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Metaheuristic optimization algorithms (MHA) play a significant role in obtaining the best (optimal) values of the system's parameters to improve its performance. This role is significantly apparent when dealing with systems where the classical analytical methods fail. Fractional-order (FO) systems have not yet shown an easy procedure to deal with the determination of their optimal parameters through traditional methods. In this paper, a recent, systematic. And comprehensive review is presented to highlight the role of MHA in obtaining the best set of gains and orders for FO controllers. The systematic review starts by exploring the most relevant publications related to the MHA and the FO controllers. The study is focused on the most popular controllers such as the FO-PI, FO-PID, FO Type-1 fuzzy-PID, and FO Type-2 fuzzy-PID. The time domain is restricted in the articles published through the last decade (2014:2023) in the most reputed databases such as Scopus, Web of Science, Science Direct, and Google Scholar. The identified number of papers, from the entire databases, has reached 850 articles. A Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology was applied to the initial set of articles to be screened and filtered to end up with a final list that contains 82 articles. Then, a thorough and comprehensive study was applied to the final list. The results showed that Particle Swarm Optimization (PSO) is the most attractive optimizer to the researchers to be used in the optimal parameters identification of the FO controllers as it attains about 25% of the published papers. In addition, the papers that used PSO as an optimizer have gained a high citation number despite the fact that the Chaotic Atom Search Optimization (ChASO) is the highest one, but it is used only once. Furthermore, the Integral of the Time-Weighted Absolute Error (ITAE) is the best nominated cost function. Based on our comprehensive literature review, this appears to be the first review paper that systematically and comprehensively addresses the optimization of the parameters of the fractional-order PI, PID, Type-1, and Type-2 fuzzy controllers with the use of MHAs. Therefore, the work in this paper can be used as a guide for researchers who are interested in working in this field. [ABSTRACT FROM AUTHOR]

One of the most efficient metaheuristic algorithms that is used to solve hard optimization problems is the firefly algorithm (FFA). In this paper we use this algorithm to solve a single machine scheduling problem, we aim to minimize the sum of the two cost functions: the maximum tardiness and the maximum earliness. This problem (P) is NP-hard so we solve this problem using FFA as a metaheuristic algorithm. To explore the search space and get a good solution to a problem (Q), we hybridize FFA by Iterated Descent Method (IDM) in three ways and the results are FFA1, FFA2, and FFA3. In the computational test, we evaluate these algorithms (FFA, FFA1, FFA2, FFA3) compared with the genetic algorithm (GA) through a simulation process with job sizes from 10 jobs to 100 jobs. The results indicate that these modifications improve the performance of the original FFA and one of them (FFA3) gives better performance than others. [ABSTRACT FROM AUTHOR]

The ant system (AS) and scheduling problem are well-known concepts in literature. Ant algorithms have been known to be an effective tool for solving combinatorial optimization problems. Elitist AS (EAS), rank-based AS (RAS), ant colony system (ACS), and max-min AS (MMAS) are the variants of the AS algorithm; they are triggered by the different ways of updating the pheromone trail τ, computing the visibility η, and/or other parameters in the basic AS model. The main contribution of this article is twofold. First, the basic AS and its controlled parameters are presented, the key variants of the ant algorithms are explained, and major changes of each variant from the basic model are tracked. Second, sixty papers are collected between 2015 and 2020 based on a search strategy for tracking the implementation of different AS variants in solving scheduling problems. Numerous findings based on a statistical analysis of the collected papers are reported and discussed. This study will allow the researcher to understand the essence of the ant algorithm, recognize the fundamental differences in its five systems, and determine how each of them can be implemented. Tracking a sample of articles that apply an ant algorithm for a specific case study gives researchers new ideas on how to adjust the original model to fit their problem. [ABSTRACT FROM AUTHOR]

This paper introduces a new variant of the Bees Algorithm (BA) called Bees Algorithm with 2-parameter (BA2), which is a population-based metaheuristic algorithm designed to solve continuous and combinatorial optimisation problems. The proposed algorithm simplified the BA's parameters by combining exploration and exploitation strategies while preserving the algorithm's core principles to efficiently search for optimal solutions. The paper provides a detailed description of the algorithm's core principles and its application to two engineering problems, the air-cooling system design (ACSD) and the printed circuit board assembly sequence optimisation (PASO). The results show that BA2 outperforms previous versions of the basic BA in terms of convergence speed and solution quality. However, the authors acknowledge that further research is needed to test the scalability and generalisability of the algorithm to larger and more diverse optimisation problems. Overall, this paper provides valuable insights into the potential of metaheuristics for solving real-world optimisation problems. [ABSTRACT FROM AUTHOR]

Introduction of digital solutions has made dentistry more efficient and effective in response to patients' demands. Moreover, digital solution helps participants to manage daily workflow simpler than traditional practices. Scanners, CAD/CAM software, CNC machines and 3D printers are components of digital solutions in current dentistry. Responding to patients as quickly as possible is essential in medical fields and dentistry has similar situations. On the other hand, demands in dentistry are highly customized that it makes managing orders more difficult because each order needs special design and production. Thus, this paper assesses orders in digital dentistry and develops a mathematical model to optimize production planning and scheduling of orders by considering different objectives and requirements that are common in dentistry. In addition, a metaheuristics algorithm was developed based on PSO to respond to NP-hard challenges of the model. The developed algorithm includes two steps that PSO metaheuristics consider in the second step to search new solutions. Finally, through case studies, performance of the developed model and proposed algorithm was investigated. Developed algorithm generates solutions with proper quality considering makespan and total completion time objectives and required time to obtain a solution with high quality depends on problem data and can increase. [ABSTRACT FROM AUTHOR]

The efficiency and the effectiveness of a machine learning (ML) model are greatly influenced by feature selection (FS), a crucial preprocessing step in machine learning that seeks out the ideal set of characteristics with the maximum accuracy possible. Due to their dominance over traditional optimization techniques, researchers are concentrating on a variety of metaheuristic (or evolutionary) algorithms and trying to suggest cutting-edge hybrid techniques to handle FS issues. The use of hybrid metaheuristic approaches for FS has thus been the subject of numerous research works. The purpose of this paper is to critically assess the existing hybrid FS approaches and to give a thorough literature review on the hybridization of different metaheuristic/evolutionary strategies that have been employed for supporting FS. This article reviews pertinent documents on hybrid frameworks that were published in the period from 2009 to 2022 and offers a thorough analysis of the used techniques, classifiers, datasets, applications, assessment metrics, and schemes of hybridization. Additionally, new open research issues and challenges are identified to pinpoint the areas that have to be further explored for additional study. [ABSTRACT FROM AUTHOR]

This paper presents a variable neighborhood search (VNS) algorithm to solve the extension of the orienteering problem known as the generalized orienteering problem (GOP). Our algorithm aims to use a reduced number of neighborhoods without compromising the quality of the results. This reduced number of neighborhoods, together with the precalculation of scores associated with points of interest, allows us, in most cases, to outperform all previous metaheuristics proposed for this problem. This is the first time a VNS is being applied to the GOP, and it provides promising computational results. In particular, in the case studies considered in the paper, we were able to find 35 new best solutions, all of which were found using a shorter computational time. Furthermore, the information regarding other best‐known solutions provided in the literature has also been improved, with corrections to some previously published errors regarding scores and distances. In addition, the benchmark has been extended with the incorporation of new case studies based on real data from three of the most popular tourist cities in Spain. [ABSTRACT FROM AUTHOR]

The university course timetable problem (UCTP) is known to be NP-hard, with solution complexity growing exponentially with the problem size. This paper introduces an algorithm that effectively tackles UCTPs by employing a combination of exploration and exploitation strategies. The algorithm comprises two main components. Firstly, it utilizes a genetic algorithm (GA) to explore the search space and discover a solution within the global optimum region. Secondly, it enhances the solution by exploiting the region using an iterated local search (ILS) algorithm. The algorithm is tested on two common variants of UCTP: the post-enrollment-based course timetable problem (PE-CTP) and the curriculum-based course timetable problem (CB-CTP). The computational results demonstrate that the proposed algorithm yields competitive outcomes when compared empirically against other existing algorithms. Furthermore, a t-test comparison with state-of-the-art algorithms is conducted. The experimental findings also highlight that the hybrid approach effectively overcomes the limitation of local optima, which is encountered when solely employing GA in conjunction with local search. [ABSTRACT FROM AUTHOR]

In this paper, a new population initialization method for metaheuristic algorithms is proposed. In our approach, the initial set of candidate solutions is obtained through the sampling of the objective function with the use of the Metropolis–Hastings technique. Under this method, the set of initial solutions adopts a value close to the prominent values of the objective function to be optimized. Different from most of the initialization methods that consider only spatial distribution, in our algorithm, the initial points represent promising regions of the search space, which deserve to be exploited to identify the global optimum. These characteristics allow the proposed approach obtains a faster convergence and improves the quality of the produced solutions. With the objective to demonstrate the capacities of our initialization method, it has been embedded in the classical Differential Evolution algorithm. To evaluate its performance, the complete system has been tested in a set of representative benchmark functions extracted from several datasets. Experimental results show that the proposed technique presents a better convergence speed and an increment in the quality of the solutions than other similar approaches. [ABSTRACT FROM AUTHOR]

In recent years, metaheuristic methods have shown remarkable efficacy in resolving complex combinatorial challenges across a broad spectrum of fields. Nevertheless, the escalating complexity of these problems necessitates the continuous development of innovative techniques to enhance the performance and reliability of these methods. This paper aims to contribute to this endeavor by examining the impact of solution initialization methods on the performance of a hybrid algorithm applied to the set union knapsack problem (SUKP). Three distinct solution initialization methods, random, greedy, and weighted, have been proposed and evaluated. These have been integrated within a sine cosine algorithm employing k-means as a binarization procedure. Through testing on medium- and large-sized SUKP instances, the study reveals that the solution initialization strategy influences the algorithm's performance, with the weighted method consistently outperforming the other two. Additionally, the obtained results were benchmarked against various metaheuristics that have previously solved SUKP, showing favorable performance in this comparison. [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]

Intrusion detection systems (IDS) play a crucial role in securing networks and identifying malicious activity. This is a critical problem in cyber security. In recent years, metaheuristic optimization algorithms and deep learning techniques have been applied to IDS to improve their accuracy and efficiency. Generally, optimization algorithms can be used to boost the performance of IDS models. Deep learning methods, such as convolutional neural networks, have also been used to improve the ability of IDS to detect and classify intrusions. In this paper, we propose a new IDS model based on the combination of deep learning and optimization methods. First, a feature extraction method based on CNNs is developed. Then, a new feature selection method is used based on a modified version of Growth Optimizer (GO), called MGO. We use the Whale Optimization Algorithm (WOA) to boost the search process of the GO. Extensive evaluation and comparisons have been conducted to assess the quality of the suggested method using public datasets of cloud and Internet of Things (IoT) environments. The applied techniques have shown promising results in identifying previously unknown attacks with high accuracy rates. The MGO performed better than several previous methods in all experimental comparisons. [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]

Cyber-physical systems (CPSes) are rapidly evolving in critical infrastructure (CI) domains such as smart grid, healthcare, the military, and telecommunication. These systems are continually threatened by malicious software (malware) attacks by adversaries due to their improvised tactics and attack methods. A minor configuration change in a CPS through malware has devastating effects, which the world has seen in Stuxnet, BlackEnergy, Industroyer, and Triton. This paper is a comprehensive review of malware analysis practices currently being used and their limitations and efficacy in securing CPSes. Using well-known real-world incidents, we have covered the significant impacts when a CPS is compromised. In particular, we have prepared exhaustive hypothetical scenarios to discuss the implications of false positives on CPSes. To improve the security of critical systems, we believe that nature-inspired metaheuristic algorithms can effectively counter the overwhelming malware threats geared toward CPSes. However, our detailed review shows that these algorithms have not been adapted to their full potential to counter malicious software. Finally, the gaps identified through this research have led us to propose future research directions using nature-inspired algorithms that would help in bringing optimization by reducing false positives, thereby increasing the security of such systems. [ABSTRACT FROM AUTHOR]

For the past decades, practitioners and researchers have been fascinated by the job-shop scheduling problems (JSSP) and have proposed many pristine meta-heuristic algorithms to solve them. JSSP is an NP-hard problem and a combinatorial optimization problem. This paper proposes a highly efficient and superior performance strategy for the artificial algae algorithm (AAA) integrated with the differential evolution (DE), denoted AAADE, to solve JSSP. The new movement algae colonies using DE operators are introduced to the proposed hybrid artificial algae algorithm and DE (AAADE). To improve AAA's intensification ability, the movement using the DE mutation is implemented into the AAA. In the new hybrid method, the DE crossover can update its position based on both movements (helical and DE movements) to increase randomization. Two categories of problems verify the efficiency and validity of the proposed hybrid algorithm, AAADE, namely, CEC 2014 benchmark functions and different job-shop scheduling problems. The AAADE results are compared with other algorithms in the literature. Hence, comparisons numerical experiments validated and verified the quality of the proposed algorithm. Experimental results validate the effectiveness of the proposed hybrid method in producing excellent solutions that are promising and competitive to the state-of-the-art heuristic-based algorithms reported in the literature in most of the benchmark functions in CEC'14 and JSSP. [ABSTRACT FROM AUTHOR]

In this paper, the behavior and performance of Pure Random Orthogonal Search (PROS), a parameter-free evolutionary algorithm (EA) that outperforms many existing EAs on the well-known benchmark functions with finite-time budget, are analyzed. The sufficient conditions to converge to the global optimum are also determined. In addition, we propose two modifications to PROS, namely Triangular-Distributed Random Orthogonal Search (TROS) and Quadratic-Distributed Random Orthogonal Search (QROS). With our local search mechanism, both modified algorithms improve the convergence rates and the errors of the obtained solutions significantly on the benchmark functions while preserving the advantages of PROS: parameterless, excellent computational efficiency, ease of applying to all kinds of applications, and high performance with finite-time search budget. The experimental results show that both TROS and QROS are competitive in comparison to several classic metaheuristic optimization algorithms. [ABSTRACT FROM AUTHOR]

In manufacturing industries, customers demand a wide variety of products, with high quality and fast delivery. Production scheduling systems have become critical for efficient operation. However, scheduling problems in manufacturing are generally large and complex with many constraints. It is difficult to create an optimal production schedule that satisfies all constraints within a reasonable timeframe. This study targets a factory with multiple working machines and two overhead cranes. Our research aims to obtain a solution algorithm to avoid interference of overhead cranes and machine competition and a production plan that minimizes the total makespan for each job. As the problem must be solved within a reasonable timeframe, we have developed the solution algorithm using metaheuristics and scheduling simulation. In general, metaheuristic algorithms must strike a balance between an intensive search for good solutions and a search for diverse solutions. Accordingly, we propose a new algorithm using path relinking in a scatter search. This method was demonstrated to be effective in obtaining good solutions with little variation in numerical experiments. In this paper, we describe previous research, our target process, and new solution algorithm and discuss algorithm design methods based on computer experiments. [ABSTRACT FROM AUTHOR]

The cost-based hybrid flow shop (CHFS) scheduling has been immensely studied due to its huge impact on productivity. For any profit-oriented organization, it is important to optimize total production costs. However, few researchers have studied hybrid flow shops (HFS) with total production cost utilization. This paper aims to develop a computational model and test the exploration capability of metaheuristics algorithms while optimizing the CHFS problem. Carlier and Neron defined three hypothetical benchmark problems for computational experiments. The popular optimization algorithms PSO, GA, and ACO were implemented on the CHFS model with ten optimization runs. The experimental results proven that ACO performed well regarding mean fitness value for all benchmark problems. Besides this, CPU time for PSO was very high compared to other algorithms. In the future, other optimization algorithms will be tested for the CHFS model, such as Teaching Learning Based Optimization (TLBO) and the Crayfish Optimization Algorithm (COA). [ABSTRACT FROM AUTHOR]

Optimization problems are prevalent in almost all areas and hence optimization algorithms are crucial for a myriad of real-world applications. Deterministic optimization algorithms tend to be computationally costly and time-consuming. Hence, heuristic and metaheuristic algorithms are more favoured as they provide near-optimal solutions in an acceptable amount of time. Swarm intelligence algorithms are being increasingly used for optimization problems owing to their simplicity and good performance. The Dragonfly Algorithm (DA) is one which is inspired by the swarming behaviours of dragonflies, and it has been proven to have a superior performance than other algorithms in multiple applications. Hence, it is worth considering its application to the traveling salesman problem which is a predominant discrete optimization problem. The original DA is only suitable for solving continuous optimization problems and, although there is a binary version of the algorithm, it is not easily adapted for solving discrete optimization problems like TSP. We have previously proposed a discrete adapted DA algorithm suitable for TSP. However, it has low effectiveness, and it has not been used for large TSP problems. In this paper, we propose an optimized discrete adapted DA by using the steepest ascent hill climbing algorithm as a local search. The algorithm is applied to a TSP problem modelling a package delivery system in the Kuala Lumpur area and to benchmark TSP problems, and it is found to have a higher effectiveness than the discrete adapted DA and some other swarm intelligence algorithms. It also has a higher efficiency than the discrete adapted DA. [ABSTRACT FROM AUTHOR]

The prediction of PV output represents an important task for PV farm operators as it enables them to forecast the energy they will produce and sell on the energy market. Existing approaches rely on a combination of satellite/all-sky images and numerical methods which for high spatial resolutions require considerable processing time and resources. In this paper, we propose a hybrid egde–cloud platform that leverages the performance of edge devices to perform time-critical computations locally, while delegating the rest to the remote cloud infrastructure. The proposed platform relies on novel metaheuristics algorithms for cloud dynamics detection and proposes to forecast irradiance by analyzing pixel values taken with various filters/bands. The results demonstrate the scalability improvement when using GPU-enabled devices and the potential of using pixel information instead of cloud types to infer irradiance. [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]

The Fixed Set Search (FSS) is a novel metaheuristic that adds a learning mechanism to the Greedy Randomized Adaptive Search Procedure (GRASP). In recent publications, its efficiency has been shown on different types of combinatorial optimization problems like routing, machine scheduling and covering. In this paper the FSS is adapted to multi-objective problems for finding Pareto Front approximations. This adaptation is illustrated for the bi-objective Minimum Weighted Vertex Cover Problem (MWVCP). In this work, a simple and effective bi-objective GRASP algorithm for the MWVCP is developed in the first stage. One important characteristic of the proposed GRASP is that it avoids the use of weighted sums of objective functions in the local search and the greedy algorithm. In the second stage, the bi-objective GRASP is extended to the FSS by adding a learning mechanism adapted to multi-objective problems. The conducted computational experiments show that the proposed FSS and GRASP algorithm significantly outperforms existing methods for the bi-objective MWVCP. To fully evaluate the learning mechanism of the FSS, it is compared to the underlying GRASP algorithm on a wide range of performance indicators related to convergence, distribution, spread and cardinality. [ABSTRACT FROM AUTHOR]

The unrelated parallel machine scheduling problem with sequence‐dependent setup times is addressed in this paper with the objective of minimizing the elapsed time between the start and finish of a sequence of operations in a set of unrelated machines. The machines are considered unrelated because the processing speed is dependent on the job being executed and not on the individual machines. Generally, the problem is considered NP‐hard, as it presents additional complexity to find an optimal solution in terms of minimum makespan. An advanced firefly metaheuristic optimization algorithm is introduced to solve this problem. The proposed method, called the FAII algorithm, aims to improve the standard firefly algorithm's performance by incorporating an enhanced global best solution update mechanism and adaptive mutation‐based local and global neighborhood search scheme to improve the quality of the proposed algorithm's generated solution. Several experiments were conducted to compare and validate the proposed algorithms' performance on small and large‐scale benchmarked problem instances with up to 12 machines and 120 job combinations. Moreover, the performance of the FAII was also compared with eight other metaheuristic algorithms, which were implemented in parallel with the FAII method. Furthermore, the numerical results of the FAII algorithm were compared with the scheduling results of six other well‐known metaheuristics from the literature. The comparison results backed with a comprehensive statistical analysis showed the superiority of the enhanced FA‐style scheduling optimization over other metaheuristic methods to find good quality solutions or minimum average makespan. [ABSTRACT FROM AUTHOR]

Metaheuristic and heuristic methods have many tunable parameters, and choosing their values can increase their ability to deal with hard optimization problems. Automated approaches for finding good parameter settings have attracted significant research and development efforts in the last few years. Because parameter tuning became commonly utilized in industry and research and there is a significant advancement in this area, a comprehensive review is an important requirement. Although there is very wide literature about algorithm configuration problems, a detailed survey analysis has not been conducted yet to the best of our knowledge. In this paper, we will briefly explain the automatic algorithm configuration problem and then survey the automated methods developed to handle this problem. After explaining the logic of these methods, we also argued about their main advantages and disadvantages to help researchers or practitioners select the best possible method for their specific problem. Moreover, some recommendations and possible future directions for this topic are provided as a conclusion. [ABSTRACT FROM AUTHOR]

Many metaheuristic approaches are inherently stochastic. In order to compare such methods, statistical tests are needed. However, choosing an appropriate test is not trivial, given that each test has some assumptions about the distribution of the underlying data that must be true before it can be used. Permutation tests (P-Tests) are statistical tests with minimal number of assumptions. These tests are simple, intuitive and nonparametric. In this paper, we argue researchers in the field of metaheuristics to adopt P-Tests to compare their algorithms. We define two statistic tests and then present an algorithm that uses them to compute the p-value. The proposed process is used to compare 5 metaheuristic algorithms on 10 benchmark functions. The resulting p-values are compared with the p-values of two widely used statistical tests. The results show that the proposed P-test is generally consistent with the classical tests, but more conservative in few cases. [ABSTRACT FROM AUTHOR]

Metaheuristic algorithms are techniques that have been successfully applied to solve complex optimization problems in engineering and science. Many metaheuristic approaches, such as Differential Evolution (DE), use the best individual found so far from the whole population to guide the search process. Although this approach has advantages in the algorithm's exploitation process, it is not completely in agreement with the swarms found in nature, where communication among individuals is not centralized. This paper proposes the use of stigmergy as an inspiration to modify the original DE operators to simulate a decentralized information exchange, thus avoiding the application of a global best. The Stigmergy-based DE (SDE) approach was tested on a set of benchmark problems to compare its performance with DE. Even though the execution times of DE and SDE are very similar, our proposal has a slight advantage in most of the functions and can converge in fewer iterations in some cases, but its main feature is the capability to maintain a good convergence behavior as the dimensionality grows, so it can be a good alternative to solve complex problems. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to outline a new approach to represent the randomness that we can find in different metaheuristics as a stochastic process which helps in the performance of the analyzed metaheuristic. This new way of viewing randomness is based on the behavior of sine waves that we can find in many situations in nature or in physics laws. In this paper, we evaluate this proposed randomness with three metaheuristics: the grey wolf optimizer, firefly algorithm and flower pollination algorithm, with the goal of studying the performance of the proposed randomness method in different types of metaheuristics. A set of standard benchmark functions were used to test the proposed randomness method, which are classified as unimodal and multimodal benchmark functions. In addition, the benchmark functions of the CEC 2015 Competition are used. Finally, we present tests with functions that were presented in the CEC 2017 competition for constrained real-parameter optimization. We also present a comparative study of the analyzed metaheuristics, and this comparison is between their original randomness method and the proposed randomness method for each algorithm. Finally, we present the performance and results of the methods with different number of dimensions to complete the study. [ABSTRACT FROM AUTHOR]

Data analysis becomes more important since rapid technology developments. In data analysis, data clustering is one of the very useful approaches. It can reveal important information hiding inside the dataset by organizing the instances based on their similarity. The objectives of data clustering are maximizing dissimilarity between clusters and minimizing dissimilarity within clusters. In order to construct a good clustering results, many clustering algorithms have been proposed, including the metaheuristic-based clustering algorithms. Recently, a new metaheuristic algorithm named gradient evolution has been proposed. This algorithm shows a good performance on solving the optimization problems. Therefore, this paper employs this GE algorithm for solving the clustering problem. In order to obtain a better clustering result, this paper considers multi-objective clustering instead of single-objective clustering. In this paper, the original GE algorithm is improved so then it is suitable for the multi-objective problem. The proposed modification includes the procedure for vector updating and jumping which involves Pareto rank assignment. In addition, it also employs K-means algorithm to provide the final clustering result. The proposed algorithm is verified using some benchmark datasets. It is also compared with some other multi-objective metaheuristic-based clustering algorithms. The experimental results show that the proposed algorithm can obtain better results than other metaheuristic-based algorithms. [ABSTRACT FROM AUTHOR]

At a high level, data centres are large IT facilities hosting physical machines (servers) that often run a large number of virtual machines (VMs)—but at a lower level, data centres are an intricate collection of interconnected and virtualised computers, connected services, complex service-level agreements. While data centre managers know that reassigning VMs to the servers that would best serve them and also minimise some cost for the company can potentially save a lot of money—the search space is large and constrained, and the decision complicated as they involve different dimensions. This paper consists of a comparative study of heuristics and exact algorithms for the multi-objective machine reassignment problem. Given the common intuition that the problem is too complicated for exact resolutions, all previous works have focused on various (meta)heuristics such as First-Fit, GRASP, NSGA-II or PLS. In this paper, we show that the state-of-art solution to the single objective formulation of the problem (CBLNS) and the classical multi-objective solutions fail to bridge the gap between the number, quality and variety of solutions. Hybrid metaheuristics, on the other hand, have proven to be more effective and efficient to address the problem—but as there has never been any study of an exact resolution, it was difficult to qualify their results. In this paper, we present the most relevant techniques used to address the problem, and we compare them to an exact resolution (ϵ -Constraints). We show that the problem is indeed large and constrained (we ran our algorithm for 30 days on a powerful node of a supercomputer and did not get the final solution for most instances of our problem) but that a metaheuristic (GeNePi) obtains acceptable results: more (+ 188%) solutions than the exact resolution and a little more than half (52%) the hypervolume (measure of quality of the solution set). [ABSTRACT FROM AUTHOR]

Bat Algorithm, is an evolutionary computation technique based on the echolocation behaviour of microbats while looking for their prey. It is used to perform global optimization. It was developed by Xin-She Yang in 2010. Since then, it has extensively been applied in various optimization problems because of its simple structure and robust performance. Continuous, discrete, or binary, many variants were proposed over the last few years, with applications to solve real-world cases in different fields. Yet, it has one major drawback: its premature convergence due to a lack in its exploration ability. In this paper, we introduce a selection-based improvement and three other modifications to the standard version of this metaheuristic in order to enhance the diversification and intensification capabilities of the algorithm. The newly proposed method has been then tested on 20 standard benchmark functions and the CEC2005 benchmark suit. Some non-parametric statistical tests were also used to compare the New Bat algorithm with other algorithms, and results indicate that the new method is very competitive and outperforms some of the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a novel metaheuristic optimization algorithm inspired by the geometrical features of circles, called the circle search algorithm (CSA). The circle is the most well-known geometric object, with various features including diameter, center, perimeter, and tangent lines. The ratio between the radius and the tangent line segment is the orthogonal function of the angle opposite to the orthogonal radius. This angle plays an important role in the exploration and exploitation behavior of the CSA. To evaluate the robustness of the CSA in comparison to other algorithms, many independent experiments employing 23 famous functions and 3 real engineering problems were carried out. The statistical results revealed that the CSA succeeded in achieving the minimum fitness values for 21 out of the tested 23 functions, and the p-value was less than 0.05. The results evidence that the CSA converged to the minimum results faster than the comparative algorithms. Furthermore, high-dimensional functions were used to assess the CSA's robustness, with statistical results revealing that the CSA is robust to high-dimensional problems. As a result, the proposed CSA is a promising algorithm that can be used to easily handle a wide range of optimization problems. [ABSTRACT FROM AUTHOR]

Internet of Things (IoT) is transforming the technical setting of conventional systems and finds applicability in smart cities, smart healthcare, smart industry, etc. In addition, the application areas relating to the IoT enabled models are resource-limited and necessitate crisp responses, low latencies, and high bandwidth, which are beyond their abilities. Cloud computing (CC) is treated as a resource-rich solution to the above mentioned challenges. But the intrinsic high latency of CC makes it nonviable. The longer latency degrades the outcome of IoT based smart systems. CC is an emergent dispersed, inexpensive computing pattern with massive assembly of heterogeneous autonomous systems. The effective use of task scheduling minimizes the energy utilization of the cloud infrastructure and rises the income of service providers by the minimization of the processing time of the user job. With this motivation, this paper presents an intelligent Chaotic Artificial Immune Optimization Algorithm for Task Scheduling (CAIOA-RS) in IoT enabled cloud environment. The proposed CAIOA-RS algorithm solves the issue of resource allocation in the IoT enabled cloud environment. It also satisfies the makespan by carrying out the optimum task scheduling process with the distinct strategies of incoming tasks. The design of CAIOA-RS technique incorporates the concept of chaotic maps into the conventional AIOA to enhance its performance. A series of experiments were carried out on the CloudSim platform. The simulation results demonstrate that the CAIOA-RS technique indicates that the proposed model outperforms the original version, as well as other heuristics and metaheuristics. [ABSTRACT FROM AUTHOR]

Parameter-free algorithms are of an increasing interest in applications that require out-of-the-box solving techniques. For instance, scheduling in volatile environments or control parameters optimisation often requires flexible solving approaches without the need to tune or retune the parameters. In addition, parameter-free algorithms are usually beneficial in solving previously unexplored real-world problem instances. In this paper, we propose a parameter-free local search strategy to solve graph colouring, which is the underlying problem for a number of scheduling applications. Two variants of parameter-free local search are computationally investigated: PFLS-A and PFLS-B. Both of these algorithms are based on accepting strictly improving moves and operating as a random walk if no strictly improving move is found. PFLS-A and PFLS-B differ in randomised versus systematic exploration of the neighbourhood of the current solution. Their cooperative variant CPFLS is also proposed. We compare the results of these three algorithms to the results obtained by 13 other local search methods from the literature. CPFLS provides better or equal results as the other local search algorithms in 67.25 % of per-instance comparisons. This is without employing any explicit or implicit parameters that are usually used in metaheuristics. This hints the promising nature of parameter-free metaheuristics not only for this problem but also metaheuristics in general. [ABSTRACT FROM AUTHOR]

Metaheuristics are a class of approximate methods, which are designed to attack hard combinatorial optimization problems. In metaheuristics, a neighborhood is defined by the specified move operation for a solution. The neighborhood plays an essential role in the performance of its algorithms. It is important to capture the statistical properties of neighborhoods. In this paper, we present a theoretical analysis of neighborhoods for a wide class of combinatorial optimization problems, instead of just for restricted instances. First, we give a probabilistic model which allows us to compute statistics for various types of neighborhoods. Here we introduce an approach in which the solution space (the landscape) for a wide class of combinatorial optimization problems can be approximated to AR(1), which can be used to capture the statistics of the solution space. The theoretical results obtained from our proposed model closely match empirically observed behavior. Second, we present an application in which we use our probabilistic model of neighborhoods. [ABSTRACT FROM AUTHOR]

Metaheuristics are algorithms that have proven their efficiency on multi-objective combinatorial optimisation problems. They often use local search techniques, either at their core or as intensification mechanisms, to obtain a well-converged and diversified final result. This paper surveys the use of local search techniques in multi-objective metaheuristics and proposes a general structure to describe and unify their underlying components. This structure can instantiate most of the multi-objective local search techniques and algorithms in literature. [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]

A novel nature-inspired metaheuristic optimization algorithm, called the quantum firefly algorithm, is proposed in this paper. The algorithm imitates (a) the social behaviour of fireflies mating in nature, (b) laws of quantum physics, and (c) laws of natural evolution. The algorithm combines the powers of two well-known algorithms: the firefly algorithm and the quantum genetic algorithm. The proposed quantum firefly algorithm's performance is tested on 15 mathematical test functions and one structural design problem. The obtained results show that the quantum firefly algorithm is very competitive compared to the firefly algorithm and the quantum genetic algorithm. [ABSTRACT FROM AUTHOR]

Feature transformation methods can be used effectively to improve the performance of the machine learning techniques, such as classification and clustering, via enhancing the discrimination among the samples. Additionally, binary representation of features may be necessary in several circumstances. For example, distributed systems may have limited bandwidth, storage, and energy that necessitate rough quantization of the measurements. This paper proposes a random projection-based feature transformation method that maps the data points from the original space into a new binary space. In the proposed transformation method, the random projection process is formulated as an optimization problem. A modified chaotic version of the sine–cosine algorithm is used to find the optimal random projector. The performance of the proposed transformation method is validated using 15 standard UCI benchmark datasets against the linear discernment analysis. Moreover, it is compared to other metaheuristic-based feature reduction methods including the gray wolf optimizer, the genetic algorithm, and the antlion optimizer. The obtained results assure the superiority of the proposed transformation method in terms of classification accuracy and storage requirements. [ABSTRACT FROM AUTHOR]

The search for a better approach to design a convenient controlling scheme is one of the main challenges of the research field related to power converters. This paper brings forward a significant contribution as part of this challenge. In this regard, novel approaches have been proposed for both controller scheme and tuning algorithm. In terms of controlling scheme, a fractional-order proportional–integral–derivative (FOPID) controller was used alongside the Bode's ideal transfer function to achieve optimum performance of a buck converter system. To achieve a greater performance of the FOPID controller, a novel metaheuristic algorithm, which consists of a balanced structure in terms of explorative and exploitative phases, has also been developed by hybridizing the hunger games search algorithm with simulated annealing technique. The proposed hybrid algorithm helped tuning the FOPID controller optimally. The proposed algorithm and controlling scheme have been proved to be a better approach for controlling a buck converter system in terms of time and frequency domains along with disturbance rejection. To further verify the effectiveness of the proposed hybrid algorithm–based controlling scheme, it was compared with other reported and capable approaches which have also confirmed the greater performance of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we study the quadratic assignment problem with a rank-one cost matrix (QAP-R1). Four integer-programming formulations are introduced of which three are assumed to have partial integer data. Unlike the standard quadratic assignment problem, some of our formulations can solve reasonably large instances of QAP-R1 with impressive running times and are faster than some metaheuristics. Pairwise relative strength of the LP relaxations of these formulations are also analyzed from theoretical and experimental points of view. Finally, we present a new metaheuristic algorithm to solve QAP-R1 along with its computational analysis. Our study offers the first systematic experimental analysis of integer-programming models and heuristics for QAP-R1. The benchmark instances with various characteristics generated for our study are made available to the public for future research work. Some new polynomially solvable special cases are also introduced. Summary of Contribution: This paper aims to advance our knowledge and ability in solving an important special case of the quadratic assignment problem. It shows how to exploit inherent properties of an optimization problem to achieve computational advantages, a strategy that was followed by researchers in model building and algorithm developments for decades. Our computational results attest to this time-tested general philosophy. The paper presents the first systematic computational study of the rank one quadratic assignment problem, along with new mathematical programming models and complexity analysis. We believe the theoretical and computational results of this paper will inspire further research on the topic and will be of significant value to practitioners using rank one quadratic assignment models. [ABSTRACT FROM AUTHOR]

Optimization is a very important issue to efficiently solve engineering problems. The clear comprehension of the elements and processes of optimizer algorithms is fundamental to ensure that engineer students are capable to apply, tune, and design new algorithms. This paper presents an educational platform based on LEGO© EV3 and MATLAB to assist the learning of the principles of classical and metaheuristic optimization algorithms at undergraduate level, by providing a simple and easy-to-follow teaching setup. The proposed study aims to accompany students through the learning of optimization fundamentals by building hands-on robotic experiments. The proposed educational platform has been successfully applied to several undergraduate courses within the Electronics Department at the University of Guadalajara. The description of each experiment and the evaluation of their impact in the student performance are both provided in the paper. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid bio-inspired metaheuristic optimization approach namely emperor penguin and salp swarm algorithm (ESA) is proposed. This algorithm imitates the huddling and swarm behaviors of emperor penguin optimizer and salp swarm algorithm, respectively. The efficiency of the proposed ESA is evaluated using scalability analysis, convergence analysis, sensitivity analysis, and ANOVA test analysis on 53 benchmark test functions including classical and IEEE CEC-2017. The effectiveness of ESA is compared with well-known metaheuristics in terms of the optimal solution. The proposed ESA is also applied on six constrained and one unconstrained engineering problems to evaluate its robustness. The results reveal that ESA offers optimal solutions as compared to the other competitor algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes a reactive VNS metaheuristic for the maximum intersection of k-subsets problem (kMIS). The kMIS is defined as: Given a set of elements, a subset family of the first set and an integer k. The problem consists of finding k subset so that the intersection is maximum. Our VNS metaheuristic incorporates strategies used in GRASP metaheuristics, such as the GRASP construction phase and the Reactive GRASP. Both were used in the shaking phase as a reactive components to VNS. We also propose what we call teh Dynamic Step, a new way to increase the VNS neighborhood. All of these strategies, as well as the Skewed VNS, were added to our Reactive VNS algorithm for kMIS. Computational results showed that the new algorithm outperforms the state-of-the-art algorithm. [ABSTRACT FROM AUTHOR]

This paper considers the no-wait job shop (NWJS) problem with makespan minimisation criteria. It is well known that this problem is strongly NP-hard. Most of the previous studies decompose the problem into a timetabling sub-problem and a sequencing sub-problem. Each study proposes a different sequencing and timetabling algorithm to solve the problem. In this research, this important question is aimed to be answered: is the timetabling or the sequencing algorithm more important to the effectiveness of the developed algorithm? In order to find the answer, three different sequencing algorithms are developed; a tabu search (TS), a hybrid of tabu search with variable neighbourhood search (TSVNS), and a hybrid of tabu search with particle swarm optimisation (TSPSO). Afterwards, the sequencing algorithms are combined with four different timetabling methods. All the approaches are applied to a large number of test problems available in the literature. Statistical analysis reveals that although some of the sequencing and timetabling algorithms are more complicated than the others, they are not necessarily superior to simpler algorithms. In fact, some of the simpler algorithms prove to be more effective than complicated and time-consuming methods. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the contention aware task scheduling problem on a grid topology of processors. By contention awareness, we mean that simultaneous communication on a link has to be serialized. To solve this problem, we propose several nature inspired metaheuristic algorithms: Simulated Annealing (SA), Genetic Algorithm (GA), Differential Evolution (DE), Particle Swarm Optimization (PSO), Bat Algorithm (BA), Cuckoo Search (CS), and Firefly Algorithm (FA). We perform benchmark evaluation of these algorithms for the Normalized Schedule Length (NSL) parameter. The benchmark task graphs that we consider are: random task graphs, peer set task graphs, systolic array task graphs, Gaussian elimination task graphs, divide and conquer task graphs, and fast Fourier transform task graphs. [ABSTRACT FROM AUTHOR]

Agent-based metaheuristics computing paradigm (EMAS) has been proposed over 20 years ago by Cetnarowicz. Since then, many efforts were made in order to evaluate, formally analyze and further develop this paradigm towards creating new algorithms as EMAS hybrids, or EMAS-inspired techniques. However, at the same time a significant work has been done in order to build efficient software frameworks supporting this (and similar) computing paradigms. These frameworks were based not only on classic object-oriented programming, but also on functional approach and recently also utilizing heterogeneous infrastructure. This paper presents an overview of the most important findings in this area, including novel ways of processing the agents and component orientation, which allow for both high flexibility and high efficiency of provided solutions. The discussed concepts are illustrated with a case study of a system solving hard computational problem leveraging GPGPU. [ABSTRACT FROM AUTHOR]

Recently, practitioners and researchers have concentrated on the use of meta-heuristics in the design of multi-objective supply chain networks. The number of publications in this field reflects this interest. The purpose of this paper is to propose a novel metaheuristic approach for designing supply chain network problems in the case of multi-objective supply chains. The proposed algorithm hybridizes three meta-heuristic approaches; simulated annealing, tabu search, and variable neighborhood algorithms. The proposed algorithm is also combined with a linear programming approach. The purpose of hybridization is to aggregate the approaches in order to benefit from the advantages of these solution algorithms. The features of these algorithms are investigated in this paper for the first time. The most useful characteristics of each algorithm are then utilized for developing the new algorithm. The performance of the proposed algorithm is compared with an exact algorithm, simulated annealing, and tabu search algorithms. The results indicated that the proposed algorithm is comparable to the exact in the case of small and medium-sized supply chain problems. The findings revealed that the proposed algorithm takes on an average of 6.3 min to solve small and medium problems, while the exact algorithm takes 412 min. Moreover, the proposed algorithm outperforms other algorithms with a mean ideal distance (MID) of 13,606,871, a percent of domination (POD) of 0.84, and a computational time of 15.64 min compared to the tabu search algorithm's MID of 15,574,523, a POD of 0.55, and a computational time of 21.46 min. The simulated annealing algorithm, on the other hand, achieved an average MID of 18,145,931, a POD of 0.40, and a computational time of 30 min. Furthermore, the findings showed that the proposed algorithm is capable of solving complex and large supply chain problems in a reasonable time when exact approaches fail. [Display omitted] • Developing a novel metaheuristic algorithm for solving the MOSC network. • Optimizing the proposed algorithm parameters using regression models. • Comparing the proposed algorithm with other algorithms. • Confirming the performance of the proposed algorithm for solving MOSC problems. [ABSTRACT FROM AUTHOR]

The Binary Integer Programming problem (BIP) is a mathematical optimization problem, with linear objective function and constraints, on which the domain of all variables is {0, 1}. In BIP, every variable is associated with a determined cost coefficient. The Minmax regret Binary Integer Programming problem under interval uncertainty (M-BIP) is a generalization of BIP in which the cost coefficient associated to the variables is not known in advance, but are assumed to be bounded by an interval. The objective of M-BIP is to find a solution that possesses the minimum maximum regret among all possible solutions for the problem. In this paper, we show that the decision version of M-BIP is Σp2 Σ 2 p $ {\mathrm{\Sigma }}_2^p$ -complete. Furthermore, we tackle M-BIP by both exact and heuristic algorithms. We extend three exact algorithms from the literature to M-BIP and propose two fix-and-optimize heuristic algorithms. Computational experiments, performed on the Minmax regret Weighted Set Covering problem under Interval Uncertainties (M-WSCP) as a test case, indicates that one of the exact algorithms outperforms the others. Furthermore, it shows that the proposed fix-and-optimize heuristics, that can be easily employed to solve any minmax regret optimization problem under interval uncertainty, are competitive with ad-hoc algorithms for the M-WSCP. [ABSTRACT FROM AUTHOR]

In this paper, the water cycle algorithm (WCA), a recently developed metaheuristic method is proposed for solving multi-objective optimization problems (MOPs). The fundamental concept of the WCA is inspired by the observation of water cycle process, and movement of rivers and streams to the sea in the real world. Several benchmark functions have been used to evaluate the performance of the WCA optimizer for the MOPs. The obtained optimization results based on the considered test functions and comparisons with other well-known methods illustrate and clarify the robustness and efficiency of the WCA and its exploratory capability for solving the MOPs. [ABSTRACT FROM AUTHOR]

Despite the ability of Low-Power Wide-Area Networks to offer extended range, they encounter challenges with coverage blind spots in the network. This article proposes an innovative energy-efficient and nature-inspired relay selection algorithm for LoRa-based LPWAN networks, serving as a solution for challenges related to poor signal range in areas with limited coverage. A swarm behavior-inspired approach is utilized to select the relays' localization in the network, providing network energy efficiency and radio signal extension. These relays help to bridge communication gaps, significantly reducing the impact of coverage blind spots by forwarding signals from devices with poor direct connectivity with the gateway. The proposed algorithm considers critical factors for the LoRa standard, such as the Spreading Factor and device energy budget analysis. Simulation experiments validate the proposed scheme's effectiveness in terms of energy efficiency under diverse multi-gateway (up to six gateways) network topology scenarios involving thousands of devices (1000–1500). Specifically, it is verified that the proposed approach outperforms a reference method in preventing battery depletion of the relays, which is vital for battery-powered IoT devices. Furthermore, the proposed heuristic method achieves over twice the speed of the exact method for some large-scale problems, with a negligible accuracy loss of less than 2%. [ABSTRACT FROM AUTHOR]