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It is well recognized that human societies and their problem-solving capabilities have evolved much faster than biological evolution. The inspiration from human behaviors, knowledge exchange, and transformation has given rise to a new evolutionary computation paradigm. Multiple research endeavors have been reported in the literature inspired by the diverse aspects of human societies with corresponding terminologies to describe the algorithm. These endeavors have resulted in piles of algorithms, worded differently but with more or less similar underlying mechanisms causing immense confusion for a new reader. This paper presents a generalized framework for these socio-inspired evolutionary algorithms (SIEAs) or socio-inspired meta-heuristic algorithms. A survey of various SIEAs is provided to highlight the working of these algorithms on a common framework, their variations and improved versions proposed in the literature, and their applications in various fields of search and optimization. The algorithmic description and the comparison of each SIEA with the general framework enable a clearer understanding of the similarities and differences between these methodologies. Efforts have been made to provide an extensive list of references with due context. This paper could become an excellent reference as a starting point for anyone interested in this fascinating field of research. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is among the best evolutionary algorithms for global optimization. However, the basic DE has several shortcomings, like the slow convergence speed, and it is more likely to be stuck at local optima. Additionally, DE's performance is sensitive to its mutation strategies and control parameters for mutation and crossover. In this scope, we present in this paper three mechanisms to overcome DE limitations. First, two novel mutations called DE/mean-current/2 and DE/best-mean-current/2 are proposed and integrated in the DE algorithm, and they have both exploration ability and exploitation trend. On the other hand, to avoid being trapped in local minima of hard functions, a new exploration operator has been proposed called Weibull flight based on the Weibull distribution. Finally, new adapted control parameters based on the Weibull distribution are integrated. These parameters contribute to the optimization process by adjusting mutation scale and alleviating the parameter setting problem often encountered in various metaheuristics. The efficacy of the proposed algorithms called meanDE, MDEW, AMDE, and AMDEW is validated through intensive experimentations using classical tests, some challenging tests, the CEC2017, CEC2020, the most recent CEC2022, four constraint engineering problems, and the data clustering problem. Moreover, comparisons with several popular, recent, and high-performance optimization algorithms show a high effectiveness of the proposed algorithms in locating the optimal or near-optimal solutions with higher efficiency. The experiments clearly indicate the effectiveness of the new mutations compared to the standard DE mutations. Moreover, the proposed Weibull flight has a great capacity to deal with the hard composition functions of CEC benchmarks. Finally, the use of adapted control parameters for the mutation scale helps overcome the parameter setting problem commonly encountered in various metaheuristics. [ABSTRACT FROM AUTHOR]

In the past few decades, meta-heuristic algorithms have become a research hotspot in the field of evolutionary computing. The electric fish optimization algorithm (EFO) is a new meta-heuristic algorithm. Because of its simplicity and easy implementation, it has attracted the attention of researchers. However, it still faces premature convergence and poor balance between exploration and exploitation. To address this problems, an orthogonal electric fish optimization algorithm with quantization (QOXEFO) is proposed in this paper. In QOXEFO, orthogonal cross-design and quantification technique are employed to enhance the diversity of population and convergence precision of EFO. Secondly, the dynamic boundary mechanism is adopted to improve the convergence speed of EFO. At the same time, a sine-based update strategy of active electrolocation is used to change the direction of movement of individuals, thereby helping them jump out of the local optimum. Finally, the CEC2017 benchmark function and Speed reducer design problem are used to verify the performance of the proposed QOXEFO. Experimental results and statistical analysis show that compared with 9 famous evolutionary algorithms, QOXEFO is competitive in solution accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

This paper introduces the Golf Sport Inspired Search (GSIS) algorithm as an evolutionary search method for numerical optimization. Each solution is generated with the aid of the step-length and search direction. The step-length is determined with the aid of the Tait's model of the trajectory of the golf ball, which is a physical model. The search direction is from the current position in the search space toward the position of a different individual or its reflected position. Such a direction determines the movement direction in the optimization process. A crossover operator is introduced to increase exploration at the starting and exploitation at the ending stages of the search. Performance of the GSIS is compared with many algorithms on 23 + 14 unconstrained classic functions, 29 functions of CEC 2017 benchmark suite and six constrained engineering design problems. Experiments indicate that with the aid of its cleverly designed operators, GSIS is able to produce promising results. Besides a cooperative game theoretic approach is introduced, which is able to measure the effectiveness of different operators in reducing the search cost. Such an approach can be used to measure the effectiveness of different operators that an evolutionary or swarm-intelligence algorithm owns. [ABSTRACT FROM AUTHOR]

During the optimization process, a large number of data are generated through the search. Machine learning techniques and algorithms can be used to handle the generated data to contribute to the optimization process. The use of machine learning enhancing metaheuristics applied to optimization problems has been drawing attention due to their capacity to add domain knowledge during the search process. This knowledge can accelerate metaheuristics and lead to better and promising solutions. This work provides a systematic literature review of machine learning enhancing metaheuristics and summarizes the current state of the classification of the research field, main techniques and machine learning models, validations strategies, and real-world optimization problems that the approach was applied. Our keyword search found 1.960 papers, published in the last 10 years. After considering the inclusion and exclusion criteria and performing backward snowballing procedure, we have analyzed 111 primary studies. The results show the predominance of the use of surrogate-assisted evolutionary algorithms (SAEAs) for improving the efficiency of the optimization, and the use of estimation of distribution algorithms (EDAs) to increase the effectiveness of the optimization. The objective function value is the mostly applied evaluating criteria to validate the algorithm with other methods. The developed techniques of the studies found are applied in diverse real-world applications such as developing machine learning models, physics simulations with expensive function evaluation, and the variants of the classical job shop scheduling problem. We also discuss trends and opportunities of the research field. [ABSTRACT FROM AUTHOR]

Model-based testing is an automated process in which executable tests are derived from behavioral models of a system. Model checking is a verification technique to reveal errors in which all reachable states of a system can be generated as state space. In the literature, different approaches suggest using model checkers for model-based testing. Model checker explores all possible system states, so utilizing the various paths in the state-space as test cases seems a promising solution. However, these approaches suffer from two main challenges. The first challenge is state space explosion, which prevents generating all reachable states by the model checker. The second one is generating redundant test cases. Recently, several methods using meta-heuristic and evolutionary approaches have been proposed to cope with these problems. Therefore, exploring a portion of state space using an optimization approach to detect the test objectives can be a proper way to manage the state space explosion and generate an optimal test suite with the least redundancy. In this paper, a method is proposed using a Bayesian optimization algorithm (BOA), and a model checker is as a bed to generate test cases for the service-oriented systems. In the proposed approach, the test suite is a set of paths on the state space starting from an initial state and leading to the state in which all the test objectives are satisfied. In this research, we have implemented BOA with three different structures in GROOVE toolset, an open-source toolset for designing and model checking graph transformation. Experimental results show that our solution generates better results in terms of coverage and speed in different case studies than the existing approaches. [ABSTRACT FROM AUTHOR]

Hazardous wastes' volume produced by human activities has increased in recent years. Consequently, associated risks involved in the treatment, recycling, disposing, and transportation of these hazardous materials have become more attractive for the researchers. In this study, we propose a new model for hazardous waste location routing problem. Appending the service time window and workload balance to the previous mathematical models can be taken into account as the major contributions of this study. Three objective functions including two systematic goals (cost and risk) and one social goal (workload balancing) have been considered for the model. Compatibility between wastes and a heterogeneous fleet of vehicles, which are rarely investigated in the literature, is discussed in this paper. Since the proposed model is classified as a multi-objective model, three multi-objective evolutionary algorithms, namely Non-dominated Sorting Genetic Algorithm II (NSGA-II), Pareto Envelope-based Selection Algorithm II (PESA-II), and Strength Pareto Evolutionary Algorithm II (SPEA-II) are employed. As two other innovations, an adaptive penalty function is developed and the PESA-II is modified by removing replicated solutions from its archive and their obtained results are discussed. Finally, by experimenting a number of test problems in different sizes, it is demonstrated that proposed modified PESA-II and SPEA-II perform better than NSGA-II in most of comparison metrics including feasible answers exploration, CPU time, spacing metric, inverted generational distance, quality metric, etc., whereas, NSGA-II creates more spread Pareto frontiers which are suitable for decision-maker to choose, from among a range of different options. [ABSTRACT FROM AUTHOR]

Salp Swarm Algorithm (SSA) is a new type of metaheuristic and has shown superiority over other well-known algorithms such as Particle Swarm Optimization and Grey Wolf Optimizer in solving challenging optimization problems. Despite its superior performance, SSA still has problems such as insufficient convergence speed. Moreover, its local optima avoidance ability is not as good as those evolutionary algorithms using crossover operators. In this paper, we propose a modified Salp Swarm Algorithm (m-SSA) which improves the exploitation and exploration of SSA by integrating random walk strategy and especially enhances exploration by adding a new controlling parameter. In addition, a simulated annealing-type acceptance criterion is adopted to accept the fittest follower position as the new best leader position. The performance of the proposed algorithm is benchmarked on a set of classical functions and CEC2014 test suite. The proposed algorithm (m-SSA) outperforms SSA significantly on most test functions. When compared with other state-of-the-art metaheuristics, it also presents very competitive results. Besides, we apply the proposed algorithm on training feedforward neural networks (FNNs) and the results prove the effectiveness and efficiency of m-SSA. [ABSTRACT FROM AUTHOR]

Nature has been considered as an inspiration of several recent meta-heuristic algorithms. This paper firstly studies and mimics the behavior of Scottish red deer in order to develop a new nature-inspired algorithm. The main inspiration of this meta-heuristic algorithm is to originate from an unusual mating behavior of Scottish red deer in a breading season. Similar to other population-based meta-heuristics, the red deer algorithm (RDA) starts with an initial population called red deers (RDs). They are divided into two types: hinds and male RDs. Besides, a harem is a group of female RDs. The general steps of this evolutionary algorithm are considered by the competition of male RDs to get the harem with more hinds via roaring and fighting behaviors. By solving 12 benchmark functions and important engineering as well as multi-objective optimization problems, the superiority of the proposed RDA shows in comparison with other well-known and recent meta-heuristics. [ABSTRACT FROM AUTHOR]

This paper deals with hybrid flow shop scheduling problem with unrelated and eligible machines along with fuzzy processing times and fuzzy due dates. The objective is to minimize a linear combination of total completion time and maximum lateness of jobs. A mixed integer mathematical model is presented for the problem. The most challenging parts of hybrid evolutionary algorithms are determination of efficient strategies by which the whole search space is explored to perform local search around the promising search areas. In this study, a clustering-based approach as a data mining tool is introduced to identify the promising search areas. A repetitive clustering with an evolutionary algorithm is simultaneously employed to determine more promising parts of the solution space. Then, the searches in those parts are intensified with a local search. Here, two clustering-based meta-heuristic algorithms are applied to solve the problem, namely particle swarm optimization and genetic algorithm. The parameters are tuned by Taguchi experimental design, and various randomly generated test problems are used to evaluate the efficiency of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Plenty of problems are related to the calculation of edges and nodes in the realistic networks. It also influences the realization of shortest path problem (SPP) because of its essential fuzziness. This paper presents a fuzzy-based modified particle swarm optimization (fuzzy-based MPSO) algorithm for resolving the shortest path issue. The proposed work also evaluates the uncertainties of this shortest path problem through the utilization of offered algorithm. Actually, the normal PSO algorithm is altered and estimated to tackle the fuzzy-based SPP (FSPP) with uncertain edges. The performance of the planned algorithm will be improved; also the results are compared with the existing methodologies. The early convergence of the PSO technique can be alleviated and travelled via the dynamic operation of fuzzy method. And the proposed method is compared with other metaheuristic algorithms such as evolutionary random weight networks (GA-RWNs), grasshopper optimization algorithm with evolutionary population dynamics (GOA-EPD), levy weight grey wolf optimization (LGWO) and PSO in terms of cost and time consumption. The related results and discussion is performed in the working platform of MATLAB tool for the demonstration of the proposed work to manage the FSPP in indeterminate networks. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is one of the most powerful and effective evolutionary algorithms for solving global optimization problems. However, just like all other metaheuristics, DE also has some drawbacks, such as slow and/or premature convergence. This paper proposes a new subset-to-subset selection operator to improve the convergence performance of DE by randomly dividing target and trial populations into several subsets and employing the ranking-based selection operator among corresponding subsets. The proposed framework gives more survival opportunities to trial vectors with better objective function values. Experimental results show that the proposed method significantly improves the performance of the original DE algorithm and several state-of-the-art DE variants on a series of benchmark functions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a multi-objective imperialistic competitive algorithm (MOICA) for solving global multi-objective optimization problems. The MOICA is a modified and improved multi-objective version of the single-objective imperialistic competitive algorithm previously proposed by Atashpaz-Gargari and Lucas (IEEE Congr Evolut Comput 7:4661-4666. doi:10.1109/CEC.2007.4425083, 2007). The presented algorithm utilizes the metaphor of imperialism to solve optimization problems. Accordingly, the individuals in a population are referred to as countries, of which there are two types—colonies and imperialists. The MOICA incorporates competition between empires and their colonies for the solution of multi-objective problems. To this end, it employs several non-dominated solution sets, whereby each set is referred to as a local non-dominated solution (LNDS) set. All imperialists in an empire are considered non-dominated solutions, whereas all colonies are considered dominated solutions. In addition to LNDS sets, there is one global non-dominated solution (GNDS) set, which is created from the LNDS sets of all empires. There are two primary operators in the proposed algorithm, i.e., assimilation and revolution, which use the GNDS and LNDS sets, respectively. The significance of this study lies in a notable feature of the proposed algorithm, which is that no special parameter is used for diversity preservation. This enables the algorithm to prevent extra computation to maintain the spread of solutions. Simulations and experimental results on multi-objective benchmark problems show that the MOICA is more efficient compared to a few existing major multi-objective optimization algorithms because it produces better results for several test problems. [ABSTRACT FROM AUTHOR]

The selection mechanisms that are most commonly adopted by multi-objective evolutionary algorithms (MOEAs) are based on Pareto optimality. However, recent studies have provided theoretical and experimental evidence regarding the unsuitability of Pareto-based selection mechanisms when dealing with problems having four or more objectives. In this paper, we propose a novel MOEA designed for solving many-objective optimization problems. The selection mechanism of our approach is based on the transformation of a multi-objective optimization problem into a linear assignment problem, which is solved by the Kuhn-Munkres’ (Hungarian) algorithm. Our proposed approach is compared with respect to three state-of-the-art MOEAs, designed for solving many-objective optimization problems (i.e., problems having four or more objectives), adopting standard test problems and performance indicators taken from the specialized literature. Since one of our main aims was to analyze the scalability of our proposed approach, its validation was performed adopting test problems having from two to nine objective functions. Our preliminary experimental results indicate that our proposal is very competitive with respect to all the other MOEAs compared, obtaining the best results in several of the test problems adopted, but at a significantly lower computational cost. [ABSTRACT FROM AUTHOR]

Harmony search (HS) has shown promising performance in a wide range of real-world applications. However, in many cases, the basic HS exhibits strong exploration ability but weak exploitation capability. In order to enhance the exploitation capability of the basic HS, this paper presents an improved global harmony search with generalized opposition-based learning strategy (GOGHS). In GOGHS, the valuable information from the best harmony is utilized to enhance the exploitation capability. Moreover, the generalized opposition-based learning (GOBL) strategy is incorporated to increase the probability of finding the global optimum. The performance of GOGHS is evaluated on a set of benchmark test functions and is compared with several HS variants. The experimental results show that GOGHS can obtain competitive results. [ABSTRACT FROM AUTHOR]

Evolutionary computation is a research field dealing with black-box and complex optimization problems whose fitness landscapes are usually unknown in advance. It is difficult to select an appropriate evolutionary algorithm and parameters for a given problem due to the black-box setting although many evolutionary algorithms have been developed. In this context, several landscape features have been proposed and their usefulness examined for understanding the problem. In this paper, we propose a novel feature vector by focusing on the local landscape in order to characterize the fitness landscape. The proposed landscape features are a vector form and composed of a histogram of quantized local landscape features. We introduce two implementation methods of this concept, called the bag of local landscape patterns (BoLLP) and the bag of evolvability (BoEvo). The BoLLP uses the fitness pattern of the neighbors of a certain candidate solution, and the BoEvo uses the number of better candidate solutions in the neighbors as the local landscape features. Furthermore, the hierarchical versions of the BoLLP and the BoEvo, concatenated feature vectors with different sample sizes, are considered to capture the landscape characteristic with various resolutions. We extract the proposed landscape feature vectors from well-known continuous optimization benchmark functions and the BBOB benchmark function set to investigate their properties; the visualization of the proposed landscape features, clustering and running time prediction experiments are conducted. Then the effectiveness of the proposed landscape features for the fitness landscape analysis is discussed based on the experimental results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new parallel optimization algorithm that combines ideas from the fields of metaheuristics and Systolic Computing. The algorithm, called Systolic Genetic Search (SGS), is designed to explicitly exploit the high degree of parallelism available in modern Graphics Processing Unit (GPU) architectures. In SGS, solutions circulate synchronously through a grid of processing cells, which apply adapted evolutionary operators on their inputs to compute their outputs that are then ejected from the cells and continue moving through the grid. Four different variants of SGS are experimentally studied for solving two classical benchmarking problems and a real-world application. An extensive experimental analysis, which considered several instances for each problem, shows that three of the SGS variants designed are highly effective since they can obtain the optimal solution in almost every execution for the instances and problems studied, as well as they outperform a Random Search (sanity check) and two Genetic Algorithms. The parallel implementation on GPU of the proposed algorithm has achieved a high performance obtaining runtime reductions from the sequential implementation that, depending on the instance considered, can arrive to around a hundred times, and have also exhibited a good scalability behavior when solving highly dimensional problem instances. [ABSTRACT FROM AUTHOR]

In recent years, search-based software testing (SBST) is the active research topic in software testing. SBST is the process of generating test cases that use metaheuristics for optimization of a task in the framework of software testing to solve difficult NP-hard problems. The best fitness results must be found with the heuristic search among many possibilities for a more cost-effective testing process and automate the process of generating test cases. Although search-based test data generation is a field of interest, some challenges remain unknown. The main objective of this survey is to find the main topics and trends in this emerging field of search-based software testing by examining the methods and the literature of software testing. A review of earlier studies of search-based software testing from the year 1996 to 2016 is discussed with the application of metaheuristics for the optimization of software testing. [ABSTRACT FROM AUTHOR]

Cognitive radio networks have been gaining widespread attraction among researchers especially with the increasing demand for radio frequency spectrum whose availability is quite scarce. Cognitive radio networks provide an ideal solution to allocate spectrum to users on an intelligent basis through a series of spectrum sensing and decision making. A metaheuristic soft computing framework is proposed and implemented in this research work by using powerful optimization concepts of evolutionary algorithm, namely ant colony algorithm, coupled with graph-cut modeling of given wireless network to provide the expected precision of detection. Channel characteristics have been taken as the feature vectors which are modeled as n-tuple graph to decide upon the maximization of channel allocation probability based on availability in an opportunistic basis. Exhaustive experimentations have been conducted and optimal performance justified against other benchmark algorithms. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is a remarkable evolutionary algorithm for global optimization over continuous search space, whose performance is significantly influenced by its mutation operator and control parameters (scaling factor and crossover rate). In order to enhance the performance of DE, we adopt a novel Gaussian mutation operator and a modified common mutation operator to collaboratively produce new mutant vectors, and employ a periodic function and a Gaussian function to generate the required values of scaling factor and crossover rate, respectively. In the proposed variant of DE (denoted by GPDE), the two adopted mutation operators are adaptively applied to generate the corresponding mutant vector of each individual based on their own cumulative scores, the periodic scaling factor can provide a better balance between exploration ability and exploitation ability, and the Gaussian function-based crossover rate will possess fluctuant value, which possibly enhance the population diversity. To verify the performance of proposed GPDE, a suite of thirty benchmark functions and four real-world problems are applied to conduct the simulation experiment. The simulation results demonstrate that the proposed GPDE performs significantly better than five state-of-the-art DE variants and other two meta-heuristics algorithms. [ABSTRACT FROM AUTHOR]

Population-based metaheuristic algorithms have been extensively applied to solve discrete optimization problems. Generally speaking, they work with a set of candidate solutions in the population which evolve during generations using variant reproduction and selection operations to find the optimal solution(s). The population is similar to a small society having several individuals which seek a common goal/solution. This study is motivated from the election systems of societies which can be applied in the population-based algorithms. We propose utilizing the majority voting for discrete population-based optimization algorithms which uses the information of all candidate solutions in the current generation to create a new trial candidate solution, called a president candidate solution. During optimization process, after applying the evolutionary operations, all candidate solutions vote collectively to determine the values of the president's variables. In the proposed method, a majority voting is utilized to choose a value for each variable (gene) of the president candidate solution. This method keeps untouched all other steps of population-based algorithms; therefore, it can be used with any kind of population-based algorithm. As case studies, the discrete differential evolution (DDE) algorithm and the discrete particle swarm optimization (DPSO) are used as the parent algorithms to develop majority voting-based discrete DE (MVDDE) and majority voting-based discrete PSO (MVDPSO). These two algorithms are evaluated on the fifteen discrete benchmark functions with the dimensions of D = 10, 30, 50, 100, 200 and 500. Simulation results confirm that majority voting-based discrete optimization algorithms obtain a promising performance on the majority of the benchmark functions. In addition, we have conducted some tests on large-scale 0-1 knapsack problems with large scales as a real-world application. [ABSTRACT FROM AUTHOR]

Index tracking belongs to one of the most important types of problems in portfolio management. In contrast to classical (active) portfolio management and optimization, passive portfolio management usually seeks to replicate a given index for a financial market. Due to transaction costs or legal or other practical limitation on the tradability of the respective assets, such indexes are often not fully replicated by a respective portfolio. Instead, one seeks to use a subset of the index assets (or other types of assets) to obtain a portfolio most similar to the index. This index tracking problem can be formulated as an optimization problem with respect to the minimization of the tracking error. In this article, we explore possibilities to solve the index tracking problem with invasive weed optimization (IWO), a rather new population-based metaheuristics algorithm. The complexity of this real-life problem and especially its solution space and restrictions require substantial adaptation of the original IWO algorithm. We explore different possibilities to adapt IWO to the considered type of problem. The adapted IWO method is tested using MSCI USA Value data, and systematic studies to find suitable parameter values are conducted. Although the method basically works well, the obtained results do not fully reach our intended benchmark. Reasons for that and possibilities for further improvement of the methodology are discussed. [ABSTRACT FROM AUTHOR]

Interest in multimodal function optimization is expanding rapidly as real-world optimization problems often demand locating multiple optima within a search space. This article presents a new multimodal optimization algorithm named as the collective animal behavior. Animal groups, such as schools of fish, flocks of birds, swarms of locusts, and herds of wildebeest, exhibit a variety of behaviors including swarming about a food source, milling around a central location, or migrating over large distances in aligned groups. These collective behaviors are often advantageous to groups, allowing them to increase their harvesting efficiency to follow better migration routes, to improve their aerodynamic, and to avoid predation. In the proposed algorithm, searcher agents are a group of animals which interact with each other based on the biologic laws of collective motion. Experimental results demonstrate that the proposed algorithm is capable of finding global and local optima of benchmark multimodal optimization problems with a higher efficiency in comparison with other methods reported in the literature. [ABSTRACT FROM AUTHOR]