world and, for that, a new science called swarm
intelligence based (SIB) has been coined as shared knowledge
and collective concepts of a sequence of algorithms and models.
On the grounds of this, this science is based mainly on the
natural social behavior of the biological populations.
[26][45][31]
Motivated by the above-stated inspirations, scientists try to
come up with new goal-oriented techniques to tackle various
real-world optimization problems. And, thus, the so-called
“nature-inspired computing” is evolved out as a field of
computer science that is targeted directly toward making
computers imitate the intelligence of the swarms (i.e. SIB).
Broadly speaking, solving optimization problems, particularly
the complex ones, and operating numerous complicated
systems can be drawn out by this field of science, namely SI.
[13][18]
In view of this, many metaheuristic algorithms have been
proposed that take direct inspiration by the collective
intelligence and the ways of exchanging in-depth information
among each other [31]. These algorithms are used expansively
not only in resolving optimization problems but also with many
other real-world automation fields like healthcare,
manufacturing, military, and other related domains [3].
The sea lions are amphibians and aggregate inside swarms
called colonies where each colony has a massive number of
members that are grouped into subgroups. While the whole
group has a leader, each subgroup has a leader, as well. The
important point is that each colony can be considered as a
hierarchical paradigm where all the low-level components (i.e.
subgroups) inside this hierarchy work together to form a higher
level-hierarch. The whole system behavior is determined by
aggregating and integrating together all the lower components
of this hierarchy to form a higher collective behavior or as so
named global behavior. Based on the commanding orders, the
joined members of any subgroup can be moved to another
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subgroup inside this hierarchy according to their age, gender,
and the tasks that are entrusted to them. However, each
member may be subject to this moving over and over through
their lifetimes. The whole group or some of its subgroups may
hunt together which increases their chances of gaining more
feeding prey. From this, a self-organized teamwork system is
formed by grouping together and coordinating all the different
interactions within the lower level of the hierarchy.
Compared to the other creatures feeding on the relatively
species-rich seawater, each colony has a very strict coherent
strategy in their fishing together. In the subject of the
optimization literature, Sea Lion Optimization (SLnO)
algorithm is relatively one of the best-known dominant
examples of this category which is based mainly on imitating
both the hunting manners and associated direct communication
channels among any swarm of sea lions during their chase for
the preys [2][26].
There is a continued need for all the swarm members to
interact with each other by direct communication channels
upon seeing prey. Chasing and catching the detected prey is the
joint venture of all the related swarm members. In accordance
with their social hunting nature, moving towards an optimal
target implicitly exists in their primitiveness and all the
associated activities are parts of their nature. Since it is a joint
hunting process, it is clear that the primary responsibility for
hunting implementation and success rests with all the agents
themselves.
As do all the other nature-inspired paradigms, SLnO is a
population-based algorithm that is based on using the fitness
concepts to determine the quality of the solution. By this means,
the proposed algorithm starts by generating a population
containing multiple search agents. To assess these search
agents, the fitness function of an efficient solution which is
based on the maximum value is computed for every search
agent. At that instant, the best search agent “
” who has the
best fitness among the group of candidate solutions is defined
and all the related locations belonging to the other search
agents should be modified directly in-keeping-with this
modification.
Out of all of this, there is a pressing need to address the
following appealing concerns related to the organizational
structure of their social behavior: [46][2][31]
· Solution search space: What are their feasible regions,
namely their solution search space? How are sea lions
responding to any vital action in the hope of finding more
superior solutions? Is it an on-demand and self-adaptive
strategy? How are these animals moving in the direction of
the optimum goal or near-optimum one?
· Hunting process: Do the sea lions have a strategy for
feeding or it is a trivial-usual process and a sudden
inspiration? If there is a hunting strategy, is it a hunting-for-
together strategy? How does the hunting process work? Is
there a to-do list of basic tasks that should be initiated? Is
this foraging process behavioral, evolutionary, or both? Is
the hunting process a one-team concerted effort?
· Collective behavior: Is the collective behavior of the sea
lions centralized or decentralized? In other words, does the
collective behavior of the sea lions rely on only one sea lion
that is responsible for making every single decision related
to the whole swarm, and so it is a centralized system, or
several sea lions are responsible for making decisions, and
so it is a decentralized system or as so-called self-organized.
· Communication process: How are sea lions
communicating with each other? What are the guidelines
for managing this communication process in the followed
direction? How do they communicate to update their
locations to be turned towards the new target position of the
prey after any movement?
Along the way of revealing these research concerns, the SIB, in
particular the sea lions which are considered the major
inspiration of this technique, is systemically the collective
behavior of the following attractive notions and patterns of
behaviors: [46][2][13][31]
· Solution search space: The theater of the events depends
on the environment. It is the sea beach in the case of sea
lions. The whole graph is the search space (i.e. search
agents) and the prey is the target node that these animals
are looking to reach and catch.
· Collective knowledge: Given that the teamwork of the sea
lions is greatly self-organized, global behavior is essentially
derived from and based on the authority of self-organized
agents and their tendency in reaching the goal. Therefore,
the emergence of collective behavior is achieved by
collecting all the local communications between all
individuals. This leads to having a coin with two faces: the
formation of the tuned-global-collective knowledge arises
from the exchange of the different information among the
sea lions and, on the other side, the different rhythmic
interactions and communications among individuals in the
system lead to global-collective coordination. And so, the
depth of collective knowledge is based on this teamwork
communication.
It is worth mentioning that a successful solution is
constructed by a subscription of all agents and a single sea
lion, on his own, has a lower possibility to efficiently solve
a problem. On the other hand, it is an undeniable fact that
the collection of the sea lions composing the team has an
overall stronger possibility of getting closer productive
results and better markedly solutions.
· Natural laws: Behind the scenes, functions and operations
of the wholly-embedded components are regulated
according to natural laws. For this well-defined reason,
these high-level systems activate repetitively forever
without any troubles.
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· Hunting stages: To track and hunt the prey in case of the
sea lions, the chronological framework for the hunting
events goes through five stages:
- Detecting and tracking phase: The sea lions have faces
with elliptical cross-sections that are different than the
other mammals which have faces with circular cross-
sections. In addition to that, they have the longest
whiskers among all the mammals which can be moved
in all directions. Depending on the feeling of these
whiskers, these animals track and determine precisely
all the related information concerning the prey such as
location, shape, and size. [2][47]
Furthermore, sea lions habitually swimming randomly
in a zigzag course during their searching for prey across
the sea. As well, they utilize their whiskers to get a keen
sense of the prey. [47]
- Searching for prey (Exploration phase): When the prey
is composed of few fish, sea lions hunt individually.
Otherwise, when the prey is composed of plenty of fish,
they are chasing down together and hunting together as
groups. The sea lion (search agent) who successfully
detects the position of the prey is considered as the best
search agent and, in turn, this lion is assigned as the
leader that commands the hunting process. This leader
starts the process of hunting by telling and guiding the
other members about the prey which is considered as
the current best candidate solution [2][47]. Whenever
the best search agent is determined as a leader among
the other ones, all the other search agents should
arrange and update their current locations accordingly.
Nevertheless, if a better prey is detected by another
search agent, then this new prey is considered as the
new best candidate solution. In view of that new
situation, the leader, as well as the current best
candidate solution is replaced.
- Vocalization phase: many sea lions from a variety of
swarms begin to group together (i.e. forming a cluster)
around the prey and so the cooperative clusters are
formulated. The key significant factor of this stage is
how fast their immediate reactions to the prey
movement as soon as the prey position is determined.
On the basis of that, the sea lions are chasing down
together to force the prey headed for narrow balls at the
shallow water near the ocean's surface and the beach.
- Attacking phase (Exploitation phase): the encircling
process which is related to the process of getting
around the target prey after determining its position.
This process is directed by the leader of the sea lions
and requires updating the search agents' positions
according to these new circumstances.
- The actual feeding process: When the prey becomes
close to the surface of the ocean, the feeding process is
started.
· The distance function: The best candidate solution for the
sea lions is represented by the current best location that has
the minimum distance from the target prey which the
swarm has obtained yet. All the joined members should
keep track of this location and update their locations
accordingly. Equation 9 is used here to mathematically
model this behavior which is the most significant
characteristic of this technique [2]:
(9)
Where “
”, “
”, “t”, “
”, and “
” represent the
distance vector between the sea lion and the target prey, a
random vector in [0, 1], the current iteration, the position
vector of the target prey, and the position vector of the sea
lion, respectively. It is important to draw attention that the
vector “
” is duplicated when it is multiplied by the
number two in order to give the search space a closer
opportunity to explore a more optimal solution.
· The positions vectors: The vectors of the sea lions'
positions in any subsequent iteration “t + 1” are depending
on the preceding iteration which is denoted by “t”. This is
mathematically modeled by using Equation 10 [2]:
(10)
Where the vector “” points to the position of the target
prey and the vector “
” is as it has already indicated in
Equation 9. The vector “
” in this equation is reduced
linearly from “2” to “0” throughout the expanse of iteration
steps for the reason that this reduction drives the leader of
the sea lions into moving in the direction of the current
target prey and encircle them. Conversely, an increase in
this vector means that the sea lion leader is moving away
from the current prey. Thus, the aptitude of the current
position of the leader leads to the following three cases:
- If the value of “
” is less than one, then the search
agent is moving in the direction of the prey and the
other search agents should adjust their locations
according to that.
- If the value of “
” is greater than one, then the search
agent is moving away from the prey.
- If the value of “
” is equal to zero, then the optimal
solution has attained which means that the algorithm
terminates at this point.
However, if the value of (|
|) is greater than one or less
than a negative one, the search agents will move obliquely
away and search for a new cluster to join it.
· The Shrinking encircling mechanism: This mechanism
relies basically on utilizing Equation 10 that has already
been mentioned in the previous point.
· The collective communication: Since there is a need for
the sea lions (i.e. agents) to contact each other and to bring
all of them closer together particularly when they are
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tracing and hunting as subgroups, much of the success of
the SLnO algorithm lies in the collective intelligence that is
based on the collective communication. The more
collective communication and interaction between agents'
population, the more effective collective intelligence and,
in turn, the system will be more efficient in solving the
problems.
The sound as the communication language is formed by
using several vocalizations. Despite the smallness of their
ears compared to their bodies, sea lions have got the ability
to clearly detect both the sounds that are in the air as well
as that are underwater. Sea lions use this communication
behavior to call up other joined members who are currently
presenting on the beach to join the team immediately and
to manage the different hunting activities like tracking and
encircling prey. In this regard, Equation 11 is fabricated as
[2]:
(11)
Where the three vectors “
” , “
”, and “
”
represent the speed of sound of the leader of the sea lions,
the speed of sound in the water medium, and the speed of
sound in the air medium, respectively.
Normally, sound travels faster in solids than liquids and
slower in gases than liquids [48]. Under normal conditions,
sound travels in water nearly 4.3 times as fast as in air
[48]. Otherwise speaking, the sound of the leader needs to
be reflected in the two mediums: water and air that are
determined by “
” and “
”, respectively. This
sound reflection of the leader of these animals is behind
calling the other joined members that are inside the water
or at the sea beach.
· The circular updating of positions: this behavior is
mathematically formulated by using Equation 12:
(12)
Taking into account the fact that the target fishes are the
best optimal solution, the following points analyze the
elements of this equation:
- The term “
” represents the absolute
distance value between the search agent which is the
sea lion and the best optimal solution which is the
target prey.
- “” is a real random number between “-1” and “+1”.
- The term “ ” is mathematically expressed to
indicate that the sea lion (i.e. the search agent) starts
the eating process by swallowing the target fishes that
are existing at the bait ball (i.e. prey) edges. Thus, it
moves in a circular shape around the best optimal
solution (i.e. target prey).
· The global optimizer: In order to solve the MFP problem,
the proposed SLnO algorithm involves two activates:
exploration and exploitation. In the exploitation phase, the
joined members modify their locations in light of the best
search agent's position. In the exploration phase, on the
other hand, the locations of the joined members (search
agents) are updated in accordance with the position of the
selected sea lion that has been chosen randomly. Therefore,
the generalized mathematical formulation of this phase is
formulated by using both Equation 13 and Equation 14:
(13)
(14)
Where “
” is used here to point to a sea lion that is
selected randomly from the present population. It should
be stressed that when the vector “
” is bigger than one,
this equation is used for detecting the global optimal
solution. Because of that, this algorithm is considered as
being a global optimizer.
At the early phase of the iteration steps, Equation 14
demands sea lions to randomly proceed around each other.
On the other hand, Equation 12 permits other sea lions to
reposition themselves or move in a circular shape in the
direction of the best search agent which draws the reason
behind that this proposed algorithm has high exploitation.
In addition to this high exploitation, this algorithm has also
a high exploration and the capability to go beyond local-
optima traps.
· Related to the graph theory, the sea lions are represented by
agents and, in turn, this algorithm is a multi-agent
algorithm. The followings are beyond this point:
- The maximum flow problem is considered as one of
the various well known basic problems of optimization
in weighted directed graphs. It is a type of network
optimization problem in the flow graph theory.
- The SLnO graph-based for sea lions is usually
bidirectional.
- The weight at each edge (arc) interconnects two
vertices (nodes) representing the flow capacity of this
arc.
- The inputs should be converted to a graph with nodes
and weighted edges
· All the operations and data-processing activities are
ordinarily goal-oriented and real-time functions.
· All the team members (i.e. agents) are accelerating toward
discovering better solutions. Much, if not all, of the success
of the team, seems to lay upon the tendency of all team
members to hurtle past their target.
· Since the supervision of SIB is a self-organized natural
system, it is a decentralized system which means that
making decisions at the different hunting levels is rooted in
the team-environment not only in their leaders. In other
words, the fine-tuned vision comes from the fact that all the
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
58
6.1 Initialization Stage
The main algorithm that contains the population initialization
of the search agents (sea lions) is depicted in Fig. 10. In this
algorithm, a bunch of initial candidate solutions is generated
randomly. Overall, this set is so-named as a swarm. Next, two
of these search agents are selected randomly, one to refer to the
source and the other to refer to the destination which is actually
the prey itself. Then, the fitness function for every search agent
of the population is computed. For the sake of that, the distance
between each sea lion and “
” is computed. According to
the nearest “
”, the sea lion will be assigned to the nearest
group (i.e. cluster).
On the other hand, the issue of enhancement to find the best
solution for this norm of optimization problems is
considered the most worthy of this algorithm. In order to avoid
falling in the local optima and to converge to the best solution
within the predefined time, this algorithm also addresses the
case where these lions may make a random search moving
towards finding other better positions instead of remaining
stuck with one of the current search solutions (i.e. one of the
local optimas); this what is known as “exploration”. In this
feature, as soon as the best solution has been determined
among the other ones, all the other search agents should
rearrange their current locations accordingly.
6.2 Fitness Function
The goodness of the overall solution is evaluated thoroughly by
the quality of each possible position which is determined by
using the fitness function. The perfect choice of the fitness
function has, therefore, a great impact on the selection of the
candidate solutions and in the direct evaluation process for
identifying the solutions' qualities based on the degree of
efficiency. Based on that, there is a need to re-compute the
fitness function for each one of the search agents in any new
trial. Thus, the best search agent “
” is chosen and all the
locations of the other search agents should be updated
accordingly.
By using its special vocalization to tell them about the prey,
“
”, as a leader, send a vocal message to other sea lions
that exist on the shore or under the water. In accordance with
that, all the sea lions that have heard the vocalization of their
leader will join the cluster and then update their locations
toward the “
” position depending on the value of (|
|).
Hence, the general steps for updating the positions of these
animals are clearly depicted in both of the figures Fig. 11 and
Fig. 12.
6.3 Clustering
The philosophy behind clustering is the decomposing of the
original flow problem into a number of tractable subproblems
(i.e. local MFs). Then, a range of near-optimal solutions to
each one of these smaller subproblems is calculated. After that,
the collection of solutions for these subproblems is combined
altogether to create a global solution, namely global MF.
After the initialization stage and determining the fitness
function, the proposed algorithm can proceed forward to the
clustering of the network graph. This clustering is used for the
purpose of finding the overall solution for a given network
graph where the global search space (global MF) is broken
down into a set of local search spaces (local MFs), each is
referred to as a cluster. Each cluster contains a number of
separated subnetworks and each subnetwork is composed of a
group of nodes and their edges.
For satisfactory, “
” is selected randomly for each cluster.
Then the fitness function for each search agent is computed to
check whether it should join any cluster or not. More
precisely, each particular agent (sea lion) is managed in the
sense that it is identified to which cluster it belongs. So,
according to the value of the fitness function, each sea lion is
identified whether it will join this group or another.
In order to get the overall global maximum flow
( ), the local maximum flow (
) is
computed for each specific cluster and then the overall
summation of them is computed. This is illustrated in Fig. 13.
6.4 Maximum Flow Function
As mentioned in the preceding subsection, the local MFP is
calculated for each cluster by calling MFP function which is
introduced by Ford Fulkerson (FF). MFP function relies on
augmentation paths in residual graphs to find the maximum
flow from the source to the destination (i.e. source-to-sink
path).
The local MFP is computed for each cluster using the FF
technique that returns the local MFP for each specific one.
Then, the global Maximum Flow (
) of the network is
calculated using Equation 15:
(15)
Where “
”, and “N” represent the maximum flow
for ith cluster and the count of the clusters, respectively. On this
point, the algorithm shown in Fig. 14 is used to calculate the
Local Maximum Flow (i.e. ) for each cluster.
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
59
Fig. 11. The flowchart of the proposed framework
Calculate the distance between each search
agent (j) and “
” by Equation 9
True
If
SP
leader
<0.25
False
Update B, C, SL
Calculate “
” by using Equation 7
Update the location of
the current search agent
by using Equation 5.
Start
Obtain “
” calls others search agents by using Equation 7
True
If
|C| < 1
False
Update the location of
the current search agent
by using Equation 9.
Select a new random
search agent “
”
Update the location of
the current search agent
by using Equation 8.
Select the first search agent
Is this
agent ≤ the last
agent?
False
True
Select the next agent
Input data: population size, no. of iterations
End
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
62
As shown in Table V, the average speedup ( ) of
execution is calculated by finding the row-wise summation of
the numeric values of the speedup (i.e. last column) multiplied
by the network size (i.e. second column) of every experiment,
and then dividing by the total number of the network sizes (i.e.
summation of the second column). This is expressed in
Equation 17:
(17)
Where “
”, “M”, and “
” represent the jt h size of
the network, the count of the elements in the data set, and the
speedup of the jth dataset’s size which was computed as
indicated by Equation 16, respectively. It is to be noted that the
reported average speedup of the processing is comparatively
recorded to be (7.4902) faster than FF. Hence, this result
proves that this proposed algorithm is highly comparable in
terms of the execution time.
Table V. An execution time comparison between SLnO-MFP and FF
j
Average run-
time of FF
(per seconds)
Average run-time
of SLnO-MFP
(per seconds)
Relative Speedup
SLnO-MFP is
faster than FF by:
1
100
0.159
0.051
3.1176
2
200
0.312
0.072
4.3333
3
300
0.485
0.082
5.9146
4
400
0.698
0.091
7.6703
5
500
0.749
0.116
6.4569
6
600
0.913
0.125
7.3040
7
700
1.216
0.142
8.5634
8
800
1.549
0.212
7.3066
9
900
2.260
0.255
8.8627
10
1000
2.402
0.310
7.7484
The average speedup
7.4902
In a nutshell, it is clearly observed from this comparison that
the proposed model SLnO-MFP performs best and gives better
performance results than FF in terms of speed and time
efficiency; it is faster than FF by an average of (7.4902) times.
Furthermore, there is a dramatic increase in the difference in
speed between the two algorithms when large-sized network
instances are used. It would be important to know that the
perceived complexity is remarkably behind this speedup and
has a strong influence on the implementation of any
metaheuristic algorithms. As reflected in the plot of Fig. 15, the
execution complexity is a quadratic polynomial. More
precisely, it begins to mount when the number of nodes
increases.
To make a further comparison and evaluation, the impact of the
network sizes on the speedup of both algorithms where both
the first and last columns of Table V are graphically depicted in
Fig. 16 for both of the two algorithms.
Fig. 15. The average CPU's computational run time for FF versus SLnO-MFP
Fig. 16. The relative speedup of SLnO-MFP in comparison with FF algorithm
7.2 Relative Estimation Error Rate
Table VI illustrates the estimated-theoretical ( ) and
the actual-experimental ( ) run time of SLnO-MFP
algorithm with a Relative Estimation Error rate (REE) which is
calculated by using Equation 18:
(18)
0
0.5
1
1.5
2
2.5
3
100 200 300 400 500 600 700 800 900 1000
Average run time (seconds)
Network size (i.e. No. of nodes)
Average run time of FF
Average run time of SLnO-MFP
0
1
2
3
4
5
6
7
8
9
10
100 200 300 400 500 600 700 800 900 1000
Speedup Ratio
Network size (i.e. No. of nodes)
Speedup of SLnO-MFP over FF
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
63
Since the “analysis run time” represents “the estimated
theoretical run time”, Equation 18 can be redrafted as
expressed in Equation 19:
(19)
According to the statistical analysis of the sixth column of
Table VI, it is seen that the proposed algorithm has low error
rates compared to the FF algorithm.
Like the notion of Equation 17, the Mean Relative Estimation
Error (MREE) is calculated and viewed in this table by
summing up products between each element of the last column
and the second column; then dividing this summation over the
summation of the second column. This is expressed by using
Equation 20:
(20)
Where “”, “
”, and “M” represent the relative error
of the jth dataset’s size which was computed as indicated by
Equation 18, the jth dataset’s size of the network, and the count
of the elements in the data set, respectively.
Table VI. Theoretical versus experimental Run-Time error of SLnO-MFP algorithm
j
Estimated theoretical
run time (T)
Estimated experimental
run time (E)
Error=abs(T-E)
REEj=abs(T-E)/T
1
100
0.0929
0.0621
0.0308
0.3315
33.1500
10.9892
2
200
0.4785
0.0759
0.4026
0.8414
168.2800
141.5908
3
300
0.2762
0.0846
0.1916
0.6937
208.1100
144.3659
4
400
0.5998
0.9001
0.3003
0.5007
200.2800
100.2802
5
500
0.8672
0.9975
0.1303
0.1503
75.1500
11.2950
6
600
1.5341
0.1167
1.4174
0.9239
554.3400
512.1547
7
700
3.0921
0.1627
2.9294
0.9474
663.1800
628.2967
8
800
4.2753
0.1998
4.0755
0.9533
762.6400
727.0247
9
900
6.3782
0.2274
6.1508
0.9643
867.8700
836.8870
10
1000
8.3462
0.2681
8.0781
0.9679
967.9000
936.8304
MREE=0.8183
MSE = 0.7363
DMSE = 0.8581
The result of this equation, namely Equation 20, was calculated
using the seventh column of Table VI and then viewed in the
last cell of the same column and table. Here again, it is
noteworthy that the proposed algorithm is able to reduce the
error rate to be (0.8183). Hence, this result proves that this
proposed algorithm is highly comparable in terms of the error
rate.
In an analogy with Equation 19, the average of the squared
errors for all network sizes, which is referred to as the value of
the Mean Square Error (MSE), was also selected to be an
authentic validation measurement as shown in Equation 21:
(21)
The result of this equation was calculated using the last column
of Table VI and then viewed in the last cell of the same column
and table. By analyzing this calculated value, it is easily seen
that the proposed model has achieved a very worthy result
where the recorded MSE value is (0.7363). Remarkably, this
slight difference occurs due to randomness inside the equations
that are used in building the algorithm, like the ninth and the
fourteenth equations. Yet again, this result also ensures that
SLnO-MFP is highly comparable in terms of the MSE.
Furthermore, the last cell of Table VI is related to the deviation
of the MSE, termed as (DMSE), which is calculated by taking
the square root of the MSE. It should be noted that MSE and
DMSE are calculated in the same way as the variance and
standard deviation are usually computed, respectively. So, they
have obviously the same unit type of measurement as in the
case of the estimated quantities of variance and standard
deviation.
Additionally, Fig. 17 exhibits a visualization of the
enhancement that is accomplished in this work compared to the
FF technique in terms of execution time. In view of this, it is
relatively clear that the proposed technique has accomplished
better performance especially for resolving the networks of
large-sized instances.
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
64
7.3 Results Accuracy and Discussion
In order to examine the obtained results and to make a
comparative analysis between the maximum flow value of the
proposed algorithm SLnO-MFP and the FF algorithm, two
major factors related to the overall performance evaluation are
taken into consideration: the average execution time and the
accuracy of the results. While the first evaluation of
performance has been mentioned in the first subsection, the
second evaluation is described here in this subsection.
As clearly viewed in the comparison of Table VII, the
maximum flow values were calculated for both techniques
using ten experiments, each has a different network size. After
those experiments were conducted, the accuracy comparison
for both techniques was calculated by using Equation 22 as a
measure of accuracy (Acc):
(22)
Where “ ” represents the maximum value using the
FF technique and “ ” indicates the maximum
value using the suggested algorithm (SLnO-MFP).
In order to compute the overall validation accuracy of SLnO-
MFP algorithm, the average accuracy of all the network sizes
in the dataset was calculated by utilizing Equation 23:
(23)
Where “
” represents the jth the dataset’s size, and the
“” is computed as indicated by Equation 22. The result of
this equation was calculated and then viewed in the last row of
Table VII. As represented in this comparative analysis, the
proposed algorithm is able to attain a high accuracy percentage
of (94.3205%). It is observed that the main intuition behind the
overall accuracy relates to the difference between the
maximum value for the proposed algorithm and the maximum
value for FF technique which comes from the way of catching
the network graph in the search space where the SLnO-MFP
technique divides the network graph into a number of
subgraphs.
These outstanding findings prove that the algorithm has
superior performance and it is a viable alternative algorithm
that can be efficiently used to solve many optimization
problems of large-scale sizes, as in the case of this underlying
problem (MFP).
As a final point, the empirical evidence substantiates that this
proposed algorithm is proportionally scaling with the problem
size, in both memory and time. The interesting interpretation
behind this issue is highly associated with network complicity.
Anyway, this solution can be applied successfully to other
styles of optimization problems, and the outcomes presented
here have far-reaching consequences in many other domains.
Fig. 17. FF versus SLnO-MFP in terms of execution time
Table VII. The accuracy results of SLnO-MFP compared with FF algorithm
j
FF-MFP
(E)
SLnO-MFP
(F)
abs(E- F)
abs(E – F) / E
Accuracy=
1- abs(E – F) / E
Accuracy percentage=
(1- (abs(E – F) / E) * 100%
1
100
718
758
40
0.0557
0.9443
94.4290%
2
200
889
899
10
0.0112
0.9888
98.8751%
3
300
1873
1985
112
0.0598
0.9402
94.0203%
4
400
2465
2625
160
0.0649
0.9351
93.5091%
5
500
3167
3347
180
0.0568
0.9432
94.3164%
6
600
3708
4106
398
0.1073
0.8927
89.2665%
7
700
4568
4872
304
0.0665
0.9335
93.3450%
8
800
5097
5179
82
0.0161
0.9839
98.3912%
9
900
5826
6506
680
0.1167
0.8833
88.3282%
10
1000
6325
6346
21
0.0033
0.9967
99.6680%
The Overall accuracy
0.9432
94.3205%
0
1
2
3
4
5
6
7
8
9
100 200 300 400 500 600 700 800 900 1000
Average run time (seconds)
Network size (i.e. No. of nodes)
Theoretical run time
Experimental run time
Relative error
MSE
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
65
8. Conclusions
Evidently, the intuition behind optimization is born out of the
necessity for finding the best available solution among a set of
candidate ones. When scientists make an insightful look behind
the scenes of many creatures, they every day find numerous
thought-provoking blips that can be used in overcoming a great
portion of real-life optimization problems. Nowadays, swarm-
intelligence-based (SIB) algorithms are one of the most
Artificial Intelligence (AI) prevalent pillars which due to its
remarkable advantages become an essential part of modern
global optimization algorithms as well as the most widely
implemented.
At its broadest, it is important to realize that optimization
algorithms have their radical significance in the context of
solving the Maximum Flow Problem (MFP). Besides that this
added-value research paper covers and outlines the theoretical
vision and the practical aspects of the metaheuristics, it
introduces a population-based and nature-inspired
metaheuristic algorithm to solve the Maximum Flow Problem
(MFP) based on drawing inspiration from one of the core
activities of the sea lions (SLn) which is the joint hunting
behavior. As well, this paper can be used as a platform for
selecting whichever approach is the best one out of the
metaheuristics community.
After the research work reported in this paper, namely SLnO-
MFP, has been applied, tested, and evaluated on various-scales
datasets, the overall outcomes of have both theoretical and
applied implications and the empirically-based results
demonstrate that this algorithm is a highly-efficient in the long
run and has a superior performance and competitive findings
when compared with the other available optimization
algorithms. Moreover, it is relatively clear that these viable
outcomes in a way or another reinforce the algorithm's power
to impose itself on solving the MFP.
According to the empirical analysis of the experiments, the
overall performance of the proposed algorithm was compared
with the Ford-Fulkerson (FF) algorithm. The worthy findings
which have arrived with have shown that the proposed
algorithm performs better compared to other similar research
methods; it has attained a high accuracy percentage of
(94.3205%) with an acceptable Mean Relative Estimation
Error (MRE) rate of (0.8183), a Mean Square Error (MSE) of
(0.7363), and an average speedup of (7.4902). Armed with
these facts, these impressive experimental results give
sufficient sound evidence and reinforce the conclusion that this
proposed metaheuristic algorithm has far-reaching
consequences in solving various real-world applications
including the considered problem.
9. Future Work and Outlook
As the chronological progress poses new challenges and on the
basis of the structure of the problem in hand, here are six vital
pivots which need to be significantly addressed in the next few
years as inspiring directions for further research and
experimentation:
· Parallel implementation: From a purely practical
standpoint, it will be more effective if the search time is
reduced by applying the algorithm presented in this
research work in a distributed parallel execution
environment with an efficient dynamic clustering algorithm.
Rather than implementing the whole MFP graph on a single
processor, the graph is segmented into a number of
independent partitions; each one is computed on a single
processor. Then, the optimal maximum flow of these
partitions is selected. [12][43][20]
· Adaptive intelligent metaheuristics: It is a timely stage
where the other interested researchers can work to modify
the proposed algorithm, SLnO-MFP, such that the
parameters are more self-tuned during the running time
according to the objective function values.
· Optimization and performance metrics: Rather than
using a number of the classical ad-hoc statistical
measurements that are utilized as assessment and
comparison criteria for making performance measurements,
improvement percentages, and function evaluations such as
standard deviation, variance, correlation, skewness, and the
simple mean, it is strongly recommended without
reservation to establish a well-defined quantitative
measuring framework that will be used as an in-depth
assessment tool and an authentic criterion for efficiency
validating of most metaheuristics [6][20].
On the other hand, since most researchers, use the
computational run-time of the CPU as their only primary
resource for comparing the performance values of their
algorithms, their perceptions should be extended to tackle
other vital resources measurements that cannot be neglected
or relegated, such that memory, and network bandwidth
and other parameters that are used to measure the resources'
efficiencies.
Since the success of any optimization algorithm is topped
by the active balancing between exploration and
exploitation, there is also a need to establish a smart agreed
criterion that guarantees this balancing ratio over the
SLnO-MFP.
· Convergence' acceleration and analysis: Accelerating the
objective function convergence has a great effect in raising
the outcome efficiency and shrinking the needed number of
generations necessary in arriving at the ultimate solution.
Likewise, this might make the chance of arriving at the
most-fit solution tend to be greater. Metaheuristics'
convergence analysis of the objective functions has not still
been fully addressed to reach a maturity level. Thus,
another potential-open research area could be raised for
further literature. [20]
IJCSNS International Journal of Computer Science and Network Security, VOL.20 No.8, August 2020
66
· Cloud Computing (CC): Due to the voluminous amounts
of today's data and on behalf of the Internet advances, CC
applications are nowadays becoming more prevalent than it
was a few years ago and, in turn, the most endurable place
for hosting and activating optimization community. Since
each cloud-based application should be premised on the
faith that a large-pool of scalable, parallel, and distributed
computing resources is granted to thousands and even
millions of customers by the cloud vendor, it's time to go an
important step forward to devote the efforts in integrating
the metaphors of the metaheuristics to fully cope within the
CC platform. This is particularly relevant to the case of
hosting this presented algorithm. [12][43][51]
· Hybridization: Since it turns out that things work
differently with hybridization of two or more exact,
heuristic, or metaheuristic techniques, many promising
outlets and opportunities for further research could be
opened by using adaptive hybridization. From another
direction, the degree of this adaptively should be used as a
crucial tool that goes with the problem complexity. [20]
Acknowledgments
The author is grateful to WISE University, Amman, Jordan for
the financial support granted to cover the publication fee of
this research article. Secondly, the author would like to
express his cordial thanks to Dr. Adel Hamdan, Eng. Nabeel
Abuhamdeh, and Dr. Raja Masadeh in/for the great support
and assistance rendered to carry out this research work.
Finally, special gratitude to the editor and the honorable
anonymous reviewers of IJCSNS for their perceptive
comments, valuable suggestions, and magnificent efforts that
helped the author to improve this paper.
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Author’s Profile
Nidhal K. T. El-Omari received his B.Sc. in
Computer Science and his M. Eng. degree in
Computer Engineering in 1986 and 2005,
respectively, both from Yarmouk University, Irbid-
Jordan. In 1989, he received his Higher Diploma of
Branch Automation Officer from the Department of
Defense (DoD), Fort Gordon / Georgia-USA. In
2008, he received a doctorate in Computer
Information Systems and Image Processing from
The Arab Academy for Banking and Financial
Science (AABFS), Amman-Jordan.
He joined the Information Technology Directorate of the Jordanian
Ministry of Defense in 1986 and retired in 2009. During those 24 years,
he chaired a number of IT-related departments including the Systems
Follow-up Department, Technical Support Department, and Automation
Department. He has been at the Faculty of IT since 2009, WISE
University, during which he worked as the director of the Computer
Center, the Chair of the Department of Computer Science and Basic
Science, and the head of the Department of Software Engineering. Since
2015, he is an Associate Professor. His research interests include, but are
not limited to, image compression & segmentation, evolutionary
computation, heuristic optimization, and methodologies for building both
secure and strategical-efficient software. Dr. El-Omari has authored/co-
authored two computer books and published more than thirty research
articles and conference papers in top-quality journals and conference
proceedings. By last, he can be reached via e-mails at
nidhal.omari@wise.edu.jo or omari_nidhal@yahoo.com
