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Hindawi Computational Intelligence and Neuroscience Volume 2020, Article ID 4854895, 20 pages https://doi.org/10.1155/2020/4854895 Review Article Cat Swarm Optimization Algorithm: A Survey and Performance Evaluation 1,2 3 2 Aram M. Ahmed , Tarik A. Rashid , and Soran Ab. M. Saeed International Academic Oﬃce, Kurdistan Institution for Strategic Studies and Scientiﬁc Research, Sulaymaniyah 46001, Iraq Information Technology, Sulaimani Polytechnic University, Sulaymaniyah 46001, Iraq Computer Science and Engineering, University of Kurdistan Hewler, Erbil 44001, Iraq Correspondence should be addressed to Aram M. Ahmed; aramahmed@kissr.edu.krd Received 25 July 2019; Revised 15 December 2019; Accepted 20 December 2019; Published 22 January 2020 Academic Editor: Juan A. Go´mez-Pulido Copyright © 2020 Aram M. Ahmed et al. +is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. +is paper presents an in-depth survey and performance evaluation of cat swarm optimization (CSO) algorithm. CSO is a robust and powerful metaheuristic swarm-based optimization approach that has received very positive feedback since its emergence. It has been tackling many optimization problems, and many variants of it have been introduced. However, the literature lacks a detailed survey or a performance evaluation in this regard. +erefore, this paper is an attempt to review all these works, including its developments and applications, and group them accordingly. In addition, CSO is tested on 23 classical benchmark functions and 10 modern benchmark functions (CEC 2019). +e results are then compared against three novel and powerful optimization algorithms, namely, dragonﬂy algorithm (DA), butterﬂy optimization algorithm (BOA), and ﬁtness dependent optimizer (FDO). +ese algorithms are then ranked according to Friedman test, and the results show that CSO ranks ﬁrst on the whole. Finally, statistical approaches are employed to further conﬁrm the outperformance of CSO algorithm. with each other in a decentralized manner to ﬁnd the op- 1. Introduction timal solution. Agents usually move in two phases, namely, Optimization is the process by which the optimal solution is exploration and exploitation. In the ﬁrst one, they move on a selected for a given problem among many alternative so- global scale to ﬁnd promising areas, while in the second one, lutions. One key issue of this process is the immensity of the they search locally to discover better solutions in those search space for many real-life problems, in which it is not promising areas found so far. Having a trade-oﬀ between feasible for all solutions to be checked in a reasonable time. these two phases, in any algorithm, is very crucial because Nature-inspired algorithms are stochastic methods, which biasing towards either exploration or exploitation would are designed to tackle these types of optimization problems. degrade the overall performance and produce undesirable results [1]. +erefore, more than hundreds of swarm in- +ey usually integrate some deterministic and randomness techniques together and then iteratively compare a number telligence algorithms have been proposed by researchers to of solutions until a satisfactory one is found. +ese algo- achieve this balance and provide better solutions for the rithms can be categorized into trajectory-based and pop- existing optimization problems. ulation-based classes [1]. In trajectory-based types, such as a Cat swarm optimization (CSO) is a swarm Intelligence simulated annealing algorithm [2], only one agent is algorithm, which was originally invented by Chu et al. in searching in the search space to ﬁnd the optimal solution, 2006 [4, 5]. It is inspired by the natural behavior of cats, and whereas, in the population-based algorithms, also known as it has a novel technique in modeling exploration and ex- swarm Intelligence, such as particle swarm optimization ploitation phases. It has been successfully applied in various (PSO) [3], multiple agents are searching and communicating optimization ﬁelds of science and engineering. However, the 2 Computational Intelligence and Neuroscience literature lacks a recent and detailed review of this algorithm. In addition, since 2006, CSO has not been compared against CSO and its variants novel algorithms, i.e., it has been mostly compared with PSO Original CSO with artificial neural Variants of CSO algorithm algorithm while many new algorithms have been introduced networks since then. So, a question, which arises, is whether CSO competes with the novel algorithms or not? +erefore, experimenting CSO on a wider range of test functions and comparing it with new and robust algorithms will further Applications of CSO reveal the potential of the algorithm. As a result, the aims of this paper are as follows: ﬁrstly, provide a comprehensive Figure 1: General framework for conducting the survey. and detailed review of the state of art of CSO algorithm (see Figure 1), which shows the general framework for con- ducting the survey; secondly, evaluate the performance of (2) Randomly generate N cats (solution sets) and spread CSO algorithm against modern metaheuristic algorithms. them in the M dimensional space in which each cat +ese should hugely help researchers to further work in the has a random velocity value not larger than a pre- domain in terms of developments and applications. deﬁned maximum velocity value. +e rest of the paper is organized as follows. Section 2 (3) Randomly classify the cats into seeking and tracing presents the original algorithm and its mathematical modes according to MR. MR is a mixture ratio, modeling. Section 3 is dedicated to reviewing all modiﬁed which is chosen in the interval of [0, 1]. So, for versions and variants of CSO. Section 4 summarizes the example, if a number of cats N is equal to 10 and MR hybridizing CSO algorithm with ANN and other non- is set to 0.2, then 8 cats will be randomly chosen to go metaheuristic methods. Section 5 presents applications of through seeking mode and the other 2 cats will go the algorithm and groups them according to their disci- through tracing mode. plinary. Section 6 provides performance evaluation, where (4) Evaluate the ﬁtness value of all the cats according to CSO is compared against dragonﬂy algorithm (DA) [6], the domain-speciﬁed ﬁtness function. Next, the best butterﬂy optimization algorithm (BOA) [7], and ﬁtness cat is chosen and saved into memory. dependent optimizer (FDO) [8]. Finally, Section 7 provides the conclusion and future directions. (5) +e cats then move to either seeking or tracing mode. (6) After the cats go through seeking or tracing mode, for the next iteration, randomly redistribute the cats 2. Original Cat Swarm Optimization Algorithm into seeking or tracing modes based on MR. +e original cat swarm optimization is a continuous and (7) Check the termination condition; if satisﬁed; termi- single-objective algorithm [4, 5]. It is inspired by resting and nate the program; otherwise, repeat Step 4 to Step 6. tracing behaviours of cats. Cats seem to be lazy and spend most of their time resting. However, during their rests, their consciousness is very high and they are very aware of what is 2.2. Seeking Mode. +is mode imitates the resting behavior happening around them. So, they are constantly observing of cats, where four fundamental parameters play important the surroundings intelligently and deliberately and when roles: seeking memory pool (SMP), seeking range of the they see a target, they start moving towards it quickly. selected dimension (SRD), counts of dimension to change +erefore, CSO algorithm is modeled based on combining (CDC), and self-position considering (SPC). +ese values these two main deportments of cats. are all tuned and deﬁned by the user through a trial-and- CSO algorithm is composed of two modes, namely, error method. tracing and seeking modes. Each cat represents a solution SMP speciﬁes the size of seeking memory for cats, i.e., it set, which has its own position, a ﬁtness value, and a ﬂag. +e deﬁnes number of candidate positions in which one of them position is made up of M dimensions in the search space, is going to be chosen by the cat to go to, for example, if SMP and each dimension has its own velocity; the ﬁtness value was set to 5, then for each and every cat, 5 new random depicts how well the solution set (cat) is; ﬁnally, the ﬂag is to positions will be generated and one of them will be selected classify the cats into either seeking or tracing mode. +us, we to be the next position of the cat. How to randomize the new should ﬁrst specify how many cats should be engaged in the positions will depend on the other two parameters that are iteration and run them through the algorithm. +e best cat CDC and SRD. CDC deﬁnes how many dimensions to be in each iteration is saved into memory, and the one at the modiﬁed which is in the interval of [0, 1]. For example, if the ﬁnal iteration will represent the ﬁnal solution. search space has 5 dimensions and CDC is set to 0.2, then for each cat, four random dimensions out of the ﬁve need to be modiﬁed and the other one stays the same. SRD is the 2.1. General Structure of the Algorithms. +e algorithm takes mutative ratio for the selected dimensions, i.e., it deﬁnes the the following steps in order to search for optimal solutions: amount of mutation and modiﬁcations for those dimensions that were selected by CDC. Finally, SPC is a Boolean value, (1) Specify the upper and lower bounds for the solution which speciﬁes whether the current position of a cat will sets. Computational Intelligence and Neuroscience 3 be selected as a candidate position for the next iteration or 3. Variants of CSO not. So, for example, if the SPC ﬂag is set to true, then for In the previous section, the original CSO was covered; this each cat, we need to generate (SMP-1) number of can- section brieﬂy discusses all other variants of CSO found in the didates instead of SMP number as the current position is literature. Variants may include the following points: binary or considered as one of them. Seeking mode steps are as multiobjective versions of the algorithm, changing parame- follows: ters, altering steps, modifying the structure of the algorithm, (1) Make as many as SMP copies of the current position or hybridizing it with other algorithms. Refer to Table 1, which of Cat . presents a summary of these modiﬁcations and their results. (2) For each copy, randomly select as many as CDC dimensions to be mutated. Moreover, randomly add 3.1. Discrete Binary Cat Swarm Optimization Algorithm or subtract SRD values from the current values, (BCSO). Sharaﬁ et al. introduced the BCSO Algorithm, which replace the old positions as shown in the which is the binary version of CSO [9]. In the seeking mode, following equation: the SRD parameter has been substituted by another pa- rameter called the probability of mutation operation (PMO). Xjd � (1 + rand∗ SRD)∗ Xjd , (1) new old However, the proceeding steps of seeking mode and the other three parameters stay the same. Accordingly, the di- where Xjd is the current position; Xjd is the old new mensions are selected using the CDC and then PMO will be next position; j denotes the number of a cat and d applied. In the tracing mode, the calculations of velocity and denotes the dimensions; and rand is a random position equations have also been changed into a new form, number in the interval of [0, 1]. in which the new position vector is composed of binary (3) Evaluate the ﬁtness value (FS) for all the candidate digits taken from either current position vector or global positions. position vector (best position vector). Two velocity vectors are also deﬁned in order to decide which vector (current or (4) Based on probability, select one of the candidate global) to choose from. points to be the next position for the cat where candidate points with higher FS have more chance to be selected as shown in equation (2). However, 3.2. Multiobjective Cat Swarm Optimization (MOCSO). if all ﬁtness values are equal, then set all the Pradhan and Panda proposed multiobjective cat swarm selecting probability of each candidate point to optimization (MOCSO) by extending CSO to deal with be 1. multiobjective problems [10]. MOCSO is combined with the concept of the external archive and Pareto dominance in FS − FS i b (2) order to handle the nondominated solutions. Pi � , where 0< i< j. FS − FS max min If the objective is minimization, then FS � FS ; oth- b max 3.3. Parallel Cat Swarm Optimization (PCSO). Tsai and pan erwise, FS � FS . b min introduced parallel cat swarm optimization (PCSO) [11]. +is algorithm improved the CSO algorithm by eliminating the worst solutions. To achieve this, they ﬁrst distribute the 2.3. Tracing Mode. +is mode copies the tracing behavior of cats into subgroups, i.e., subpopulations. Cats in the seeking cats. For the ﬁrst iteration, random velocity values are given mode move as they do in the original algorithm. However, in to all dimensions of a cat’s position. However, for later steps, the tracing mode, for each subgroup, the best cat will be velocity values need to be updated. Moving cats in this mode saved into memory and will be considered as the local best. are as follows: Furthermore, cats move towards the local best rather than the global best. +en, in each group, the cats are sorted (1) Update velocities (V ) for all dimensions according k,d according to their ﬁtness function from best to worst. +is to equation (3). procedure will continue for a number of iterations, which is (2) If a velocity value outranged the maximum value, speciﬁed by a parameter called ECH (a threshold that deﬁnes then it is equal to the maximum velocity. when to exchange the information of groups). For example, if ECH was equal to 20, then once every 20 iterations, the V � V + r c X − X . (3) k,d k,d 1 1 best,d k,d subgroups exchange information where the worst cats will be replaced by a randomly chosen local best of another (3) Update position of Cat according to the following k group. +ese modiﬁcations lead the algorithm to be com- equation: putationally faster and show more accuracy when the number of iteration is fewer and the population size is small. X � X + V . (4) k,d k,d k,d Refer to Figure 2 which recaps the whole algorithm in a 3.4. CSO Clustering. Santosa and Ningrum improved the CSO diagram. algorithm and applied it for clustering purposes [12]. +e main 4 Computational Intelligence and Neuroscience Start Generate N cats Initialize the position, velocities, and the flag of every cat Evaluate the cats based on their fitness function and save the best cat into memory No Yes Cat is in the Tracing mode Seeking mode seeking mode? No Yes Make SMP Make SMP-1 SPC flag is true Velocity value copies of the cat copies of the cat Yes Velocity = maximum velocity maximum value? No Add or substract SRD values Update velocities based on CDC for all dimensions Evaluate fitness value of cats Update positions Based on probability, select next position for the cat Redistribute cats into seeking or tracing modes according to MR Terminate? Stop Figure 2: Cat swarm optimization algorithm general structure. goal was to use CSO to cluster the data and ﬁnd the best cluster aimed at shortening the time required to ﬁnd the best cluster center. +e modiﬁcations they did were two main points: center. Secondly, always setting the CDC value to be 100%, ﬁrstly, removing the mixture ratio (MR) and hence forcing all instead of 80% as in the original CSO, in order to change all the cats to go through both seeking and tracing mode. +is is dimensions of the candidate cats and increase diversity. Computational Intelligence and Neuroscience 5 Table 1: Summary of the modiﬁed versions of the CSO algorithm. Comparison of With Testing ﬁeld Performance Reference CSO (original) PSO and weighted-PSO Six test functions Better [4, 5] Four test functions (sphere, BCSO GA, BPSO, and NBPSO Rastrigin, Ackley, and Better [9] Rosenbrock) Cooperative spectrum sensing in MOCSO NSGA-II Better [10] cognitive radio Better when the number of +ree test functions (Rosenbrock, PCSO CSO and weighted-PSO iteration is fewer and the [11] Rastrigrin, and Griewank) population size is small Four diﬀerent clustering datasets CSO clustering K-means and PSO clustering (Iris, Soybean, Glass, and Balance More accurate but slower. [12] Scale) PCSO, PSO-LDIW, PSO-CREV, Five test functions and aircraft EPCSO GCPSO, MPSO-TVAC, CPSO- Better [13] schedule recovery problem H6, PSO-DVM +ree test functions (Rastrigrin, AICSO CSO Better [14] Griewank, and Ackley) Six test functions (Rastrigrin, Better except for Griewank test ADCSO CSO Griewank, Ackley, axis parallel, [15] function. Trid10, and Zakharov) Motion estimation block- Enhanced HCSO PSO Better [16, 17] matching Motion estimation block- ICSO PSO Better [17] matching ART1, ART2, Iris, CMC, Cancer, OL-ICSO K-median, PSO, CSO, and ICSO Better [18] and Wine datasets Five test functions (Schaﬀer, Shubert, Griewank, Rastrigrin, and Rosenbrock) and multipeak CQCSO QCSO, CSO, PSO, and CPSO Better [19] maximum power point tracking for a photovoltaic array under complex conditions +e 69-bus test distribution ICSO CSO and PSO Better [20] system Twelve test functions (sphere, Rosenbrock, Rastrigin, Griewank, Ackley, Step, Powell, Schwefel, ICSO CSO, BCSO, AICSO, and EPCSO Schaﬀer, Zakharov’s, Better [21] Michalewicz, quartic) and ﬁve real-life clustering problems (Iris, Cancer, CMC, Wine, and Glass) Hybrid PCSOABC PCSO and ABC Five test functions Better [22] 66 feature points from each face of CSO-GA-PSO CSO + SVM (CSO ) Better [23] SVM SVM CK + (Cohn Kanade) dataset Hybrid CSO-based GA, EA, SA, PSO, and AFS School timetabling test instances Better [24] algorithm Seven datasets (Karate, Dolphin, Hybrid CSO-GA- SLPA and CFinder Polbooks, Football, Net-Science, Better [25] SA Power, Indian Railway) MCSO CSO Nine datasets from UCI Better [26] MCSO CSO Eight dataset Better [27] NMCSO CSO, PSO Sixteen benchmark functions Better [28] ICSO CSO Ten datasets from UCI Better [29] cCSO DE, PSO, CSO 47 benchmark functions Better [30] Binary particle swarm optimization (BPSO), binary 0/1 Knapsack optimization BBCSO Better [31] genetic algorithm (BGA), binary problem CSO VRP instances from http://neo. CSO-CS N/A N/A [32] lcc.uma.es/vrp/ 6 Computational Intelligence and Neuroscience avoid calculating some areas by deciding whether or not to 3.5. Enhanced Parallel Cat Swarm Optimization (EPCSO). Tsai et al. further improved the PCSO Algorithm in terms of do the calculation or estimate the next search location to move to. In addition, they also introduced the inertia weight accuracy and performance by utilizing the orthogonal array of Taguchi method and called it enhanced parallel cat swarm to the tracing mode. optimization (EPCSO) [13]. Taguchi methods are statistical methods, which are invented by Japanese Engineer Genichi 3.9. Improvement Structure of Cat Swarm Optimization Taguchi. +e idea is developed based on “ORTHOGONAL (ICSO). Hadi and Sabah proposed combining two concepts ARRAY” experiments, which improves the engineering together to improve the algorithm and named it ICSO. +e productivity in the matters of cost, quality, and performance. ﬁrst concept is parallel tracing mode and information ex- In their proposed algorithm, the seeking mode of EPCSO is changing, which was taken from PCSO. +e second concept the same as the original CSO. However, the tracing mode has is the addition of an inertia weight to the position equation, adopted the Taguchi orthogonal array. +e aim of this is to which was taken from AICSO. +ey applied their algorithm improve the computational cost even when the number of for eﬃcient motion estimation in block matching. +eir goal agents increases. +erefore, two sets of candidate velocities was to enhance the performance and reduce the number of will be created in the tracing mode. +en, based on the iterations without the degradation of the image quality [17]. orthogonal array, the experiments will be run and accord- ingly the position of cats will be updated. Orouskhani et al. [14] added some partial modiﬁcations to EPCSO in order to 3.10. Opposition-Based Learning-Improved CSO (OL-ICSO). further improve it and make it ﬁt their application. +e Kumar and Sahoo ﬁrst proposed using Cauchy mutation modiﬁcations were changing the representation of agents operator to improve the exploration phase of the CSO al- from the coordinate to a set; adding a newly deﬁned cluster gorithm in [34]. +en, they introduced two more modiﬁ- ﬂag; and designing custom-made ﬁtness function. cations to further improve the algorithm and named it opposition-based learning-improved CSO (OL-ICSO). +ey improved the population diversity of the algorithm by 3.6. Average-Inertia Weighted CSO (AICSO). Orouskhani adopting opposition-based learning method. Finally, two et al. introduced an inertia value to the velocity equation in heuristic mechanisms (for both seeking and tracing mode) order to achieve a balance between exploration and ex- were introduced. +e goal of introducing these two mech- ploitation phase. +ey experimented that (w) value is better anisms was to improve the diverse nature of the populations to be selected in the range of [0.4, 0.9] where at the beginning and prevent the possibility of falling the algorithm into the of the operation, it is set to 0.9, and as the iteration number local optima when the solution lies near the boundary of the moves forward, (w) value gradually becomes smaller until it datasets and data vectors cross the boundary constraints reaches 0.4 at the ﬁnal iteration. Large values of (w) assist frequently [18]. global search; whereas small values of (w) assist the local search. In addition to adding inertia value, the position equation was also reformed to a new one, in which averages 3.11. Chaos Quantum-Behaved Cat Swarm Optimization of current and previous positions, as well as an average of (CQCSO). Nie et al. improved the CSO algorithm in terms current and previous velocities, were taken in the equation of accuracy and avoiding local optima trapping. +ey ﬁrst [14]. introduced quantum-behaved cat swarm optimization (QCSO), which combined the CSO algorithm with quantum mechanics. Hence, the accuracy was improved and the al- 3.7. Adaptive Dynamic Cat Swarm Optimization (ADCSO). gorithm avoided trapping in the local optima. Next, by Orouskhani et al. further enhanced the algorithm by in- incorporating a tent map technique, they proposed chaos troducing three main modiﬁcations [15]. Firstly, they in- quantum-behaved cat swarm optimization (CQCSO) algo- troduced an adjustable inertia value to the velocity equation. rithm. +e idea of adding the tent map was to further +is value gradually decreases as the dimension numbers improve the algorithm and again let the algorithm to jump increase. +erefore, it has the largest value for dimension out of the possible local optima points it might fall into [19]. one and vice versa. Secondly, they changed the constant (C) to an adjustable value. However, opposite to the inertia weight, it has the smallest value for dimension one and 3.12. Improved Cat Swarm Optimization (ICSO). In the gradually increases until the ﬁnal dimension where it has the original algorithm, cats are randomly selected to either go largest value. Finally, they reformed the position equation by into seeking mode or tracing mode using a parameter called taking advantage of other dimensions’ information. MR. However, Kanwar et al. changed the seeking mode by forcing the current best cat in each iteration to move to the seeking mode. Moreover, in their problem domain, the 3.8. Enhanced Hybrid Cat Swarm Optimization (Enhanced HCSO). Hadi and Sabah proposed a hybrid system and decision variables are ﬁrm integers while solutions in the original cat are continuous. +erefore, from selecting the called it enhanced HCSO [16, 17]. +e goal was to decrease the computation cost of the block matching process in video best cat, two more cats are produced by ﬂooring and ceiling editing. In their proposal, they utilized a ﬁtness calculation its value. After that, all probable combinations of cats are strategy in seeking mode of the algorithm. +e idea was to produced from these two cats [20]. Computational Intelligence and Neuroscience 7 3.18. Modiﬁed Cat Swarm Optimization (MCSO). Lin et al. 3.13. Improved Cat Swarm Optimization (ICSO). Kumar and Singh made two modiﬁcations to the improved CSO algo- combined a mutation operator as a local search procedure with CSO algorithm to ﬁnd better solutions in the area of the rithm and called it ICSO [21]. +ey ﬁrst improved the tracing mode by modifying the velocity and updating po- global best [26]. It is then used to optimize the feature se- sition equations. In the velocity equation, a random uni- lection and parameters of the support vector machine. formly distributed vector and two adaptive parameters were Additionally, Mohapatra et al. used the idea of using mu- added to tune global and local search movements. Secondly, tation operation before distributing the cats into seeking or a local search method was combined with the algorithm to tracing modes [27]. prevent local optima problem. 3.19. Normal Mutation Strategy-Based Cat Swarm Optimi- 3.14. Hybrid PCSOABC. Tsai et al. proposed a hybrid system zation (NMCSO). Pappula et al. adopted a normal mutation by combining PCSO with ABC algorithms and named is technique to CSO algorithm in order to improve the ex- hybrid PCSOABC [22]. +e structure simply included ploration phase of the algorithm. +ey used sixteen running PCSO and ABC consecutively. Since PCSO per- benchmark functions to evaluate their proposed algorithm forms faster with a small population size, the algorithm ﬁrst against CSO and PSO algorithms [28]. starts with a small population and runs PCSO. After a predeﬁned number of iterations, the population size will be 3.20. Improved Cat Swarm Optimization (ICSO). Lin et al. increased and the ABC algorithm starts running. Since the improved the seeking mode of CSO algorithm. Firstly, they proposed algorithm was simple and did not have any ad- used crossover operation to generate candidate positions. justable feedback parameters, it sometimes provided worse Secondly, they changed the value of the new position so that solutions than PCSO. Nevertheless, its convergence was SRD value and current position have no correlations [29]. It faster than PCSO. is worth mentioning that there are four versions of CSO referenced in [17, 20, 21, 29], all having the same name 3.15. CSO-GA-PSOSVM. Vivek and Reddy proposed a new (ICSO). However, their structures are diﬀerent. method by combining CSO with particle swarm intelligence (PSO), genetic algorithm (GA), and support vector machine 3.21. Compact Cat Swarm Optimization (CCSO). Zhao in- (SVM) and called it CSO-GA-PSOSVM [23]. In their troduced a compact version of the CSO algorithm. A dif- method, they adopted the GA mutation operator into the ferential operator was used in the seeking mode of the seeking mode of CSO in order to obtain divergence. In proposed algorithm to replace the original mutation ap- addition, they adopted all GA operators as well as PSO proach. In addition, a normal probability model was used in subtraction and addition operators into the tracing mode of order to generate new individuals and denote a population CSO in order to obtain convergence. +is hybrid meta- of solutions [30]. heuristic system was then incorporated with the SVM classiﬁer and applied on facial emotion recognition. 3.22. Boolean Binary Cat Swarm Optimization (BBCSO). Siqueira et al. worked on simplifying the binary version of 3.16. Hybrid CSO-Based Algorithm. Skoullis et al. introduced CSO in order to increase its eﬃciency. +ey reduced the three modiﬁcations to the algorithm [24]. Firstly, they number of equations, replaced the continues operators with combined CSO with a local search reﬁning procedure. logic gates, and ﬁnally integrated the roulette wheel ap- Secondly, if the current cat is compared with the global best proach with the MR parameter [31]. cat and their ﬁtness values were the same, the global best cat will still be updated by the current cat. +e aim of this is to achieve more diversity. Finally, cats are individually selected 3.23. Hybrid Cat Swarm Optimization-Crow Search (CSO-CS) to go into either seeking mode or tracing mode. Algorithm. Pratiwi proposed a hybrid system by combining CSO algorithm with crow search (CS) algorithm. +e al- gorithm ﬁrst runs CSO algorithm followed by the memory 3.17. Hybrid CSO-GA-SA. Sarswat et al. also proposed a update technique of the CS algorithm and then new posi- hybrid system by combining CSO, GA, and SA and then tions will be generated. She applied her algorithm on vehicle incorporating it with a modularity-based method [25]. +ey routing problem [32]. named their algorithm hybrid CSO-GA-SA. +e structure of the system was very simple and straight forward as it was composed of a sequential combination of CSO, GA, and SA. 4. CSO and its Variants with Artificial +ey applied the system to detect overlapping community Neural Networks structures and ﬁnd near-optimal disjoint communities. +erefore, input datasets were ﬁrstly fed into CSO algorithm Artiﬁcial neural networks are computing systems, which for a predeﬁned number of iterations. +e resulted cats were have countless numbers of applications in various ﬁelds. then converted into chromosomes and henceforth GA was Earlier neural networks were used to be trained by con- applied on them. However, GA may fall into local optima, ventional methods, such as the backpropagation algorithm. and to solve this issue, SA was applied afterward. However, current neural networks are trained by nature- 8 Computational Intelligence and Neuroscience 4.8. CS-FLANN. Kumar et al. combined the CSO algorithm inspired optimization algorithms. +e training could be optimizing the node weights or even the network archi- with functional link artiﬁcial neural network (FLANN) to develop an evolutionary ﬁlter to remove Gaussian noise [45]. tectures [35]. CSO has also been extensively combined with neural networks in order to be applied in diﬀerent appli- cation areas. +is section brieﬂy goes over those works, in 5. Applications of CSO which CSO is hybridized with ANN and similar methods. +is section presents the applications of CSO algorithm, which are categorized into seven groups, namely, electrical 4.1. CSO + ANN + OBD. Yusiong proposes combining ANN engineering, computer vision, signal processing, system with CSO algorithm and optimal brain damage (OBD) management and combinatorial optimization, wireless and approach. Firstly, the CSO algorithm is used as an opti- WSN, petroleum engineering, and civil engineering. A mization technique to train the ANN algorithm. Secondly, summary of the purposes and results of these applications is OBD is used as a pruning algorithm to decrease the com- provided in Table 2. plexity of ANN structure where less number of connections has been used. As a result, an artiﬁcial neural network was obtained that had less training errors and high classiﬁcation 5.1. Electrical Engineering. CSO algorithm has been exten- accuracy [36]. sively applied in the electrical engineering ﬁeld. Hwang et al. applied both CSO and PSO algorithms on an electrical payment system in order to minimize electricity costs for 4.2. ADCSO + GD + ANFIS. Orouskhani et al. combined customers. Results indicated that CSO is more eﬃcient and ADCSO algorithm with gradient descent (GD) algorithm in faster than PSO in ﬁnding the global best solution [46]. order to tweak parameters of the adaptive network-based Economic load dispatch (ELD) and unit commitment (UC) fuzzy inference system (ANFIS). In their method, the an- are signiﬁcant applications, in which the goal is to reduce the tecedent and consequent parameters of ANFIS were trained total cost of fuel is a power system. Hwang et al. applied the by CSO algorithm and GD algorithm consecutively [37]. CSO algorithm on economic load dispatch (ELD) of wind and thermal generators [47]. Faraji et al. also proposed applying binary cat swarm optimization (BCSO) algorithm 4.3. CSO + SVM. Abed and Al-Asadi proposed a hybrid on UC and obtained better results compared to the previous system based on SVM and CSO. +e system was applied to approaches [48]. UPFC stands for uniﬁed power ﬂow electrocardiograms signals classiﬁcation. +ey used CSO for controller, which is an electrical device used in transmission the purpose of feature selection optimization and enhancing systems to control both active and reactive power ﬂows. SVM parameters [38]. In addition, Lin et al. and Wang and Kumar and Kalavathi used CSO algorithm to optimize Wu [39, 40] also combined CSO with SVM and applied it to UPFC in order to improve the stability of the system [49]. a classroom response system. Lenin and Reddy also applied ADCSO on reactive power dispatch problem with the aim to minimize active power loss 4.4. CSO + WNN. Nanda proposed a hybrid system by [50]. Improving available transfer capability (ATC) is very combining wavelet neural network (WNN) and CSO al- signiﬁcant in electrical engineering. Nireekshana et al. used gorithm. In their proposal, the CSO algorithm was used to CSO algorithm to regulate the position and control pa- train the weights of WNN in order to obtain the near-op- rameters of SVC and TCSC with the aim of maximizing timal weights [41]. power transfer transactions during normal and contingency cases [51]. +e function of the transformers is to deliver electricity to consumers. Determining how reliable these 4.5. BCSO + SVM. Mohamadeen et al. built a classiﬁcation transformers are in a power system is essential. Moha- model based on BCSO and SVM and then applied it in a madeen et al. proposed a classiﬁcation model to classify the power system. +e use of BCSO was to optimize SVM transformers according to their reliability status [42]. +e parameters [42]. model was built based on BCSO incorporation with SVM. +e results are then compared with a similar model based on BPSO. It is shown that BCSO is more eﬃcient in optimizing 4.6. CCSO + ANN. Wang et al. proposed designing an ANN the SVM parameters. Wang et al. proposed designing an that can handle randomness, fuzziness, and accumulative ANN that can handle randomness, fuzziness, and accu- time eﬀect in time series concurrently. In their work, the mulative time eﬀect in time series concurrently [43]. In their CSO algorithm was used to optimize the network structure work, the CSO algorithm has been used to optimize the and learning parameters at the same time [43]. network structure and learning parameters at the same time. +en, the model was applied to two applications, which were 4.7. CSO/PSO + ANN. Chittineni et al. used CSO and PSO individual household electric power consumption fore- algorithms to train ANN and then applied their method on casting and Alkaline-surfactant-polymer (ASP) ﬂooding oil stock market prediction. +eir comparison results showed recovery index forecasting in oilﬁeld development. +e current source inverter (CSI) is a conventional kind of power that CSO algorithm performed better than the PSO algo- rithm [44]. inverter topologies. Hosseinnia and Farsadi combined Computational Intelligence and Neuroscience 9 Table 2: +e purposes and results of using CSO algorithm in various applications. Purpose Results Ref. CSO applied on electrical payment system in order to CSO outperformed PSO [46] minimize electricity cost for customers CSO applied on economic load dispatch (ELD) of CSO outperformed PSO [47] wind and thermal generator CSO outperformed LR, ICGA, BF, MILP, ICA, and BCSO applied on unit commitment (UC) [48] SFLA IEEE 6-bus and 14-bus networks were used in the Applied CSO algorithm on UPFC to increase the simulation experiments and desirable results were [49] stability of the system achieved IEEE 57-bus system was used in the simulation Applied ADCSO on reactive power dispatch problem experiments, in which ADCSO outperformed 16 [50] to minimize active power loss other optimization algorithms Applied CSO algorithm to regulate the position and IEEE 14-bus and IEEE 24-bus systems were used in control parameters of SVC and TCSC to improve the simulation experiments, in which the system [51] available transfer capability (ATC) provided better results after adopting CSO Building a classiﬁcation model based on BCSO and +e model performed better compared to a similar SVM to classify the transformers according to their [42] model, which was based on BPSO and VSM reliability status. Applied CSO to optimize the network structure and learning parameters of an ANN model named CPNN-CSO outperformed ANFIS and similar [43] CPNN-CSO, which is used to predict household methods with no CSO such as PNN and CPNN electric power consumption CSO successfully optimized the switching parameters Applied CSO and selective harmonic elimination of CSI and hence minimized the total harmonic [52] (SHE) algorithm on current source inverter (CSI) distortion Applied both CSO, PCSO, PSO-CFA, and ACO-ABC IEEE 33-bus and IEEE 69-bus distribution systems on distributed generation units on distribution were used in the simulation experiments and CSO [53] networks outperformed the other algorithms Applied MCSO on MPPT to achieve global maximum MCSO outperformed PSO, MPSO, DE, GA, and HC [54] power point (GMPP) tracking algorithms IEEE 14-bus and IEEE 30-bus test systems were used Applied BCSO to optimize the location of phasor in the simulation. BCSO outperformed BPSO, measurement units and reduce the required number [55] generalized integer linear programming, and eﬀective of PMUs data structure-based algorithm Used CSO algorithm to identify the parameters of CSO outperformed PSO, GA, SA, PS, Newton, HS, [56] single and double diode models in solar cell system GGHS, IGHS, ABSO, DE, and LMSA Applied CSO and SVM to classify students’ facial +e results show 100% classiﬁcation accuracy for the [39] expression selected 9 face expressions Applied CSO and SVM to classify students’ facial +e system achieved satisfactory results [40] expression Applied CSO-GA-PSOSVM to classify students’ +e system achieved 99% classiﬁcation accuracy [23] facial expression Applied CSO, HCSO and ICSO in block matching for +e system reduced computational complexity and [16, 17, 57] eﬃcient motion estimation provided faster convergence Used CSO algorithm to retrieve watermarks similar CSO outperformed PSO and PSO time-varying [58, 59] to the original copy inertia weight factor algorithms Sabah used EHCSO in an object-tracking system to +e system yielded desirable results in terms of [60] obtain further eﬃciency and accuracy eﬃciency and accuracy Used BCSO as a band selection method for BCSO outperformed PSO [61] hyperspectral images Used CSO and multilevel thresholding for image CSO outperformed PSO [62] segmentation Used CSO and multilevel thresholding for image PSO outperformed CSO [63] segmentation Used CSO, ANN and wavelet entropy to build an CSO outperformed GA, IGA, PSO, and CSPSO [64] AUD identiﬁcation system. Used CSO and FLANN to remove the unwanted +e proposed system outperformed mean ﬁlter and [45] Gaussian noises from CT images adaptive Wiener ﬁlter. Used CSO with L-BFGS-B technique to register +e system yielded satisfactory results [65] nonrigid multimodal images Used CSO in image enhancement to optimize PSO outperformed CSO [66] parameters of the histogram stretching technique Used CSO algorithm for IIR system identiﬁcation CSO outperformed GA and PSO [67] 10 Computational Intelligence and Neuroscience Table 2: Continued. Purpose Results Ref. Applied CSO to do direct and inverse modeling of CSO outperformed GA and PSO [68] linear and nonlinear plants Used CSO and SVM for electrocardiograms signal Optimizing SVM parameters using CSO improved [38] classiﬁcation the system in terms of accuracy Applied CSO to increase reliability in a task allocation CSO outperformed GA and PSO [69, 70] system +e benchmark instances were taken from OR- Applied CSO on JSSP Library. CSO yielded desirable results compared to [71] the best recorded results in the dataset reference. ACO outperformed CSO and cuckoo search Applied BCSO on JSSP [72] algorithms Carlier, Heller, and Reeves benchmark instances were Applied CSO on FSSP used, CSO can solve problems of up to 50 jobs [73] accurately CSO performs better than six metaheuristic Applied CSO on OSSP [74] algorithms in the literature. CSO performs better than some conventional Applied CSO on JSSP [75] algorithms in terms of accuracy and speed. Applied CSO on bag-of-tasks and workﬂow CSO performs better than PSO and two other [76] scheduling problems in cloud systems heuristic algorithms +e benchmark instances were taken from TSPLIB and QAPLIB. +e results show that CSO Applied CSO on TSP and QAP [77] outperformed the best results recorded in those dataset references. +e benchmark instances are taken from STPLIB. +e Comparison between CSO, cuckoo search, and bat- results show that CSO falls behind the other [78] inspired algorithm to solve TSP problem algorithms Applied CSO and MCSO on workﬂow scheduling in CSO performs better than PSO [79] cloud systems Applied BCSO on workﬂow scheduling in cloud BCSO performs better than PSO and BPSO [80] systems Applied BCSO on SCP BCSO performs better than ABC [81] BCSO performs better than binary teaching-learning- Applied BCSO on SCP [82, 83] based optimization (BTLBO) Used a CSO as a clustering mechanism in web CSO performs better than K-means [84] services. Very good results were achieved. Silhouette Applied hybrid CSO-GA-SA to ﬁnd the overlapping coeﬃcient was used to verify these results in which [25] community structures. was between 0.7 and 0.9 Used CSO to optimize the network structures for CSO outperformed a number of heuristic methods [85] pinning control CSO outperformed genetic algorithm (GA), Applied CSO with local search reﬁning procedure to evolutionary algorithm (EA), simulated annealing [24] address high school timetabling problem (SA), particle swarm optimization (PSO) and artiﬁcial ﬁsh swarm (AFS). BCSO with dynamic mixture ratios to address the BCSO can eﬀectively tackle the MCDP problem [86] manufacturing cell design problem regardless of the scale of the problem Used CSO to ﬁnd the optimal reservoir operation in CSO outperformed GA [87] water resource management Applied CSO to classify the the feasibility of small CSO resulted in 76% of accuracy in comparison to [88] loans in banking systems 64% resulted from OLR procedure. CSO outperformed a number of metaheuristic Used CSO, AEM and RPT to build a groundwater algorithms in addressing groundwater management [89] management systems problem Applied CSO to solve the multidocument CSO outperformed harmonic search (HS) and PSO [90] summarization problem Used CSO and (RPCM) to address groundwater CSO outperformed a similar model based on PSO [91] resource management CSO-CS successfully solves the VRPTW problem. +e results show that the algorithm convergences Applied CSO-CS to solve VRPTW [32] faster by increasing population and decreasing cdc parameter. Computational Intelligence and Neuroscience 11 Table 2: Continued. Purpose Results Ref. Applied CSO and K-median to detect overlapping CSO and K-median provides better modularity than [92] community in social networks similar models based on PSO and BAT algorithm Applied MOCSO, ﬁtness sharing, and fuzzy MOCSO outperformed MOPSO, NSGA-II and [93, 94] mechanism on CR design MOBFO Applied CSO and ﬁve other metaheuristic algorithms CSO outperformed the GA, PSO, DE, BFO and ABC [95] to design a CR engine algorithms Applied EPCSO on WSN to be used as a routing EPCSO outperformed AODV, a ladder diﬀusion [33] algorithm using ACO and a ladder diﬀusion using CSO. PSO is marginally better for small networks. Applied CSO on WSN in order to solve optimal However, CSO outperformed PSO and cuckoo search [96] power allocation problem algorithm Applied CSO on WSN to optimize cluster head +e proposed system outperformed the existing [97] selection systems by 75%. Applied CSO on CR based smart grid +e proposed system obtains desirable results for communication network to optimize channel [98] both fairness-based and priority-based cases allocation Applied CSO in WSN to detect optimal location of CSO outperformed PSO in reducing total power [99, 100] sink nodes consumption. Applied CSO on time modulated concentric circular antenna array to minimize the sidelobe level of CSO outperformed RGA, PSO and DE algorithms [101] antenna arrays and enhance the directivity Applied CSO to optimize the radiation pattern CSO successfully tunes the parameters and provides [102] controlling parameters for linear antenna arrays. optimal designs of linear antenna arrays. Applied Cauchy mutated CSO to make linear +e proposed system outperformed both CSO and aperiodic arrays, where the goal was to reduce [103] PSO sidelobe level and control the null positions Applied CSO and analytical formula-based objective CSO outperformed DE algorithm [104] function to optimize well placements Applied CSO to optimize well placements CSO outperformed GA and DE algorithms [105] considering oilﬁeld constraints during development. CSO applied to optimize the network structure and +e system successfully forecast the ASP ﬂooding oil learning parameters of an ANN model, which is used [42] recovery index to predict an ASP ﬂooding oil recovery index Applied CSO to build an identiﬁcation model to CSO yields a desirable accuracy in detecting early [106] detect early cracks in beam type structures cracks selective harmonic elimination (SHE) in corporation with Block matching in video processing is computationally expensive and time consuming. Hadi and Sabah used CSO CSO algorithm and then applied it on current source in- verter (CSI) [52]. +e role of the CSO algorithm was to algorithm in block matching for eﬃcient motion estimation [57]. +e aim was to decrease the number of positions that optimize and tune the switching parameters and minimize total harmonic distortion. El-Ela et al. [53] used CSO and needs to be calculated within the search window during the PCSO to ﬁnd the optimal place and size of distributed block matching process, i.e., to enhance the performance generation units on distribution networks. Guo et al. [54] and reduce the number of iterations without the degradation used MCSO algorithm to propose a novel maximum power of the image quality. +e authors further improved their point tracking (MPPT) approach to obtain global maximum work and achieved better results by replacing the CSO al- power point (GMPP) tracking. Srivastava et al. used BCSO gorithm with HCSO and ICSO in [16, 17], respectively. algorithm to optimize the location of phasor measurement Kalaiselvan et al. and Lavanya and Natarajan [58, 59] used units and reduce the required number of PMUs [55]. Guo CSO Algorithm to retrieve watermarks similar to the original copy. In video processing, object tracking is the et al. used CSO algorithm to identify the parameters of single and double diode models in solar cell models [56]. process of determining the position of a moving object over time using a camera. Hadi and Sabah used EHCSO in an object-tracking system for further enhancement in terms of 5.2. Computer Vision. Facial emotion recognition is a bio- eﬃciency and accuracy [60]. Yan et al. used BCSO as a band metric approach to identify human emotion and classify selection method for hyperspectral images [61]. In computer them accordingly. Lin et al. and Wang and Wu [39, 40] vision, image segmentation refers to the process of dividing proposed a classroom response system by combining the an image into multiple parts. Ansar and Bhattacharya and CSO algorithm with support vector machine to classify Karakoyun et al. [62, 63] proposed using CSO algorithm student’s facial expressions. Vivek and Reddy also used incorporation with the concept of multilevel thresholding CSO-GA-PSOSVM algorithm for the same purpose [23]. for image segmentation purposes. Zhang et al. combined 12 Computational Intelligence and Neuroscience communication between applications over the web which wavelet entropy, ANN, and CSO algorithm to develop an alcohol use disorder (AUD) identiﬁcation system [64]. have many important applications. However, discovering appropriate web services for a given task is challenging. Kumar et al. combined the CSO algorithm with functional link artiﬁcial neural network (FLANN) to remove the un- Kotekar and Kamath used a CSO-based approach as a wanted Gaussian noises from CT images [45]. Yang et al. clustering algorithm to group service documents according combined CSO with L-BFGS-B technique to register non- to their functionality similarities [84]. Sarswat et al. applied rigid multimodal images [65]. Çam employed CSO algo- Hybrid CSO-GA-SA to detect the overlapping community rithm to tune the parameters in the histogram stretching structures and ﬁnd the near-optimal disjoint communities technique for the purpose of image enhancement [66]. [25]. Optimizing the problem of controlling complex net- work systems is critical in many areas of science and en- gineering. Orouskhani et al. applied CSO algorithm to 5.3. Signal Processing. IIR ﬁlter stands for inﬁnite impulse address a number of problems in optimal pinning con- response. It is a discrete-time ﬁlter, which has applications in trollability and thus optimized the network structure [85]. signal processing and communication. Panda et al. used Skoullis et al. combined the CSO algorithm with local search CSO algorithm for IIR system identiﬁcation [67]. +e au- reﬁning procedure and applied it on high school timetabling thors also applied CSO algorithm as an optimization problem [24]. Soto et al. combined BCSO with dynamic mechanism to do direct and inverse modeling of linear and mixture ratios to organize the cells in manufacturing cell nonlinear plants [68]. Al-Asadi combined CSO Algorithm design problem [86]. Bahrami et al. applied a CSO algorithm with SVM for electrocardiograms signal classiﬁcation [38]. on water resource management where the algorithm was used to ﬁnd the optimal reservoir operation [87]. Kencana et al. used CSO algorithm to classify the feasibility of small 5.4. System Management and Combinatorial Optimization. In parallel computing, optimal task allocation is a key loans in banking systems [88]. Majumder and Eldho combined the CSO algorithm with the analytic element challenge. Shojaee et al. [69, 70] proposed using CSO al- gorithm to maximize system reliability. +ere are three basic method (AEM) and reverse particle tracking (RPT) to model novel groundwater management systems [89]. Rautray and scheduling problems, namely, open shop, job shop, and ﬂow shop. +ese problems are classiﬁed as NP-hard and have Balabantaray used CSO algorithm to solve the multidocu- many real-world applications. +ey coordinate assigning ment summarization problem [90]. +omas et al. combined jobs to resources at particular times, where the objective is to radial point collocation meshfree (RPCM) approach with minimize time consumption. However, their diﬀerence is CSO algorithm to be used in the groundwater resource mainly in having ordering constraints on operations. management [91]. Pratiwi created a hybrid system by Bouzidi and Riﬃ applied the BCSO algorithm on job combining the CSO algorithm and crow search (CS) algo- rithm and then used it to address the vehicle routing scheduling problem (JSSP) in [71]. +ey also made a comparative study between CSO and two other meta- problem with time windows (VRPTW) [32]. Naem et al. proposed a modularity-based system by combining the CSO heuristic algorithms, namely, cuckoo search (CS) algorithm and the ant colony optimization (ACO) for JSSP in [72]. algorithm with K-median clustering technique to detect overlapping community in social networks [92]. +en, they used the CSO algorithm to solve ﬂow shop scheduling (FSSP) [73] and open shop scheduling problems (OSSP) as well [74]. Moreover, Dani et al. also applied CSO 5.5. Wireless and WSN. +e ever-growing wireless devices algorithm on JSSP in which they used a nonconventional approach to represent cat positions [75]. Maurya and Tri- push researchers to use electromagnetic spectrum bands more wisely. Cognitive radio (CR) is an eﬀective dynamic pathi also applied CSO algorithm on bag-of-tasks and spectrum allocation in which spectrums are dynamically workﬂow scheduling problems in cloud systems [76]. assigned based on a speciﬁc time or location. Pradhan and Bouzidi and Riﬃ applied CSO algorithm on the traveling Panda in [93, 94] combined MOCSO with ﬁtness sharing salesman problem (TSP) and the quadratic assignment and fuzzy mechanism and applied it on CR design. +ey also problem (QAP), which are two combinatorial optimization conducted a comparative analysis and proposed a gener- problems [77]. Bouzidi et al. also made a comparative study alized method to design a CR engine based on six evolu- between CSO algorithm, cuckoo search algorithm, and bat- tionary algorithms [95]. Wireless sensor network (WSN) inspired algorithm for addressing TSP [78]. In cloud computing, minimizing the total execution cost while al- refers to a group of nodes (wireless sensors) that form a network to monitor physical or environmental conditions. locating tasks to processing resources is a key problem. Bilgaiyan et al. applied CSO and MCSO algorithms on +e gathered data need to be forwarded among the nodes and each node requires having a routing path. Kong et al. workﬂow scheduling in cloud systems [79]. In addition, proposed applying enhanced parallel cat swarm optimiza- Kumar et al. also applied BCSO on workﬂow scheduling in tion (EPCSO) algorithm in this area as a routing algorithm cloud systems [80]. Set cover problem (SCP) is considered as [33]. Another concern in the context of WSN is minimizing an NP-complete problem. Crawford et al. successfully ap- the total power consumption while satisfying the perfor- plied the BCSO Algorithm to this problem [81]. +ey further mance criteria. So, Tsiﬂikiotis and Goudos addressed this improved this work by using Binarization techniques and selecting diﬀerent parameters for each test example sets problem which is known as optimal power allocation problem, and for that, three metaheuristic algorithms were [82, 83]. Web services provide a standardized Computational Intelligence and Neuroscience 13 (i) Default control parameters (ii) 30 independent runs (iii) 30 search agents (iv) 500 iterations CSO and its Classical and modern Ranking competitive benchmark functions (Friedman test) algorithms Wilcoxon matched-pairs signed-rank test (confirm the results) Figure 3: General framework of the performance evaluation process. presented and compared [96]. Moreover, Pushpalatha and which the original CSO algorithm was compared against Kousalya applied CSO in WSN for optimizing cluster head three new and robust algorithms, which were dragonﬂy selection which helps in energy saving and available algorithm (DA) [6], butterﬂy optimization algorithm (BOA) [7], and ﬁtness dependent optimizer (FDO) [8]. For this, 23 bandwidth [97]. Alam et al. also applied CSO algorithm in a clustering-based method to handle channel allocation (CA) traditional and 10 modern benchmark functions were used issue between secondary users with respect to practical (see Figure 3), which illustrates the general framework for constraints in the smart grid environment [98]. +e authors conducting the performance evaluation process. It is worth of [99, 100] used the CSO algorithm to ﬁnd the optimal mentioning that for four test functions, BOA returned location of sink nodes in WSN. Ram et al. applied CSO imaginary numbers and we set “N/A” for them. algorithm to minimize the sidelobe level of antenna arrays and enhance the directivity [101]. Ram et al. used CSO to 6.1. Traditional Benchmark Functions. +is group includes optimize controlling parameters of linear antenna arrays the unimodal and multimodal test functions. Unimodal test and produce optimal designs [102]. Pappula and Ghosh functions contain one single optimum while multimodal test also used Cauchy mutated CSO to make linear aperiodic functions contain multiple local optima and usually a single arrays, where the goal was to reduce sidelobe level and global optimum. F1 to F7 are unimodal test functions control the null positions [103]. (Table 3), which are employed to experiment with the global search capability of the algorithms. Furthermore, F8 to F23 5.6. Petroleum Engineering. CSO algorithm has also been are multimodal test functions, which are employed to ex- applied in the petroleum engineering ﬁeld. For example, it periment with the local search capability of the algorithms. was used as a good placement optimization approach by Refer to [107] for the detailed description of unimodal and Chen et al. in [104, 105]. Furthermore, Wang et al. used CSO multimodal functions. algorithm as an ASP ﬂooding oil recovery index forecasting approach [43]. 6.2. Modern Benchmark Functions (CEC 2019). +ese set of benchmark functions, also called composite benchmark 5.7. Civil Engineering. Ghadim et al. used CSO algorithm to functions, are complex and diﬃcult to solve. +e CEC01 to CEC10 functions as shown in Table 3 are of these types, create an identiﬁcation model that detects early cracks in building structures [106]. which are shifted, rotated, expanded, and combined versions of traditional benchmark functions. Refer to [108] for the detailed description of modern benchmark functions. 6. Performance Evaluation +e comparison results for CSO and other algorithms are given in Table 3 in the form of mean and standard Many variants and applications of CSO algorithm were discussed in the above sections. However, benchmarking deviations. For each test function, the algorithms are exe- cuted for 30 independent runs. For each run, 30 search these versions and conducting a comparative analysis be- tween them were not feasible in this work. +is is because: agents were searching over the course of 500 iterations. ﬁrstly, their source codes were not available. Secondly, Parameter settings are set as defaults for all algorithms, and diﬀerent test functions or datasets have been used during nothing was changed. their experiments. In addition, since the emergence of CSO It can be noticed from Table 3 that the CSO algorithm is a algorithm, many novel and powerful metaheuristic algo- competitive algorithm for the modern ones and provides rithms have been introduced. However, the literature lacks a very satisfactory results. In order to perceive the overall comparative study between CSO algorithm and these new performance of the algorithms, they are ranked as shown in algorithms. +erefore, we conducted an experiment, in Table 4 according to diﬀerent benchmark function groups. It 14 Computational Intelligence and Neuroscience Table 3: Comparison results of CSO algorithm with modern metaheuristic algorithms. CSO DA BOA FDO min Functions AV STD AV STD AV STD AV STD F1 3.50E − 14 6.34E − 14 15.24805 23.78914 1.01E − 11 1.66E − 12 2.13E − 23 1.06E − 22 0 F2 2.68E − 08 2.61E − 08 1.458012 0.869819 4.65E − 09 4.63E − 10 0.047175 0.188922 0 F3 7.17E − 09 1.16E − 08 136.259 151.9406 1.08E − 11 1.71E − 12 2.39E − 06 1.28E − 05 0 F4 0.010352 0.007956 3.262584 2.112636 5.25E − 09 5.53E − 10 4.93E − 08 9.09E − 08 0 F5 8.587858 0.598892 374.9048 691.5889 8.935518 0.02146 21.58376 39.66721 0 F6 1.151759 0.431511 12.07847 17.97414 1.04685 0.346543 7.15E − 22 2.80E − 21 0 F7 0.026026 0.015039 0.035679 0.023538 0.001513 0.00056 0.612389 0.299315 0 F8 − 2855.11 359.1697 − 2814.14 432.944 NA NA − 10502.1 15188.77 − 418.9829 × 5 F9 24.01772 6.480946 26.53478 11.20011 28.6796 20.17813 7.940883 4.110302 0 F10 3.754226 1.680534 2.827344 1.042434 3.00E − 09 1.16E − 09 7.76E − 15 2.46E − 15 0 F11 0.355631 0.19145 0.680359 0.353454 1.35E − 13 6.27E − 14 0.175694 0.148586 0 F12 1.900773 1.379549 2.083215 1.436402 0.130733 0.084891 7.737715 4.714534 0 F13 1.160662 0.53832 1.072302 1.327413 0.451355 0.138253 4.724571 6.448214 0 F14 0.998004 3.39E − 07 1.064272 0.252193 1.52699 0.841504 2.448453 1.766953 1 F15 0.001079 0.00117 0.005567 0.012211 0.000427 9.87E − 05 0.001492 0.003609 0.00030 F16 − 1.03162 1.53E − 05 − 1.03163 4.76E − 07 NA NA − 1.00442 0.149011 − 1.0316 F17 0.304253 1.81E − 06 0.304251 0 0.310807 0.004984 0.397887 5.17E − 15 0.398 F18 3.003667 0.004338 3.000003 1.22E − 05 3.126995 0.211554 3 2.37E − 07 3 F19 − 3.8625 0.00063 − 3.86262 0.00037 NA NA − 3.86015 0.003777 − 3.86 F20 − 3.30564 0.045254 − 3.25226 0.069341 NA NA − 3.06154 0.380813 − 3.32 F21 − 9.88163 0.90859 − 7.28362 2.790655 − 4.44409 0.383552 − 4.19074 2.664305 − 10.1532 F22 − 10.2995 0.094999 − 8.37454 2.726577 − 4.1496 0.715469 − 4.89633 3.085016 − 10.4028 F23 − 10.0356 1.375583 − 6.40669 2.892797 − 4.12367 0.859409 − 4.03276 2.517357 − 10.5363 CEC01 1.58E + 09 1.71E + 09 3.8E + 10 4.03E + 10 58930.69 11445.72 4585.278 20707.63 1 CEC02 19.70367 0.580672 83.73248 100.1326 18.91597 0.291311 4 3.28E − 09 1 CEC03 13.70241 2.35E − 06 13.70263 0.000673 13.70321 0.000617 13.7024 1.68E − 11 1 CEC04 179.1984 55.37322 371.2471 420.2062 20941.5 7707.688 33.08378 16.81143 1 CEC05 2.671378 0.171923 2.571134 0.304055 6.176949 0.708134 2.13924 0.087218 1 CEC06 11.21251 0.708359 10.34469 1.335367 11.83069 0.771166 12.13326 0.610499 1 CEC07 365.2358 164.997 534.3862 240.0417 1043.895 215.3575 120.4858 13.82608 1 CEC08 5.499615 0.484645 5.86374 0.51577 6.337199 0.359203 6.102152 0.769938 1 CEC09 6.325862 1.295848 8.501541 16.90603 2270.616 811.4442 2 2.00E − 10 1 CEC10 21.36829 0.06897 21.29284 0.176811 21.4936 0.079492 2.718282 4.52E − 16 1 Table 4: Ranking of CSO algorithm compared to the modern metaheuristic algorithms. Test functions Ranking of CSO Ranking of DA Ranking of BOA Ranking of FDO F1 2 4 3 1 F2 2 4 1 3 F3 2 4 1 3 F4 3 4 1 2 F5 1 4 2 3 F6 3 4 2 1 F7 2 3 1 4 F8 2 3 4 1 F9 2 3 4 1 F10 4 3 2 1 F11 3 4 1 2 F12 2 3 1 4 F13 3 2 1 4 F14 1 2 3 4 F15 2 4 1 3 F16 1 2 4 3 F17 3 4 2 1 F18 3 2 4 1 F19 2 3 4 1 F20 1 2 4 3 F21 1 2 3 4 Computational Intelligence and Neuroscience 15 Table 4: Continued. Test functions Ranking of CSO Ranking of DA Ranking of BOA Ranking of FDO F22 1 2 4 3 F23 1 2 3 4 Cec01 3 4 2 1 Cec02 3 4 2 1 Cec03 2 3 4 1 Cec04 2 3 4 1 Cec05 3 2 4 1 Cec06 2 1 3 4 Cec07 2 3 4 1 Cec08 1 2 4 3 Cec09 2 3 4 1 Cec10 3 2 4 1 Total 70 97 91 72 Overall ranking 2.121212 2.939394 2.757576 2.181818 F1–F7 subtotal 15 27 11 17 F1–F7 ranking 2.142857 3.857143 1.571429 2.428571 F8–F23 subtotal 32 43 45 40 F8–F23 ranking 2 2.6875 2.8125 2.5 CEC01–CEC10 subtotal 23 27 35 15 CEC01–CEC10 ranking 2.3 2.7 3.5 1.5 3.5 2.5 1.5 0.5 CSO DA BOA FDO Overall ranking F8–F23 ranking F1–F7 ranking CEC01–CEC10 ranking Figure 4: Ranking of algorithms according to diﬀerent groups of test functions. can be seen that CSO ranks ﬁrst in the overall ranking and variants [111], WOA and its variants [112], and other multimodal test functions. Additionally, it ranks second in modiﬁed versions of DA [113]. unimodal and CEC test functions (see Figure 4). +ese results indicate the eﬀectiveness and robustness of the CSO 7. Conclusion and Future Directions algorithm. +at being said, these results need to be con- ﬁrmed statistically. Table 5 presents the Wilcoxon matched- Cat swarm optimization (CSO) is a metaheuristic optimi- pairs signed-rank test for all test functions. In more than zation algorithm proposed originally by Chu et al. [5] in 85% of the results, P value is less than 0.05%, which proves 2006. Henceforward, many modiﬁed versions and applica- that the results are signiﬁcant and we can reject the null tions of it have been introduced. However, the literature hypothesis that there is no diﬀerence between the means. It lacks a detailed survey in this regard. +erefore, this paper is worth mentioning that the performance of CSO can be ﬁrstly addressed this gap and presented a comprehensive further evaluated by comparing it against other new algo- review including its developments and applications. rithms such as donkey and smuggler optimization algorithm CSO showed its ability in tackling diﬀerent and complex [109], modiﬁed grey wolf optimizer [110], BSA and its problems in various areas. However, just like any other Ranking 16 Computational Intelligence and Neuroscience Table 5: Wilcoxon matched-pairs signed-rank test. +is indicates that CSO is still a competitive algorithm in the ﬁeld. Test functions CSO vs. DA CSO vs. BOA CSO vs. FDO In the future, the algorithm can be improved in many F1 <0.0001 <0.0001 <0.0001 aspects; for example, diﬀerent techniques can be adapted to F2 <0.0001 <0.0001 0.0003 the tracing mode in order to solve the premature conver- F3 <0.0001 <0.0001 0.2286 gence problem or transforming MR parameter is static in the F4 <0.0001 <0.0001 <0.0001 original version of CSO. Transforming this parameter into a F5 <0.0001 0.0879 0.0732 dynamic parameter might improve the overall performance F6 0.0008 0.271 <0.0001 F7 0.077 <0.0001 <0.0001 of the algorithm. F8 0.586 N/A <0.0001 F9 0.2312 0.3818 <0.0001 Conflicts of Interest F10 0.0105 <0.0001 <0.0001 F11 <0.0001 <0.0001 0.0002 +e authors declare that there are no conﬂicts of interest F12 0.4 <0.0001 <0.0001 regarding the publication of this paper. F13 <0.0001 <0.0001 0.0185 F14 0.4 <0.0001 0.0003 F15 0.0032 0.0004 0.9515 References F16 <0.0001 N/A <0.0001 F17 <0.0001 <0.0001 <0.0001 [1] X. S. 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Published: Jan 22, 2020
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