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The flying foxes optimization (FFO) algorithm, as a newly introduced metaheuristic algorithm, is inspired by the survival tactics of flying foxes in heat wave environments. FFO preferentially selects the best-performing individuals. This tendency will cause the newly generated solution to remain closely tied to the candidate optimal in the search area. To address this issue, the paper introduces an opposition-based learning-based search mechanism for FFO algorithm (IFFO). Firstly, this paper introduces niching techniques to improve the survival list method, which not only focuses on the adaptability of individuals but also considers the population's crowding degree to enhance the global search capability. Secondly, an initialization strategy of opposition-based learning is used to perturb the initial population and elevate its quality. Finally, to verify the superiority of the improved search mechanism, IFFO, FFO and the cutting-edge metaheuristic algorithms are compared and analyzed using a set of test functions. The results prove that compared with other algorithms, IFFO is characterized by its rapid convergence, precise results and robust stability. [ABSTRACT FROM AUTHOR]

This paper delves into the intersection between discrete dynamical systems and bio-inspired metaheuristic algorithms. Chaos, an inherent phenomenon manifested by both continuous and discrete dynamic nonlinear systems has become an essential component of engineering design. This study examines the relationship between chaos and bio-inspired metaheuristic algorithms from two distinct angles: the presence of chaos within the realm of algorithms, and the application of bio-inspired algorithms for the identification, control, or synthesis of complex systems. Furthermore, this paper offers an in-depth exploration of the interplay between metaheuristics and complex nonlinear dynamics, including potential avenues for future research. The presented simulation studies, along with the design of objective functions for optimization and the implementation of metaheuristics, serve as a valuable foundation for subsequent experiments involving discrete nonlinear systems and complex systems with time delays. Such systems may benefit from multiparametric or multicriteria optimization approaches, paving the way for novel advancements in the field. [ABSTRACT FROM AUTHOR]

The Jaya Algorithm is a relatively new population-based optimization, which has become a progressively valuable tool in swarm intelligence. The Jaya algorithm incorporates the survival of the fittest principle alike evolutionary algorithm by its victorious nature as well as the ideal of an inducement towards a global optimal, which represents its swarm intelligence nature. Nevertheless, it has been applied in various areas of optimization, mainly in engineering practice, which is discussed and abridged based on each problem's domain.The Jaya optimization's vast applicability can be explained by its ability to work without any algorithm-specific parameters. The successfully solved problems may also use some of this meta-heuristic's variants, in which the algorithm has been modified or hybridized. This paper focuses on a comprehensive review, as well as a bibliometric study of the Jaya algorithm, to imply its versatility. Hence, this study is likely to emphasize this optimization's abilities, inspiring new researchers to make use of this simple and efficient algorithm for problem-solving. [ABSTRACT FROM AUTHOR]

Today, the use of permanent magnet brushless DC (PMBLDC) motors in vehicles is increasing due to the characteristics of sensorless operation. PMBLDC motor controllers can control the speed and position in the closed-loop feedback system without the need for a position sensor mounted on the shaft. Proportional – Integral – Derivative (PID) controller is one of the most common feedback control algorithms used in PMBLDC motor controllers. Optimizing problems using deterministic methods such as Lagrange and simplex methods requires basic information and complex calculations. Meta-heuristic algorithms are a type of stochastic algorithm that is used to find the optimal solution. Meta-heuristic algorithms are divided into three general categories: evolutionary algorithms, swarm intelligence algorithms, and stochastic algorithms. In this paper, using 14 metaheuristic optimisation algorithms, PID control parameters including settling time, time rise, overshoot, and stability of step response of the mentioned system are optimised. In this paper, 14 meta-heuristic algorithms are simulated and evaluated to optimise the PID coefficients of the controller, including settling time, rising time, excessive increase, and step response stability. The simulation result shows that the genetic algorithm (GA) has the best performance in terms of cost function and biogeography-based optimisation (BBO) in terms of settling time and rising time parameters. Finally, the simulation results are confirmed using experimental results. [ABSTRACT FROM AUTHOR]

The current variety of the Internet Protocol is IPv6 for addressing the networking devices as per the mechanisms proposed by past researchers to minimize the delay and improve the efficiency. It is additionally recognized as a classless addressing scheme that locates computing machines throughout the web so they can be located. Among the mechanisms, the Group Intelligence (GI) algorithms that consists of Evolutionary and Group based Optimization techniques have gained attention of the researchers to contribute an effective optimized solution towards solving an optimization problem. Thus, the aim of this paper is to study the implementation, features and effectiveness of different GI based metaheuristic machine learning optimization algorithms, so as to contribute in future towards designing and upgrade to a new IPv6 addressing scheme by blending the benefits of the metaheuristic algorithms to find good or near --optimal solutions at a reasonable computation cost in IPv6 network to enhance the execution result of addressing scheme on real time data. [ABSTRACT FROM AUTHOR]

Multi‐objective optimization problems frequently appear in many diverse research areas and application domains. Metaheuristics, as efficient techniques to solve them, need to be easily accessible to users with different expertise and programming skills. In this context, metaheuristic optimization frameworks are helpful, as they provide popular algorithms, customizable components and additional facilities to conduct experiments. Due to the broad range of available tools, this paper presents a systematic evaluation and experimental comparison of 10 frameworks, covering from multi‐purpose, consolidated tools to recent libraries specifically designed for multi‐objective optimization. The evaluation is organized around seven characteristics: search components and techniques, configuration, execution, utilities, external support and community, software implementation and performance. An analysis of code metrics and a series of experiments serves to assess the last two features. Lesson learned and open issues are also discussed as part of the comparative study. The outcomes of the evaluation process reveal a contrasted support to recent advances in multi‐objective optimization, with a lack of novel algorithms and variety of metaheuristics other than evolutionary algorithms. The experimental comparison also reports significant differences in terms of both execution time and memory usage under demanding configurations. [ABSTRACT FROM AUTHOR]

The deployment of electro-mechanical actuators plays an important role towards the adoption of the more electric aircraft (MEA) philosophy. On the other hand, a seamless substitution of EMAs, in place of more traditional hydraulic solutions, is still set back, due to the shortage of real-life and reliability data regarding their failure modes. One way to work around this problem is providing a capillary EMA prognostics and health management (PHM) system capable of recognizing failures before they actually undermine the ability of the safety-critical system to perform its functions. The aim of this work is the development of a model-based prognostic framework for PMSM-based EMAs leveraging a metaheuristic algorithm: the evolutionary (differential evolution (DE)) and swarm intelligence (particle swarm (PSO), grey wolf (GWO)) methods are considered. Several failures (dry friction, backlash, short circuit, eccentricity, and proportional gain) are simulated by a reference model, and then detected and identified by the envisioned prognostic method, which employs a low fidelity monitoring model. The paper findings are analysed, showing good results and proving that this strategy could be executed and integrated in more complex routines, supporting EMAs adoption, with positive impacts on system safety and reliability in the aerospace and industrial field. [ABSTRACT FROM AUTHOR]

• This paper presents a practical tutorial on solving optimization problems via PlatEMO, by means of abundant examples and source codes. • This paper is the first tutorial for the newest version PlatEMO v4.0. • This paper does not go deep into the technical details of algorithms, but aims to enable beginners to use PlatEMO at a low cost, which is much easier to be understood than the user manual of PlatEMO. • This paper is written according to many questions raised by users in the last five years. PlatEMO is an open-source platform for solving complex optimization problems, which provides a variety of metaheuristics including evolutionary algorithms, swarm intelligence algorithms, multi-objective optimization algorithms, surrogate-assisted optimization algorithms, and many others. Due to the problem-independent nature of most metaheuristics, they are versatile for solving problems with various difficulties such as multimodal landscapes, discrete search spaces, multiple objectives, strict constraints, and expensive evaluations, regardless of the fields the problems belong to. Since PlatEMO was published in 2017, it has been used by many researchers from both academia and industry in the computational intelligence community. However, the basic terms and concepts about optimization may confuse practitioners and junior researchers new to metaheuristics. Hence, this paper presents a practical introduction to the use of PlatEMO 4.0, focusing on the procedures of defining problems, selecting suitable metaheuristics, and collecting results. Note, however, that a description of the technical details of metaheuristics is beyond the scope of this paper and interested readers may refer to the cited references. [ABSTRACT FROM AUTHOR]

Reporting the empirical results of swarm and evolutionary computation algorithms is a challenging task with many possible difficulties. These difficulties stem from the stochastic nature of such algorithms, as well as their inability to guarantee an optimal solution in polynomial time. This research deals with measuring the performance of stochastic optimization algorithms, as well as the confidence intervals of the empirically obtained statistics. Traditionally, the arithmetic mean is used for measuring average performance, but we propose quantiles for measuring average, peak and bad-case performance, and give their interpretations in a relevant context for measuring the performance of the metaheuristics. In order to investigate the differences between arithmetic mean and quantiles, and to confirm possible benefits, we conducted experiments with 7 stochastic algorithms and 20 unconstrained continuous variable optimization problems. The experiments showed that median was a better measure of average performance than arithmetic mean, based on the observed solution quality. Out of 20 problem instances, a discrepancy between the arithmetic mean and median happened in 6 instances, out of which 5 were resolved in favor of median and 1 instance remained unresolved as a near tie. The arithmetic mean was completely inadequate for measuring average performance based on the observed number of function evaluations, while the 0.5 quantile (median) was suitable for that task. The quantiles also showed to be adequate for assessing peak performance and bad-case performance. In this paper, we also proposed a bootstrap method to calculate the confidence intervals of the probability of the empirically obtained quantiles. Considering the many advantages of using quantiles, including the ability to calculate probabilities of success in the case of multiple executions of the algorithm and the practically useful method of calculating confidence intervals, we recommend quantiles as the standard measure of peak, average and bad-case performance of stochastic optimization algorithms. [ABSTRACT FROM AUTHOR]

Formation control is one of the most concerning topics within the realm of swarm intelligence. This paper presents a metaheuristic approach that leverages a natural co-evolutionary strategy to solve the formation control problem for a swarm of missiles. The missile swarm is modeled by a second-order system with a heterogeneous reference target, and the exponential of the resultant error is accumulated to be the objective function such that the swarm converges to optimal equilibrium states satisfying specific formation requirements. Focusing on the issue of the local optimum and unstable evolution, we incorporate a novel model-based policy constraint and a population adaptation strategy that significantly alleviates the performance degradation of the existing natural co-evolutionary strategy in terms of slow training and instability of convergence. With application of the Molloy–Reed criterion in the field of network communication, we developed an adaptive topology method that assures connectivity under node failure, and its effectiveness is validated theoretically and experimentally. The experimental results demonstrate that the accuracy of formation flight achieved by this method is competitive with that of conventional control methods and is much more adaptable. More significantly, we show that it is feasible to treat the generic formation control problem as an optimal control problem for finding a Nash equilibrium strategy and solving it through iterative learning. [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]

Salp swarm algorithm (SSA) is a recently developed meta-heuristic swarm intelligence optimization algorithm based on simulating the chain movement behavior of salps sailing and foraging in the sea. In this paper, a novel hybrid meta-heuristic algorithm called SSA-FGWO is proposed to overcome the shortcomings of the original SSA, including slow convergence speed in dealing with high-dimensional and multimodal landscapes, low precision, and global optimization problems. The essential idea of SSA-FGWO is to improve the salp swarm optimization algorithm (SSA) by utilizing the Grey Wolf Algorithm (GWO) strategy. The hybridization mechanism includes two steps: First, the strong exploitation of SSA is applied to update the leaders' position of the chain population. Second, the strong exploration strategy of GWO is used to update the followers' position to increase the population variance of the proposed optimizer. The proposed algorithm is expected to enhance exploration and exploitation ability significantly by the hybrid design. The effectiveness of SSA-FGWO is investigated through CEC2020, 23 representative benchmark cases, and feature selection problems (18 data sets) are solved. The algorithm has been examined for its computational complexity and convergent behavior. In addition to GWO, SSA and other swarm optimization algorithms are employed to compare with the proposed optimizer. The obtained experimental results show that the exploitation, exploration tendencies, and convergence patterns of SSA-FGWO have significantly improved. The results show that the proposed SSA-FGWO algorithm is a promising one that outperforms the basic SSA, GWO, and other algorithms in terms of efficacy. [ABSTRACT FROM AUTHOR]

Cloud computing represents relatively new paradigm of utilizing remote computing resources and is becoming increasingly important and popular technology, that supports on-demand (as needed) resource provisioning and releasing in almost real-time. Task scheduling has a crucial role in cloud computing and it represents one of the most challenging issues from this domain. Therefore, to establish more efficient resource employment, an effective and robust task allocation (scheduling) method is required. By using an efficient task scheduling algorithm, the overall performance and service quality, as well as end-users experience can be improved. As the number of tasks increases, the problem complexity rises as well, which results in a huge search space. This kind of problem belongs to the class of NP-hard optimization challenges. The objective of this paper is to propose an approach that is able to find approximate (near-optimal) solution for multi-objective task scheduling problem in cloud environment, and at the same time to reduce the search time. In the proposed manuscript, we present a swarm-intelligence based approach, the hybridized bat algorithm, for multi-objective task scheduling. We conducted experiments on the CloudSim toolkit using standard parallel workloads and synthetic workloads. The obtained results are compared to other similar, metaheuristic-based techniques that were evaluated under the same conditions. Simulation results prove great potential of our proposed approach in this domain. [ABSTRACT FROM AUTHOR]

How to steadily find satisfactory solutions for high-dimensional multimodal and composition optimization problems is still a challenging issue. To fight against this pain-point problem, we propose sardine optimization algorithm (SOA) with agile locality and globality strategies for real optimization problems. Inspired by the survival philosophy of sardines, SOA simulates the transformation, migration, reproduction, elimination, and spread of sardines. As a varied-population-size optimization algorithm, the features of SOA are summarized as two key points. (i) Agile locality and globality strategies use adjacent and corresponding period ratios to control the local and global search behaviors. To our best knowledge, these strategies are a new technical road to balance exploration and exploitation efforts. (ii) Besides, SOA uses unique search operators based on the center movement of sardine schools. Specifically, when the center of one sardine school moves in these search operators, all sardines in this school also move in the same direction. This mobility style is different from most meta-heuristic algorithms, as far as we know. We used all unconstrained optimization problems in the CEC2013 test suite and six real-world constrained optimization problems as our benchmarks. SOA outperforms eight algorithms (like the two winning algorithms of CEC2013 and CEC2014), especially for high-dimension multimodal and composition optimization problems. For instance, Wilcoxon results between SOA and the two winning algorithms of CEC2013 and CEC2014 for 90-dimensional unconstrained optimization problems of the CEC2013 test suite are 16:10 and 18:8. The coding of SOA can be downloaded from "https://github.com/1654402787/SOA" (unzip password: soasoasoa1357). [ABSTRACT FROM AUTHOR]

In the mid 1990s two landmark metaheuristics have been proposed: Particle Swarm Optimization and Differential Evolution. Their initial versions were very simple, but rapidly attracted wide attention. During the last quarter century hundreds of variants of both optimization algorithms have been proposed and applied in almost any field of science or engineering. However, no broader comparison of performance between both families of methods has been presented so far. In the present paper ten Particle Swarm Optimization and ten Differential Evolution variants, from historical ones from the 1990s up to the most recent ones from 2022, are compared on numerous single-objective numerical benchmarks and 22 real-world problems. On average Differential Evolution algorithms clearly outperform Particle Swarm Optimization ones. Such advantage of Differential Evolution over Particle Swarm Optimization is in contradiction with popularity: In the literature Particle Swarm Optimization algorithms are two–three times more frequently used than Differential Evolution ones. Problems for which Particle Swarm Optimization performs better than Differential Evolution do exist but are relatively few. Although this result may be an effect of the choice of specific variants, experimental settings or problems used for comparison, some re-consideration of algorithmic philosophy may be needed for Particle Swarm Optimization variants to make them more competitive. [ABSTRACT FROM AUTHOR]

Like most metaheuristic algorithms, salp swarm algorithm (SSA) suffers from slow convergence and stagnation in the local optima. The study develops a novel Time-Based Leadership Salp-Based Competitive Learning (TBLSBCL) to address the SSA's flaws. The TBLSBCL presents a novel search technique to address population diversity, an imbalance between exploitation and exploration, and the SSA algorithm's premature convergence. Hybridization consists of two stages: First, a time-varying dynamic structure represents the SSA hierarchy of leaders and followers. This approach increases the number of leaders while decreasing the number of salp's followers linearly. Utilizing the effective exploitation of the SSA, the position of the population's leader is updated. Second, the competitive learning strategy is used to update the status of the followers by teaching them from the leaders. The goal of adjusting the salp swarm optimizer algorithm is to help the basic approach avoid premature convergence and quickly steer the search to the most promising likely search space. The proposed TBLSBCL method is tested using the CEC 2017 benchmark, feature selection problems for 19 datasets (including three high-dimensional datasets). The TBLSBCL was then evaluated using a benchmark set of seven wellknown constrained design challenges in diverse engineering fields defined in the benchmark set of real-world problems presented at the CEC 2020 conference (CEC 2020). In each experiment, TBLSBCL is compared with seven other state-of-the-art metaheuristics and other advanced algorithms that include seven variants of the salp swarm. Friedman and Wilcoxon rank-sum statistical tests are also used to examine the results. According to the experimental data and statistical tests, the TBLSBCL algorithm is very competitive and often superior to the algorithms employed in the studies. [ABSTRACT FROM AUTHOR]

Salp swarm algorithm (SSA) is a unique swarm intelligent algorithm widely used for various practical applications due to its simple framework and good optimization performance. However, like other swarm-based algorithms, SSA yields local optimal solutions and has a slow convergence rate and low solution accuracy when dealing with high-dimensional global optimization problems. Based on quadratic interpolation and a local escape operator (LEO), a salp swarm optimization algorithm (QSSALEO) is proposed to address these issues. Quadratic interpolation around the best search agent aids QSSALEO's exploitation ability and solution accuracy, whereas the local escaping operator employs random operators to escape local optima. These tactics complement one another to help SSA promote convergence performance. Furthermore, the algorithm strives for a balance of exploitation and exploration. The proposed QSSALEO method was tested using the CEC 2017 benchmark with 50 and 100 decision variables, as well as seven CEC2008lsgo test functions with 200, 500, and 1000 decision variables, and its performance was compared to that of other metaheuristic algorithms and advanced algorithms, including seven salp swarm variants. The experimental results reveal that QSSALEO outperforms SSA and other population-based algorithms regarding convergence rate and solution correctness. The QSSALEO was then evaluated as a feature selection algorithm on 19 datasets (including three high-dimensional datasets). Friedman and Wilcoxon rank-sum statistical tests are also used to analyze the results. According to experimental data and statistical tests, the QSSALEO algorithm is very competitive and often superior to the algorithms employed in research. Therefore, the proposed method can also be considered a specialized large-scale global optimization optimizer whose performance surpasses state-of-the-art algorithms such as CMA-ES and SHADE. The algorithm source code is available at https://github.com/MohammedQaraad/An-Innovative-Quadratic-interpolation-Salp-Swarm. [ABSTRACT FROM AUTHOR]

This paper presents a novel meta-heuristic algorithm so-called White Shark Optimizer (WSO) to solve optimization problems over a continuous search space. The core ideas and underpinnings of WSO are inspired by the behaviors of great white sharks, including their exceptional senses of hearing and smell while navigating and foraging. These aspects of behavior are mathematically modeled to accommodate a sufficiently adequate balance between exploration and exploitation of WSO and to assist search agents to explore and exploit each potential area of the search space in order to achieve optimization. The search agents of WSO randomly update their position in connection with best-so-far solutions, to eventually arrive at the optimal outcome. The performance of WSO was comprehensively benchmarked on a set of 29 test functions from the CEC-2017 test suite for several dimensions. WSO was further applied to solve the benchmark problems of the CEC-2011 evolutionary algorithm competition to prove its reliability and applicability to real-world problems. A thorough analysis of computational and convergence results was presented to shed light on the efficacy and stability levels of WSO. The performance score of WSO in terms of several statistical methods was compared with 9 well-established meta-heuristics based on the solutions generated. Friedman's and Holm's tests of the results showed that WSO revealed reasonable solutions, in terms of global optimality, avoidance of local minima and solution quality, compared to other existing meta-heuristics. [ABSTRACT FROM AUTHOR]

In this paper, we enriched Ant Colony Optimization (ACO) with interval outranking to develop a novel multi-objective ACO optimizer to approach problems with many objective functions. This proposal is suitable if the preferences of the Decision Maker (DM) can be modeled through outranking relations. The introduced algorithm (Interval Outranking-based ACO, IO-ACO) is the first ant-colony optimizer that embeds an outranking model to bear vagueness and ill-definition of the DM's preferences. This capacity is the most differentiating feature of IO-ACO because this issue is highly relevant in practice. IO-ACO biases the search towards the Region of Interest (RoI), the privileged zone of the Pareto frontier containing the solutions that better match the DM's preferences. Two widely studied benchmarks were utilized to measure the efficiency of IO-ACO, i.e., the DTLZ and WFG test suites. Accordingly, IO-ACO was compared with four competitive multi-objective optimizers: The Indicator-based Many-Objective ACO, the Multi-objective Evolutionary Algorithm Based on Decomposition, the Reference Vector-Guided Evolutionary Algorithm using Improved Growing Neural Gas, and the Indicator-based Multi-objective Evolutionary Algorithm with Reference Point Adaptation. The numerical results show that IO-ACO approximates the RoI better than leading metaheuristics based on approximating the Pareto frontier alone. [ABSTRACT FROM AUTHOR]

Companies are constantly changing in their organization and the way they treat information. In this sense, relevant data analysis processes arise for decision makers. Similarly, to perform decision-making analyses, multi-criteria and metaheuristic methods represent a key tool for such analyses. These analysis methods solve symmetric and asymmetric problems with multiple criteria. In such a way, the symmetry transforms the decision space and reduces the search time. Therefore, the objective of this research is to provide a classification of the applications of multi-criteria and metaheuristic methods. Furthermore, due to the large number of existing methods, the article focuses on the particle swarm algorithm (PSO) and its different extensions. This work is novel since the review of the literature incorporates scientific articles, patents, and copyright registrations with applications of the PSO method. To mention some examples of the most relevant applications of the PSO method; route planning for autonomous vehicles, the optimal application of insulin for a type 1 diabetic patient, robotic harvesting of agricultural products, hybridization with multi-criteria methods, among others. Finally, the contribution of this article is to propose that the PSO method involves the following steps: (a) initialization, (b) update of the local optimal position, and (c) obtaining the best global optimal position. Therefore, this work contributes to researchers not only becoming familiar with the steps, but also being able to implement it quickly. These improvements open new horizons for future lines of research. [ABSTRACT FROM AUTHOR]

For optimally designing water distribution networks (WDNs), the nondeterministic polynomial hard problem, a novel hybrid model, is introduced with the combined features of evolutionary and swarm intelligence techniques. An evolutionary algorithm with better exploration properties, differential evolution (DE), and the swarm intelligence technique with better exploitation properties, namely the krill herd algorithm (KHA), is considered for this purpose. Because exploration and exploitation are the essential features of the metaheuristic algorithms, the hybrid algorithm with a combination of the DE and KHA features, the DE-KHA, resulted in a balanced search methodology. The results on the application of the proposed model on well-studied benchmark problems have demonstrated its enhanced search behavior, converging faster to the promising results with considerable robustness. Moreover, compared with other competing algorithms reported for optimally designing the WDNs, the DE-KHA outperforms with better computational efficiency. Additionally, considering the few control parameters that have to be calibrated for their optimal values, the computational burden will be less for performing the sensitivity analysis. As a result, considering the solution precision, quick convergence ability, and robustness of DE-KHA, the study suggests the algorithm for efficiently handling real-life case studies. [ABSTRACT FROM AUTHOR]