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The chimp optimization algorithm (ChOA) is a nature-inspired algorithm that imitates chimpanzees' individual intelligence and hunting behaviors. In this algorithm, the hunting process consists of four steps: driving, blocking, chasing, and attacking. Because of the novelty of ChOA, the steps of the hunting process have been modeled in the simplest possible way, leading to slow and premature convergence similar to other iterative algorithms. This paper proposes six spiral functions and introduces two novel hybrid spiral functions (SEB-ChOA) to rectify the abovementioned deficiencies. The SEB-ChOAs' performance is evaluated on 23 standard benchmarks, 20 benchmarks of IEEE CEC-2005, 10 cases of IEEE CEC06-2019 test-suite, and 12 constrained real-world engineering problems of IEEE CEC-2020. The SEB-ChOAs are compared with three groups of optimization algorithms, including Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) as the most well-known optimization algorithms, Slime Mould Algorithm (SMA), Marine Predators Algorithm (MPA), Ant Lion Optimization (ALO), Henry Gas Solubility Optimization (HGSO), as almost novel optimization algorithms, and jDE100 and DISHchain1e+12, as winners of IEEE CEC06-2019 competition, and also EBOwithCMAR and CIPDE as superior secondary optimization algorithms. The SEB-ChOAs reached the first rank among almost all benchmarks and demonstrated very competitive results compared to jDE100 and DISHchain1e+12 as the best-performing optimizers. Statistical evidence shows that the SEB-ChOA outperforms the PSO, GA, SMA, MPA, ALO, and HGSO optimizers while producing results comparable to those of the jDE100 and DISHchain1e+12 algorithms. [ABSTRACT FROM AUTHOR]

Intrusion Detection (ID) is an essential task in the cyberattacks domain built to secure Internet applications and networks from malicious actors. The main shortcoming of the current Intrusion Detection Systems (IDSs) is their attack detection performance because the existing solutions fail to detect the threats efficiently. Therefore, improving the prediction model of the IDS can improve its performance. Several studies suggest improving the Machine Learning (ML)-based IDS prediction models by selecting the most informative features from the security data before utilizing it in the ML-IDS model. Thus, meta-heuristic algorithms such as White Shark Optimizer (WSO) are adapted to deal with such feature selection problems. For the IDS prediction model, in this paper, the WSO algorithm is improved to cope with the binary domain of the feature selection task as follows: Firstly, two transfer functions are used to map the continuous domain into binary. Secondly, the modified K-means algorithm is proposed to assess building the initial population with a high level of diversity. Finally, several crossover operators are utilized to improve the evolution process of the binary WSO. The three improved versions are BIWSO1 which is WSO with transfer functions, BIWSO2, which is BIWSO1 with a modified k-means algorithm, and BIWSO3, which is BIWSO2 with crossover operators. The proposed versions of BIWSO are tested using twelve public real-world IDS and IoT datasets. Comparative evaluations against well-established meta-heuristic algorithms are conducted where the BIWSO3 proves its efficiency in terms of classification accuracy, precision, recall, and F1 measurements. For further validation, statistical evidence using Friedman's, Wilcoxon's, and Mann–Whitney U tests has been conducted where BIWSO3 proves its performance at a remarkably significant level. [ABSTRACT FROM AUTHOR]

Recently, substantial progress has been made in developing efficient algorithms for solving combinatorial optimization problems. In this paper, following this direction, the problem of designing supply chains which is an important combinatorial optimization problem is considered. The structural properties of supply chain models are investigated to transform such models into a generalized network optimization model. The transformation to a generalized network optimization model reduces the algorithms' solution time. Moreover, this paper proposes a new efficient hybrid algorithm based on tabu search and generalized network simplex algorithm (GN-TSA) for designing multi-objectives supply chain models. The developed algorithm's parameters are tuned properly, validated, and evaluated. The algorithm's performance is then compared to an exact algorithm embedded in the General Algebraic Modeling System (GAMS) and two metaheuristic algorithms, namely a linear programming simplex algorithm integrated with the tabu search approach (LP-TSA) and simulated annealing. The findings indicated that the GN-TSA obtains solutions very close to the exact algorithm with less computation time. In addition, the proposed algorithm outperforms the LP-TSA and simulated annealing in terms of computation time, while the quality of the solutions is the same as solutions obtained by LP-TSA and better than simulated annealing. On average, the results revealed that the reduction in computational time is more than 26.30% using GN-TSA compared to LP-TSA and simulated annealing. [ABSTRACT FROM AUTHOR]

Computations that mimic nature are known as nature-inspired computing. Nature presents a wealthy source of thoughts and ideas for computing. The use of natural galvanized techniques has been found to provide machine solutions to complex problems. One of the challenging issues among researchers is high-dimensional data which contains a large number of unwanted, redundant, and irrelevant features. These redundant or unwanted features reduce the accuracy of machine learning models. Therefore, to solve this problem nowadays metaheuristic techniques are being used. The paper presents both surveys as well as comparison of five metaheuristic algorithms for feature selection. A wrapper-based feature selection approach using five nature-inspired techniques for feature selection has been applied. The binary version of the five swarm-based nature-inspired algorithms (NIAs), namely particle swarm optimization, whale optimization algorithm (WOA), grey wolf optimization (GWO), firefly algorithm, and bat algorithm. WOA and GWO are recent algorithms used for finding optimal feature subsets when there is no empirical information. The S-shape transfer function has been used to convert the continuous value to binary form and K-nearest neighbor is used to calculate the classification accuracy of selected feature subsets. To validate the results of the selected NIAs eleven benchmark datasets from the UCI repository are used. The strength of each NIA has been verified using a nonparametric test called the Friedman rank and Holm test. p value obtained shows that WOA is statistically significant and performs better than other models. [ABSTRACT FROM AUTHOR]

The discounted {0-1} knapsack problem (DKP) is an NP-hard problem that is more challenging than the classical knapsack problem. In this paper, an enhanced version of the sine-cosine algorithm (SCA) called TMHSCA is proposed to solve the DKP. The SCA is a novel metaheuristic algorithm based on sine-cosine theory. Three effective improvements are proposed for the SCA to enhance the convergence speed and exploitation capability of the algorithm. First, by dividing the initial population into three subpopulations using random, greedy and opposition-based learning (OBL) strategies, the diversity of the population can be effectively enhanced. Furthermore, a forward-inverse sine-cosine search that expands the search space by utilizing the worst solution as another target is proposed. The proposed forward-inverse sine-cosine search strategy facilitates the algorithm to explore the easily ignored solution space. The last improvement includes the use of an OBL mutation and the mutation operator of differential evolution at a two-stage mutation, which increases the algorithm's convergence speed and fitness. In our proposed two-stage mutation, the number of mutations can be adaptively adjusted based on the optimization capabilities of the optimal individual. Additionally, a reshuffling repair strategy for repairing infeasible solutions by sorting items into groups to obtain the weight-to-value ratio is proposed. Extensive experiments are conducted on 40 publicly available datasets and are compared to the greedy algorithm, 3 SCAs and 8 competitive baseline methods. The experimental results demonstrate that our method achieves a state-of-the-art performance. [ABSTRACT FROM AUTHOR]

The optimal design of Power System Stabilizer (PSS) parameters is a significant optimization problem in power systems. Metaheuristic search (MHS) algorithms are among the most commonly used methods for optimizing PSS parameters. The preferred MHS algorithm must have strong exploration capability and an effective exploitation-exploration balance. The Fitness-Distance Balance (FDB) is a novel method for MHS algorithms, and it is featured by balanced search and effective diversity capabilities. In this paper, the exploration and balanced search capabilities of the Social Network Search (SNS) have been developed by using the FDB method. The FDB method guides the search process in the SNS and enables a more efficient selection of solution candidates in the search space. The performance of FDB-based SNS (FDBSNS) has been tested in the CEC-2014 and CEC-2017 benchmark test suits, and its superiority against SNS has been verified. Moreover, the effect of the FDBSNS was investigated in WSCC 3-machine 9-bus and 10-machine 39-bus New England test systems in the optimal PSS design problem. The obtained results and statistical analyses demonstrated that FDBSNS is a robust MHS algorithm compared to the algorithms in the literature for solving the CEC benchmark suits and optimal PSS design problem. [ABSTRACT FROM AUTHOR]

Metaheuristics are algorithms that are used to solve difficult optimization problems. They are typically stochastic approaches; hence, proper statistical tests are needed to compare them. However, choosing an appropriate statistical test is not trivial given that each test requires some assumptions to be true before the test can be used. Moreover, the p-values associated with a statistical test is usually difficult to interpret. In this paper, we propose the use of Laplace's rule of succession to compare different metaheuristic approaches. The rule is simple, intuitive and easy to compute. It can be used alone or to complement a statistical test. The process of using the rule for comparison purposes is clearly explained and applied to a typical scenario encountered in the field of metaheuristics. In this scenario, an improved variant of an existing metaheuristic algorithm is proposed. To evaluate the performance of the two algorithms, Laplace's rule and a traditional statistical test are used. Analysis of the results and how to interpret them are provided. The results show that Laplace's rule is consistent with the used statistical test. Furthermore, the rule is easier to compute and interpret. [ABSTRACT FROM AUTHOR]

This paper introduces a new variant of the metaheuristic algorithm based on the naked mole rat (NMR) algorithm, called the Q-learning naked mole rat algorithm (QL-NMR), for substitution box construction and optimization. Unlike most competing works (which typically integrate a single chaotic map into a particular metaheuristic algorithm), QL-NMR assembles five chaotic maps (i.e., Chebyshev, logistic, circle, Singer, and sinusoidal) as part of the algorithm itself. Using a Q-learning table, QL-NMR remembers the historical performance of each chaotic map during the S-box construction process allowing just-in-time adaptive selection based on its current performance. Experimental results for 8 × 8 S-box generation demonstrate that the proposed QL-NMR gives competitive performance against other existing works, particularly in terms of nonlinearity and strict avalanche criteria. To further demonstrate the effectiveness of our proposed work, we have subjected the QL-NMR for image segmentation using multilevel thresholding. The results confirm that QL-NMR gives better performance than its predecessor NMR. Finally, QL-NMR S-box also outperformed NMR S-box in image encryption. [ABSTRACT FROM AUTHOR]

Feature selection techniques are considered one of the most important preprocessing steps, which has the most significant influence on the performance of data analysis and decision making. These FS techniques aim to achieve several objectives (such as reducing classification error and minimizing the number of features) at the same time to increase the classification rate. FS based on Metaheuristic (MH) is considered one of the most promising techniques to improve the classification process. This paper presents a modified method of the Slime mould algorithm depending on the Marine Predators Algorithm (MPA) operators as a local search strategy, which leads to increasing the convergence rate of the developed method, named SMAMPA and avoiding the attraction to local optima. The efficiency of SMAMPA is evaluated using twenty datasets and compared its results with the state-of-the-art FS methods. In addition, the applicability of SMAMPA to work with real-world problems is evaluated by using it as a quantitative structure-activity relationship (QSAR) model. The obtained results show the high ability of the developed SMAMPA method to reduce the dimension of the tested datasets by increasing the prediction rate. In addition, it provides results better than other FS techniques in terms of performance metrics. [ABSTRACT FROM AUTHOR]

Three-dimensional path planning for autonomous robots is a prevalent problem in mobile robotics. This paper presents three novel versions of a hybrid method designed to assist in planning such paths for these robots. In this paper, an improvement on Rapidly exploring Random Tree (RRT) algorithm, namely Adapted-RRT, is presented that uses three well-known metaheuristic algorithms, namely Grey Wolf Optimization (GWO), Incremental Grey Wolf Optimization (I-GWO), and Expanded Grey Wolf Optimization (Ex-GWO)). RRT variants, using these algorithms, are named Adapted-RRTGWO, Adapted-RRTI-GWO, and Adapted-RRTEx-GWO. The most significant shortcoming of the methods in the original sampling-based algorithm is their inability in finding the optimal paths. On the other hand, the metaheuristic-based algorithms are disadvantaged as they demand a predetermined knowledge of intermediate stations. This study is novel in that it uses the advantages of sampling and metaheuristic methods while eliminating their shortcomings. In these methods, two important operations (length and direction of each movement) are defined that play an important role in selecting the next stations and generating an optimal path. They try to find solutions close to the optima without collision, while providing comparatively efficient execution time and space complexities. The proposed methods have been simulated employing four different maps for three unmanned aerial vehicles, with diverse sets of starting and ending points. The results have been compared among a total of 11 algorithms. The comparison of results shows that the proposed path planning methods generally outperform various algorithms, namely BPIB-RRT*, tGSRT, GWO, I-GWO, Ex-GWO, PSO, Improved BA, and WOA. The simulation results are analysed in terms of optimal path costs, execution time, and convergence rate. [ABSTRACT FROM AUTHOR]

Deep neural networks (DNNs) have evolved as a beneficial machine learning method that has been successfully used in various applications. Currently, DNN is a superior technique of extracting information from massive sets of data in a self-organized method. DNNs have different structures and parameters, which are usually produced for particular applications. Nevertheless, the training procedures of DNNs can be protracted depending on the given application and the size of the training set. Further, determining the most precise and practical structure of a deep learning method in a reasonable time is a possible problem related to this procedure. Meta-heuristics techniques, such as swarm intelligence (SI) and evolutionary computing (EC), represent optimization frames with specific theories and objective functions. These methods are adjustable and have been demonstrated their effectiveness in various applications; hence, they can optimize the DNNs models. This paper presents a comprehensive survey of the recent optimization methods (i.e., SI and EC) employed to enhance DNNs performance on various tasks. This paper also analyzes the importance of optimization methods in generating the optimal hyper-parameters and structures of DNNs in taking into consideration massive-scale data. Finally, several potential directions that still need improvements and open problems in evolutionary DNNs are identified. [ABSTRACT FROM AUTHOR]

To develop new meta-heuristic algorithms and evaluate on the benchmark functions is the most challenging task. In this paper, performance of the various developed meta-heuristic algorithms are evaluated on the recently developed CEC 2021 benchmark functions. The objective functions are parametrized by inclusion of the operators, such as bias, shift and rotation. The different combinations of the binary operators are applied to the objective functions which leads to the CEC2021 benchmark functions. Therefore, different meta-heuristic algorithms are considered which solve the benchmark functions with different dimensions. The performance of some basic, advanced meta-heuristics algorithms and the algorithms that participated in the CEC2021 competition have been experimentally investigated and many observations, recommendations, conclusions have been reached. The experimental results show the performance of meta-heuristic algorithms on the different combinations of binary parameterized operators. [ABSTRACT FROM AUTHOR]

This paper addresses a new multi-level serial closed-loop supply chain (CLSC) model with an integrated formulation of batch deliveries, quality-dependent return rate, random defective rate, rework process, and learning effects. The vendor managed inventory contract has motivated companies to cope with the bullwhip effect and its associated shortages. However, getting precise information on manufacturing/remanufacturing time is a challenge owing to human learning. Accordingly, this paper tries to incorporate the learning effect on the inventory control problem. This is a bridge to fill the gaps in the literature by considering how the learning process affects the production time and system costs in a CLSC problem. Moreover, the mean-standard deviation utility function is used in order to take the random defective rate into account, to minimize mean system costs with respect to the standard deviation. Due to the complexity of the proposed mixed-integer nonlinear programming model, three metaheuristic algorithms named, genetic algorithm, invasive weed optimization algorithm, and moth flame optimization algorithm are used to solve the problem, and Fibonacci algorithm will examine the validity of the applied methods. Two sets of numerical examples in small, medium, and large sizes are presented to illustrate the performance of the algorithms in terms of objective function values and required CPU-time. Afterward, a statistical analysis is utilized in order to evaluate the proposed algorithms. Finally, the results show how significantly the learning effect in manufacturing/remanufacturing time affects the costs of CLSC problem. [ABSTRACT FROM AUTHOR]

Cluster analysis is an essential tool in data mining. Several clustering algorithms have been proposed and implemented, most of which are able to find good quality clustering results. However, the majority of the traditional clustering algorithms, such as the K-means, K-medoids, and Chameleon, still depend on being provided a priori with the number of clusters and may struggle to deal with problems where the number of clusters is unknown. This lack of vital information may impose some additional computational burdens or requirements on the relevant clustering algorithms. In real-world data clustering analysis problems, the number of clusters in data objects cannot easily be preidentified and so determining the optimal amount of clusters for a dataset of high density and dimensionality is quite a difficult task. Therefore, sophisticated automatic clustering techniques are indispensable because of their flexibility and effectiveness. This paper presents a systematic taxonomical overview and bibliometric analysis of the trends and progress in nature-inspired metaheuristic clustering approaches from the early attempts in the 1990s until today's novel solutions. Finally, key issues with the formulation of metaheuristic algorithms as a clustering problem and major application areas are also covered in this paper. [ABSTRACT FROM AUTHOR]

This paper introduces a novel population-based vortex search algorithm (PVS) to improve the weakness of the global search capability of the original Vortex Search (VS) algorithm which is a simple and efficient physics-based metaheuristic and originally has a single-solution-based structure. Single-solution-based metaheuristics perform a local search in the neighborhood of a single solution, whereas population-based metaheuristics conduct the search process by creating several candidate solutions at different points in the search space. The fast-running structures of single-solution-based algorithms may cause the search process to get stuck in the local optimum in some cases. The proposed algorithm transforms VS into a population-based structure with a location update operator and the polynomial mutation operator. Also, the strategy of generating solutions based on the radius reduction mechanism around a center is maintained. Furthermore, two variants of PVS, called PVS_a and PVS_b, are presented in this study. The performance of the proposed approach is investigated by applying a set of experimental series. Three different benchmark sets involving (i) 20 classical benchmark functions, (ii) 29 CEC2017 test functions, and (iii) 10 CEC2019 test functions are employed in experiments. In addition, four real-world-constrained optimization problems are used to evaluate the effectiveness of PVS. Considering the experimental results obtained from the comparison of the proposed algorithm with both state-of-the-art and recent metaheuristics, the developed PVS_a algorithm provides highly quite promising and superior outcomes in solution quality and robustness. [ABSTRACT FROM AUTHOR]

The minimum vertex cover problem (MVCP) is one of the well-known NP-complete problems that can be used to formulate numerous real-life applications. The MVCP has been solved using different approaches, exact, heuristic, and metaheuristic. Chemical reaction optimization (CRO) is a population-based metaheuristic algorithm that simulates what happens in chemical reactions to solve many problems. In this paper, the MVCP is solved using hybridization of a modified version of the CRO algorithm and the best-first search (BFS) algorithm. This hybridization is symbolized by MCROA-BFS. The BFS algorithm is exploited to generate initial populations with high-quality initial solutions in comparison with the random bit-vector (RBV) approach as a traditional approach for generating initial populations for several population-based metaheuristic algorithms. At first, the MCROA is evaluated analytically in terms of run time complexity. Then the performance of the MCROA is evaluated experimentally to show the effectiveness of exploiting the BFS in terms of quality of gained solutions and run time. The most valuable player algorithm (MVPA), genetic algorithm (GA), and hybrid CRO algorithm (HCROA) are metaheuristic algorithms that used the RBV approach to generate the initial population. MCROA-BFS is compared, under the selected performance metrics, with these metaheuristic algorithms in addition to MCROA with the RBV approach (MCROA-RBV). The conducted experiments were carried out using 18 instances of DIMACS and BHOSLIB benchmarks. The experimental results revealed the superiority of MCROA-BFS over MVPA, GA, and MCROA-RBV in terms of both performance metrics. Although HCROA has the smallest run time, it failed to obtain high-quality solutions in comparison with MCROA. [ABSTRACT FROM AUTHOR]

In this paper, to keep the researchers interested in nature-inspired algorithms and optimization problems, a comprehensive survey of the group search optimizer (GSO) algorithm is introduced with detailed discussions. GSO is a nature-inspired optimization algorithm introduced by He et al. (IEEE Trans Evol Comput 13:973–990, 2009) to solve several different optimization problems. It is inspired by animal searching behavior in real life. This survey focuses on the applications of the GSO algorithm and its variants and results from the year of its suggestion (2009) to now (2020). GSO algorithm is used to discover the best solution over a set of candidate solution to solve any optimization problem by determining the minimum or maximum objective function for a specific problem. Meta-heuristic optimizations, nature-inspired algorithms, have become an interesting area because of their rule in solving various decision-making problems. The general procedures of the GSO algorithm are explained alongside with the algorithm variants such as basic versions, discrete versions, and modified versions. Moreover, the applications of the GSO algorithm are given in detail such as benchmark function, classification, networking, engineering, and other problems. Finally, according to the analyzed papers published in the literature by the all publishers such as IEEE, Elsevier, and Springer, the GSO algorithm is mostly used in solving various optimization problems. In addition, it got comparative and promising results compared to other similar published optimization algorithm. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive Fluctuant Population size Slime Mould Algorithm (FP-SMA) is proposed. Unlike the original SMA where population size is fixed in every epoch, FP-SMA will adaptively change population size in order to effectively balance exploitation and exploration characteristics of SMA's different phases. Experimental results on 13 standard and 30 IEEE CEC2014 benchmark functions have shown that FP-SMA can achieve significant reduction in run time while maintaining good solution quality when compared to the original SMA. Typical saving in terms of function evaluations for all benchmarks was between 20 and 30% on average with a maximum being as high as 60% in some cases. Therefore, with its higher computation efficiency, FP-SMA is much more favorable choice as compared to SMA in time stringent applications. [ABSTRACT FROM AUTHOR]

Power system stabilizers (PSSs) are extensively used in generator units to enhance the transient stability of the power system. Hence, optimal tuning and placement of the parameters of PSS are crucial for the efficiency of the stabilizer. Researchers have been proposed many methods for optimizing such parameters. In this paper, the Crow search algorithm (CSA), which is based on the intelligence of crows, was employed in a single-machine infinite-bus (SMIB) system to determine the optimum parameters of the PSS. Modeling and simulation of the SMIB and designing of PSS were made by MATLAB/Simulink. PSSs are designed to minimize low-frequency oscillations such as power angle, rotor speed, and field current deviation following a large disturbance. Our objective in this study is the minimization of the rotor speed deviation. The results of the simulations proved the effectiveness and robustness of the optimization process compared to other metaheuristic algorithms such as particle swarm optimization (PSO) and genetic algorithm (GA). When compared to the performance attained by the GA-based and PSO-based PSS controller designs, the simulations show that the CSA-based PSS delivers a far better dynamic response when the system is disrupted. The CSA-based PSS settles 48.1% faster than the PSO-based PSS and 55.7% faster than the GA-based PSS. CSA has just 2 parameters to adjust, making it much easier to implement than other methods. These parameters for PSO and GA are 4 and 6. When CSA-based PSS is used in the SMIB system, overshoot and low-frequency oscillations are also significantly reduced compared to other methods. [ABSTRACT FROM AUTHOR]

In recent years, significant attentions have been devoted to design of metaheuristic optimization algorithms in order to solve optimization problems. Metaheuristic optimizers are methods which are inspired by observing the phenomena occurring in nature. In this paper, a comprehensive and exhaustive review has been carried out on water cycle algorithm (WCA) and its applications in a wide variety of study fields. The WCA is one of the novel metaheuristic optimization algorithms which is inspired by water cycle process in nature and how streams and rivers flow into the sea. Good exploitation and exploration capabilities have made the WCA a good alternative for solving large-scale optimization problems. Due to its capabilities and strengths, the WCA has been utilized in many and various majors including mechanical engineering, electrical and electronic engineering, civil engineering, industrial engineering, water resources and hydropower engineering, computer engineering, mathematics, and so forth. A variety of articles based on WCA have been published in different international journals such as Elsevier, Springer, IEEE Transactions, Wiley, Taylor & Francis, and in the proceedings of international conferences as well, since 2012 to the present. Thus, it is highly believed that this paper can be appropriate, beneficial and practical for students, academic researchers, professionals, and engineers. Also, it can be an innovative and comprehensive reference for subsequent academic papers and books relevant to the WCA, optimization methods, and metaheuristic optimization algorithms. [ABSTRACT FROM AUTHOR]

This paper introduces a new evolutionary computing method inspired by the seed transmission process of garden balsam. Garden balsam, a beautiful and attractive flower, randomly ejects the seeds within a certain range by virtue of mechanical force originating from cracking of mature seed pods, which is different from natural expansion of most species of plants. The seeds scattered to suitable growth area will have greater reproductive capacity in the next generation, followed by iteration until the most suitable point for growth in a particular space is eventually found. This phenomenon can more intuitively show the process of searching the problem solution space in the optimization problem. The garden balsam optimization algorithm proposed in this paper incorporates two different types of search processes and has a mechanism to maintain population diversity. Through the optimization experiment on 24 constrained optimization problems, the results obtained by using this algorithm are compared with those of some known meta-heuristic search algorithms. The statistical analysis of the experimental results has been implemented by Friedman rank test and Holm–Sidak test. The comparison results verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

A recent metaheuristic algorithm, such as Whale optimization algorithm (WOA), was proposed. The idea of proposing this algorithm belongs to the hunting behavior of the humpback whale. However, WOA suffers from poor performance in the exploitation phase and stagnates in the local best solution. Grey wolf optimization (GWO) is a very competitive algorithm comparing to other common metaheuristic algorithms as it has a super performance in the exploitation phase, while it is tested on unimodal benchmark functions. Therefore, the aim of this paper is to hybridize GWO with WOA to overcome the problems. GWO can perform well in exploiting optimal solutions. In this paper, a hybridized WOA with GWO which is called WOAGWO is presented. The proposed hybridized model consists of two steps. Firstly, the hunting mechanism of GWO is embedded into the WOA exploitation phase with a new condition which is related to GWO. Secondly, a new technique is added to the exploration phase to improve the solution after each iteration. Experimentations are tested on three different standard test functions which are called benchmark functions: 23 common functions, 25 CEC2005 functions, and 10 CEC2019 functions. The proposed WOAGWO is also evaluated against original WOA, GWO, and three other commonly used algorithms. Results show that WOAGWO outperforms other algorithms depending on the Wilcoxon rank-sum test. Finally, WOAGWO is likewise applied to solve an engineering problem such as pressure vessel design. Then the results prove that WOAGWO achieves optimum solution which is better than WOA and fitness-dependent optimizer (FDO). [ABSTRACT FROM AUTHOR]

Modifying the metaheuristics as a striking alternative of basic algorithms is outstanding and efficient scientific approach in optimization of engineering problems to improve robustness and convergence rate. Firefly algorithm (FA) is one of the new metaheuristics inspired by the flashing behavior of fireflies, where the performance of each randomly generated solution on objective function is evaluated by the brightness. In the current paper, a modified firefly algorithm (MFA) was introduced using expectation value and generalized weighted average of a random brightness and then evaluated with different benchmark functions. Since brightness varies with movements of fireflies, the parameter settings can adaptively be tuned for different problems. The capability of the MFA then in hybridizing with a developed automated multi-objective radial-based function network (MORBF) was examined. In blasting engineering, multi-objective models covering the peak particle velocity (PPV) and the vibration frequency (Fvib) due to providing more insight on safety criteria significantly are essential and great of interested. The hybrid MORBF-MFA then was applied on 78 blasting data comprising stemming, burden, spacing, total charge, distance, and charge per delay to provide more accurate predictive model. Detailed executed analyses through different metrics showed 1.01% and 2.43% improvement in hybrid MORBF-MFA corresponding to PPV and Fvib over MORBF-FA. The observed results approved that the introduced MFA as a reliable and feasible tool with accurate enough response can effectively be applied to multi-objective problems. Implemented sensitivity analyses scored the distance and burden as the most and least influences factors on predicted outputs. [ABSTRACT FROM AUTHOR]

This paper presents a novel meta-heuristic algorithm called Ali Baba and the forty thieves (AFT) for solving global optimization problems. Recall the famous tale of Ali Baba and the forty thieves, where Ali Baba once saw a gang of forty thieves enter a strange cave filled with all kinds of treasures. The strategies pursued by the forty thieves in the search for Ali Baba inspired us to design ideas and underlie the basic concepts to put forward the mathematical models and implement the exploration and exploitation processes of the proposed algorithm. The performance of the AFT algorithm was assessed on a set of basic benchmark test functions and two more challenging benchmarks called IEEE CEC-2017 and IEEE CEC-C06 2019 benchmark test functions. These benchmarks cover simple and complex test functions with various dimensions and levels of complexity. An extensive comparative study was performed between the AFT algorithm and other well-studied algorithms, and the significance of the results was proved by statistical test methods. To study the potential performance of AFT, its further development is discussed and carried out from five aspects. Finally, the applicability of the AFT algorithm was subsequently demonstrated in solving five engineering design problems. The results in both benchmark functions and engineering problems show that the AFT algorithm has stronger performance than other competitors' algorithms. [ABSTRACT FROM AUTHOR]

Cloud providers deliver heterogeneous virtual machines to run complicated jobs submitted by users. The task scheduling issue is formulated to a discrete optimization problem which is well-known NP-Hard. This paper presents a hybrid meta-heuristic algorithm based on genetic and thermodynamic simulated annealing algorithms to solve this problem. In the proposed algorithm, the genetic and simulated annealing algorithms have respective global and local search inclinations covering each other's shortcomings. A novel theorem is presented and applied to produce a semi-conducted initial population. In a used genetic algorithm with a global trend, the crossover operator is performed to explore search space. The thermodynamic simulated annealing algorithm is utilized to improve the efficiency, which considers entropy and energy difference concepts in the cooling schedule process. After obtaining a suitable solution, one of the three novel neighbor operators is randomly called to enhance the given solution potentially. In this way, the efficient balance between exploration and exploitation in the search space is achieved. Simulation results prove that the proposed hybrid algorithm has 10.17%, 9.31%, 7.76%, and 8.21% dominance in terms of makespan, schedule length ratio, speedup, and efficiency against other comparative algorithms. [ABSTRACT FROM AUTHOR]

Cryptography often involves substituting (and converting) the secret information into dummy data so that it could reach the desired destination without leakage. Within symmetric key cryptography, substitution-box (S-box) is often adopted to perform the actual block cipher substitution. To address the nonlinear requirement of cryptography (i.e., ensuring the generated S-box is sufficiently robust against linear and differential cryptanalysis attacks), many chaos-based metaheuristic algorithms have been developed in the literature. This paper introduces a new variant of a metaheuristic algorithm based on Tiki-Taka algorithm, called selective chaotic maps Tiki-Taka algorithm (SCMTTA). Unlike competing works (which typically integrates a single chaotic map into a particular metaheuristic algorithm), SCMTTA assembles five chaotic maps (i.e., tent map, logistic map, Chebyshev map, singer map and sine map) as part of the algorithm itself in order to further enhance ergodicity and unpredictability of the generated solution. Based on a simple penalized and reward mechanism, one best performing chaotic map will be selected in the current cycle, while the poor performing one will miss its current turn. Experimental results on the case study related to the generation of 8 × 8 substitution-box demonstrate that the proposed SCMTTA gives competitive performance against other existing works due to its ability to adaptively modify its chaotic behavior based on the performance feedback of the current search process. [ABSTRACT FROM AUTHOR]

This paper propounds a new metaheuristic optimization algorithm to obtain the optimum site and size of distributed generation (DG) in radial distribution system (RDS). This problem is concomitant with reducing the active power loss, the total voltage deviation and the voltage stability index of the RDS considering different types of load models (such as constant power (CP), industrial (IL), residential (RES) as well as commercial (COM)). To solve this weighting factor-based multi-objective DG allocation problem, a novel metaheuristic optimization algorithm, student psychology-based optimization (SPBO), is suggested in this article. A multi-criteria approach (such as the analytic hierarchy process) is employed to optimize the weighting factors involved. To the best of the authors' knowledge, this is the first time that this novel SPBO algorithm is being used for optimal siting and sizing of DGs in the RDS for different types of load models (like CP, IL, RES and COM) for IEEE 33-bus, IEEE 69-bus and practical Brazil 136-bus RDS. The simulation results attained by the proposed SPBO algorithm are compared with the results provided by recently surfaced Harris hawks optimization (HHO) algorithm and other state-of-the-art algorithms. The outcomes prove that the suggested SPBO algorithm is more efficient to solve the optimal multiple DG allocation problem with minimum real power loss, less computational time and prominent convergence rate. [ABSTRACT FROM AUTHOR]

This paper presents a powerful swarm intelligence metaheuristic optimization algorithm called Dynamic Cat Swarm Optimization. The formulation is through modifying the existing Cat Swarm Optimization Algorithm. The original Cat Swarm Optimization suffers from the shortcoming of "premature convergence," which is the possibility of entrapment in local optima which usually happens due to the off balance between exploration and exploitation phases. Therefore, the proposed algorithm suggests a new method to provide a proper balance between these phases by modifying the selection scheme and the seeking mode of the algorithm. To evaluate the performance of the proposed algorithm, 23 classical test functions, 10 modern test functions (CEC 2019) and a real-world scenario are used. In addition, the dimension-wise diversity metric is used to measure the percentage of the exploration and exploitation phases. The optimization results show the effectiveness of the proposed algorithm, which ranks first compared to several well-known algorithms available in the literature. Furthermore, statistical methods and graphs are also used to further confirm the outperformance of the algorithm. Finally, the conclusion and future directions to further improve the algorithm are discussed. [ABSTRACT FROM AUTHOR]

In this paper, a new stochastic optimizer called slime mould algorithm (SMA) for solving the optimal coordination of directional overcurrent relays in meshed power networks is proposed. The proposed SMA-based method deals with the coordination problem using the most recent digital relays by selecting the optimal tripping standardized curve plus time dial and current pickup. Afterwards, the problem gets more sophisticated by bounding the relay tripping time inside a practical range to simulate the real network conditions. SMA's performance is evaluated on two different test cases including highly penetrated distributed generators in the second one. The results of SMA are compared with other recent metaheuristic and conventional approaches reported in the literature under same conditions aimed at fair comparisons. It is declared that the SMA attains 29.9% reduction in the relays total operating time for the first test case compared to the well-matured water cycle algorithm. Even, if the tested network is a highly penetrated by distributed generators, more reduction is achieved by 33.7% with better convergence characteristics. It can be established that the SMA-based method demonstrates a competitive and reliable tool for minimizing the relays total operating time satisfying all the constraints even for the sophisticated scenarios. [ABSTRACT FROM AUTHOR]

Computer-aided diagnosis system is becoming a more and more important tool in clinical treatment, which can provide a verification of the doctors' decisions. In this paper, we proposed a novel abnormal brain detection method for magnetic resonance image. Firstly, a pre-trained AlexNet was modified with batch normalization layers and trained on our brain images. Then, the last several layers were replaced with an extreme learning machine. A searching method was proposed to find the best number of layers to be replaced. Finally, the extreme learning machine was optimized by chaotic bat algorithm to obtain better classification performance. Experiment results based on 5 × hold-out validation revealed that our method achieved state-of-the-art performance. [ABSTRACT FROM AUTHOR]

Salp swarm algorithm (SSA) is a newly swarm-based metaheuristic algorithm that simulate the swimming and foraging behaviour of salps in oceans so to search for global optimum solution. Similarly to other metaheuristic algorithms, SSA suffers from poor convergence rate and stagnation in local optima. In this paper, three different improvements to the original population update process are proposed in order to enhance its exploitation and exploration capabilities. The first modification (MSSA1) introduces the concept of local best information to the followers salps update process allowing a better exploration of local search neighbourhood. The second improvement (MSSA2) provide two followers update process. The first is based on a differential evolution combined with a randomly selected local best position, and the second uses a local search in the global best neighbourhood which is triggered by a non-improvement in the corresponding local best. A third modification to the SSA algorithm (MSSA3) penalises a non-improvement of the local best solution by computing a new corresponding follower's position based on a local jump in the local best neighbourhood for better exploitation. The performances of the proposed algorithms are tested on 27 CEC'15 test suite, and two real-world optimisation problems. A comparative study using nonparametric statistical tests of the obtained results is conducted against those of eight well-known metaheuristics, including the original SSA. The results indicate an overall distinctive performance of all three modification compared to the remaining algorithms, while MSSA1 scored generally better than MSSA2 and MSSA3. [ABSTRACT FROM AUTHOR]

This paper discusses a new variant of Henry Gas Solubility Optimization (HGSO) Algorithm, called Hybrid HGSO (HHGSO). Unlike its predecessor, HHGSO allows multiple clusters serving different individual meta-heuristic algorithms (i.e., with its own defined parameters and local best) to coexist within the same population. Exploiting the dynamic cluster-to-algorithm mapping via penalized and reward model with adaptive switching factor, HHGSO offers a novel approach for meta-heuristic hybridization consisting of Jaya Algorithm, Sooty Tern Optimization Algorithm, Butterfly Optimization Algorithm, and Owl Search Algorithm, respectively. The acquired results from the selected two case studies (i.e., involving team formation problem and combinatorial test suite generation) indicate that the hybridization has notably improved the performance of HGSO and gives superior performance against other competing meta-heuristic and hyper-heuristic algorithms. [ABSTRACT FROM AUTHOR]

Swarm intelligence is all about developing collective behaviours to solve complex, ill-structured and large-scale problems. Efficiency in collective behaviours depends on how to harmonise the individual contributors so that a complementary collective effort can be achieved to offer a useful solution. The main points in organising the harmony remain as managing the diversification and intensification actions appropriately, where the efficiency of collective behaviours depends on blending these two actions appropriately. In this paper, a hybrid bee algorithm is presented, which harmonises bee operators of two mainstream well-known swarm intelligence algorithms inspired of natural honeybee colonies. The parent algorithms have been overviewed with many respects, strengths and weaknesses are identified, first, and the hybrid version has been proposed, next. The efficiency of the hybrid algorithm is demonstrated in comparison with the parent algorithms in solving two types of numerical optimisation problems; (1) a set of well-known functional optimisation benchmark problems and (2) optimising the weights of a set of artificial neural network models trained for medical classification benchmark problems. The experimental results demonstrate the outperforming success of the proposed hybrid algorithm in comparison with two original/parent bee algorithms in solving both types of numerical optimisation benchmarks. [ABSTRACT FROM AUTHOR]

Cloud computing provides infinite resources and various services for the execution of variety of applications to end users, but still it has various challenges that need to be addressed. Objective of cloud users is to select the optimal resource that meets the demand of end users in reasonable cost and time, but sometimes users pay more for short time. Most of the proposed state-of-the-art algorithms try to optimize only one parameter at a time. Therefore, a novel compromise solution is needed to make the balance between conflicting objectives. The main goal of this research paper is to design and develop a task processing framework that has the decision-making capability to select the optimal resource at runtime to process the applications (diverse and complex nature) at virtual machines using modified particle swarm optimization (PSO) algorithm within a user-defined deadline. Proposed algorithm gives non-dominance set of optimal solutions and improves various influential parameters (time, cost, throughput, task acceptance ratio) by series of experiments over various synthetic datasets using Cloudsim tool. Computational results show that proposed algorithm well and substantially outperforms the baseline heuristic and meta-heuristic such as PSO, adaptive PSO, artificial bee colony, BAT algorithm, and improved min–min load-balancing algorithm. [ABSTRACT FROM AUTHOR]

Cloud manufacturing as an emerging service-oriented manufacturing paradigm integrates and manages geographically distributed manufacturing resources such that complex and highly customized manufacturing tasks can be performed cooperatively. The service composition and optimal selection (SCOS) problem, in which manufacturing cloud services are optimally selected for performing subtasks, is one of the key issues for implementing a cloud manufacturing system. In this paper, we propose a new mixed-integer programming model for solving the SCOS problem with sequential composition structure. Unlike the majority of previous research on the problem, in the proposed model, the transportation between distributed resources and its effects on quality of services are considered. Although a wide variety of metaheuristics have been tailored for solving the SCOS problem, no consistent and comprehensive conclusion has been reached so far on the superiority of a specific algorithm. Therefore, for the first time, solution space landscape of the problem was analyzed through several statistical criteria which demonstrated that the landscape is rugged and local optima are clustered in a small region of the search space. Therefore, to find good solutions, a metaheuristic algorithm needs to perform both proper exploitation and exploration of the search space. According to the landscape analysis, the basic imperialist competitive algorithm (ICA) was hybridized with a local search (LS) algorithm resulting in the hybrid ICA (HICA). To examine the performance of the proposed HICA, an example of online motorcycle production in the USA as well as four randomly generated large-scale instances, were solved through the LS, ICA, and HICA. Computational results showed that transportation consideration is indispensable for obtaining more realistic solutions in cloud manufacturing. The results also revealed that the HICA outperformed the LS and basic ICA in terms of the value of cost objective function, the stability of solutions and convergence speed. Hence, not only statistically but also analytically, it was proved that algorithms incorporating both exploitation and exploration are able to solve the SCOS problem more efficiently. [ABSTRACT FROM AUTHOR]

For the purpose of usability feature extraction and prediction, an innovative metaheuristic algorithm is introduced. Generally, the term "usability" is defined by the several researchers with respect to the hierarchical-based software usability model and it has become one of the important methods in terms of software quality. In hierarchically based software, its usability factors, attributes, and its characteristics are combined. The paper presented an algorithm, i.e., modified crow search algorithm (MCSA) mainly for extraction of usability features from hierarchical model with the optimal solution under the search for useful features. MCSA is an extension of original crow search algorithm (CSA), which is a naturally inspired algorithm. The mechanism of this algorithm is based on the process of hiding food and prevents theft and hence introduced this CSA in the field of software engineering practices as an inspiration. The algorithm generates a particular number of selected features/attributes and is applied on software development life cycles models, finding out the best among them. The results of the presented algorithm are compared with the standard binary bat algorithm (BBA), original CSA, and modified whale optimization algorithm (MWOA). The outcomes conclude that the proposed MCSA performs well than the standard BBA and original CSA as the proposed algorithms generate fewer number of feature selection equal to 17 than 18 in BBA, 23 in CSA, and 19 in MWOA. [ABSTRACT FROM AUTHOR]

Most real-world optimization problems often come with multiple global optima or local optima. Therefore, increasing niching metaheuristic algorithms, which devote to finding multiple optima in a single run, are developed to solve these multimodal optimization problems. However, there are two difficulties urgently to be solved for most existing niching metaheuristic algorithms: how to set the niching parameter values for different optimization problems and how to jump out of the local optima efficiently. These two difficulties limit their practicality largely. Based on Whale Swarm Algorithm (WSA) we proposed previously, this paper presents a new multimodal optimizer named WSA with Iterative Counter (WSA-IC) to address these two difficulties. On the one hand, WSA-IC improves the iteration rule of the original WSA for multimodal optimization, which removes the need of specifying different values of attenuation coefficient for different problems to form multiple subpopulations, without introducing any niching parameter. On the other hand, WSA-IC enables the identification of extreme points during the iterations relying on two new parameters (i.e., stability threshold T s and fitness threshold T f ), to jump out of the located extreme points. Moreover, the convergence of WSA-IC is proved. Finally, the proposed WSA-IC is compared with several niching metaheuristic algorithms on CEC2015 niching benchmark test functions and on five additional high-dimensional multimodal functions. The experimental results demonstrate that WSA-IC statistically outperforms other niching metaheuristic algorithms on most test functions. [ABSTRACT FROM AUTHOR]

In this research, a quantum computing idea based bat algorithm (QBA) is proposed to solve many-objective combined economic emission dispatch (CEED) problem. Here, CEED is represented using cubic criterion function to reduce the nonlinearities of the system. Along with economic load dispatch, emissions of SO2, NOx, and CO2 are considered as separate three objectives, thus making it a four-objective (many-objective) optimization problem. A unit-wise price penalty factor is considered here to convert all the objectives into a single objective in order to compare the final results with other previously used methods like Lagrangian relaxation (LR), particle swarm optimization, and simulated annealing. QBA is applied in six-unit power generation system for four different loads. The obtained results show QBA successfully solve many-objective CEED problem with greater superiority than other methods found in the literature in terms of quality results, robustness, and computational performance. In the end of this paper, a detailed future research direction is provided based on the simulation results and its analysis. The outcome of this research demonstrates that the inclusion of quantum computing idea in metaheuristic technique provides a useful and reliable tool for solving such many-objective optimization problem. [ABSTRACT FROM AUTHOR]

This paper proposes a self-organizing hierarchical monkey algorithm (SHMA) with a time-varying parameter to improve the performance of the original monkey algorithm (MA). In the proposed SHMA, we adopt a hierarchical structure to organize the climb, watch, and somersault operations and apply a self-organizing mechanism to coordinate these operations. Moreover, a time-varying parameter is employed to adjust the exploration ability and exploitation ability during the optimization process. The SHMA also applies the fitness information of solutions to guide the optimization process and introduces a selection operator, a fitness-based replacement operator, and a repulsion operator into the climb, watch and somersault operations, respectively. To investigate the performance of the SHMA, we compare it with eight different metaheuristic algorithms on 30 benchmark problems and four real-world optimization problems. The simulation results show that the SHMA exhibits better overall performance than the eight compared algorithms. [ABSTRACT FROM AUTHOR]

Salp swarm algorithm (SSA) is one of the recent meta-heuristic algorithms that imitate the behaviors of salps during the navigating and foraging in oceans to perform global optimization. However, the original study of this algorithm was proposed to solve continuous problems, and it cannot be applied to binary problems directly. In this paper, a new binary version of the SSA named BSSA is proposed based on a modified Arctan transformation. This modification has two features regarding the transfer function, namely multiplicity and mobility. By this modification, the exploration and exploitation capabilities can be enhanced. The proposed BSSA is compared among four variants of transfer functions for solving global optimization problems. Also, a comparative study with different binary algorithms including binary particle swarm, binary bat algorithm and binary sine–cosine algorithm on twenty-four benchmark problems is conducted. Furthermore, the nonparametric statistical test based on Wilcoxon's rank-sum is carried out at 5% significance level to judge statistically the significant of the obtained results among the different algorithms. The results affirm the superior performance of the modified BSSA variant over the other variants as well as the existing approaches regarding solution quality. [ABSTRACT FROM AUTHOR]

Just-In-Time (JIT) is a popular philosophy in many industrial practices. The concept of JIT in early studies concerned with improving operational efficiency and waste minimization. In recent decades, however, JIT principles have also connected to logistics efficiency particularly for distribution of raw materials and finished goods. In the literature, several attempts have been made to optimize JIT logistics networks. On the one hand, most studies have typically focused on deterministic and small-scale problems which have been solved by exact algorithms. On the other hand, when large-scale problems were considered and usually were solved by metaheuristics algorithms, uncertainty sources and fine-tuning of the metaheuristics parameters were generally ignored. In this paper, we develop a mixed-integer linear optimization model to investigate a large-scale JIT logistics problem with 15 different sizes. To deal with different uncertainty sources, the customers demand and suppliers’ capacity as the two main sources of uncertainty in practice are considered as triangular fuzzy parameters. The proposed model aims to minimize total logistics cost including costs of transportation, inventory holding and backorders. A particle swarm optimization algorithm is applied to solve the problem, and its results are then validated by a harmony search algorithm. Both algorithms parameters are tuned using response surface methodology and Taguchi method. Finally, the conclusion and some directions for future research are proposed. [ABSTRACT FROM AUTHOR]

This paper proposes Drone Squadron Optimization (DSO), a new self-adaptive metaheuristic for global numerical optimization which is updated online by a hyper-heuristic. DSO is an artifact-inspired technique, as opposed to many nature-inspired algorithms used today. DSO is very flexible because it is not related to natural behaviors or phenomena. DSO has two core parts: the semiautonomous drones that fly over a landscape to explore, and the command center that processes the retrieved data and updates the drones’ firmware whenever necessary. The self-adaptive aspect of DSO in this work is the perturbation/movement scheme, which is the procedure used to generate target coordinates. This procedure is evolved by the command center during the global optimization process in order to adapt DSO to the search landscape. We evaluated DSO on a set of widely employed single-objective benchmark functions. The statistical analysis of the results shows that the proposed method is competitive with the other methods, but we plan several future improvements to make it more powerful and robust. [ABSTRACT FROM AUTHOR]