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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]

Classification is used to categorize data and produce decisions for several domains. To improve the accuracy of classification, researchers have tended to hybridize the neural network with other metaheuristic algorithms in order to better exploit and explore the search space and thereby solve many different classification problems in an effective manner. The hybridization of algorithms is now commonplace and has resulted in the creation of novel methods that are more effective in comparison with those that employ a sole algorithm. Therefore, in this paper, a hybridization approach is employed to utilize the African buffalo optimization (ABO) algorithm as an optimizer to adjust the weights of the probabilistic neural network (PNN). The effectiveness of the proposed (ABO-PNN) method is investigated by applying it to several different classification problems. The efficiency of the ABO algorithm is assessed based on the PNN training results produced and its performance is compared with that of different types of optimization algorithm. The performance of the proposed algorithm in terms of classification accuracy is tested on 11 benchmark datasets. The results show that the ABO is better than the firefly algorithm (FA) in terms of both classification accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

New metaheuristic algorithms have soared over the past ten years. A common practice in proposing a new algorithm is validating it on several benchmark functions and engineering problems. Although CEC benchmark problems are specifically designed to validate the performance of new meta-heuristics, engineering design problems from pressure vessels to springs have been used in hundreds of papers to prove algorithm efficiency. To date, no benchmark practices have been established yet, i.e., researchers design their own benchmark to validate their algorithm. Thus, the high number of new algorithms combined with the high number of different benchmarking setups complicates the comparing and validating processes. In this paper, we study benchmark practices related to engineering applications. In particular, our exhaustive qualitative systematic review focuses on metaheuristics applied to the tension/compression spring design problem (TCSDP). The aim of this study is threefold: (i) evaluate where the field stands in regards of algorithm performance on the TCSDP, (ii) evaluate benchmarking practices, and (iii) facilitate future algorithm comparison. For these purposes, we first review all the existing metaheuristics applied to the TCSDP in their first publication. For each paper, we gather the data regarding the problem definition, the simulation setup, and the optimized design. We evaluated the data through several metrics to find the best-optimized design so far. Our findings and analysis concluded that the field of metaheuristics and its benchmarking practice have not reached maturity yet. Thus, we recommend some actions to address the issues and provide future research directions. [ABSTRACT FROM AUTHOR]

• We introduce an RVRP where the last-mile delivery of some demands can be outsourced. • We propose construction and improvement heuristics handling outsourcing decisions. • The routes include the driving and rest periods according to European regulations. • We solve 60 artificial instances using our algorithms in classic metaheuristics. • The impact of the construction procedure and the outsourcing decisions are evaluated. This paper addresses a Rich Vehicle Routing Problem (RVRP) characterized by the following attributes: long-haul transport, driver hours regulation, incompatibility among goods, multiple depots and pickup locations, heterogeneous vehicles, time windows, and outsourcing decisions for last-mile delivery. Addressing the latter aspect is especially challenging, since it requires substantial changes in the algorithms for generating initial feasible solutions (construction heuristic) and for modifying existing solutions (improvement heuristics). Our work develops new heuristics adapted to the above attributes, and evaluates their performance in combination with common solving metaheuristics. We also assess the impact and the cost-effectiveness of the outsourcing attribute. [ABSTRACT FROM AUTHOR]

Metaheuristics, providing high level guidelines for heuristic optimisation, have successfully been applied to many complex problems over the past decades. However, their performances often vary depending on the choice of the initial settings for their parameters and operators along with the characteristics of the given problem instance handled. Hence, there is a growing interest into designing adaptive search methods that automate the selection of efficient operators and setting of their parameters during the search process. In this study, an adaptive binary parallel evolutionary algorithm, referred to as ABPEA, is introduced for solving the uncapacitated facility location problem which is proven to be an NP-hard optimisation problem. The approach uses a unary and two other binary operators. A reinforcement learning mechanism is used for assigning credits to operators considering their recent impact on generating improved solutions to the problem instance in hand. An operator is selected adaptively with a greedy policy for perturbing a solution. The performance of the proposed approach is evaluated on a set of well-known benchmark instances using ORLib and M*, and its scaling capacity by running it with different starting points on an increasing number of threads. Parameters are adjusted to derive the best configuration of three different rewarding schemes, which are instant, average and extreme. A performance comparison to the other state-of-the-art algorithms illustrates the superiority of ABPEA. Moreover, ABPEA provides up to a factor of 3.9 times acceleration when compared to the sequential algorithm based on a single-operator. • This paper proposes a multi-threaded adaptive evolutionary algorithm. • The proposed approach (ABPEA) is tested on the well-known binary-encoded problem UFLP. • An operator is selected adaptively with a greedy policy for perturbing a solution. • Three rewarding schemes, which are instant, average and extreme, are discussed. • Effect of varying the number of threads on the performance of ABPEA is investigated. [ABSTRACT FROM AUTHOR]

• A new method to solve global optimization called BGWO. • The beetle antenna strategy is adopted to provide hearing for the leader wolf. • Exploration and exploitation are balanced by a new nonlinear strategy. • Evaluation of proposed method on 23 benchmark functions and 4 engineering problems. • The performance of BGWO is better than other state-of-the-art algorithms. Finding feasible solutions to real-world problems is a crucial task. Metaheuristic algorithms are widely used in many fields due to the variety of solutions they can produce. The grey wolf optimizer (GWO) is a relatively novel population-based metaheuristic algorithm that has been shown to have good optimization performance. However, due to the insufficient diversity of wolves in some cases, this approach can lead to locally optimal situations. Therefore, this paper proposes a grey wolf optimization method based on a beetle antenna strategy (BGWO) that gives the leader wolf a sense of hearing to improve the global search ability and reduce unnecessary searches. In addition, to balance exploration and exploitation, a nonlinear dynamic control parameter update strategy based on the cosine function is proposed. To evaluate the performance of the proposed BGWO, this paper uses 23 standard benchmark functions to test the method in different dimensions. Moreover, four well-known engineering problems are used to evaluate the ability of the proposed algorithm to obtain real-world problem solutions. The experimental results show that BGWO has superior performance and is competitive with many state-of-the-art algorithms in terms of solution accuracy, convergence rate, and stability. [ABSTRACT FROM AUTHOR]

The Capacitated Vehicle Routing Problem is a well-known combinatorial problem. In this paper, we propose a hybrid algorithm based on a discrete adaptation of the Differential Evolution metaheuristic, which is designed for continuous problems, combined with local search procedures to solve CVRP. An individual in the algorithm represents a CVRP solution. The algorithm presents a discrete adaptation for DE that consists on exchanging customers considering their routes positions, instead of arithmetically modifying the individuals. The proposed algorithm, called CDELS, is compared with three state-of-the-art algorithms. The computational experiments are performed on six classical datasets, with an extensive study for parameter tuning. A statistical analysis of the results was also conducted. It showed that the CDELS algorithm is highly significantly better than state-of-the-art methods with a confidence level of 99%. CDELS is open-source. • Discrete adaptation for the Differential Evolution (DE) Algorithm. • Extensive calibration for DE parameters. • Statistical analysis of the algorithm results compared with state-of-the-art algorithms. • The proposed algorithm presents outstanding performance. [ABSTRACT FROM AUTHOR]

Transportation problem is one of combinatorial problems interesting to discuss. Generalized Orienteering Problem (GOP) is a transportation problem. GOP is the development of Traveling Salesman Problem. The purpose of GOP is to maximize total score with a maximum mileage limit. In GOP, there is set of scores which represents level of satisfaction that can be achieved by an orienteer by visiting some places. GOP is a combinatorial optimization problem where metaheuristics is suitable tool to solve it. In this paper, Viral System (VS) is used to solve GOP. VS is a new algorithm that mimics the pattern of virus life. The algorithm performed good enough for other combinatorial cases. To evaluate our VS on GOP, the test data of 27 cities were used. Five different weights have been tried and VS showed promising performance. Therefore, VS still needs further modification in order to compete with other algorithm s. [ABSTRACT FROM AUTHOR]

Sine cosine algorithm (SCA) is a recently developed and widely used metaheuristic to perform global optimization tasks. Due to its simplicity in structure and reasonable performance, it has been utilized to solve several real-world applications. This paper proposes an alternate version of the SCA by adopting the greedy approach of search, crossover and exponentially decreased transition control parameter to overcome the issues of low exploitation, insufficient diversity and premature convergence. The proposed algorithm, called ECr-SCA, is validated and compared with the original SCA using computational time, diversity, performance index, statistical and convergence analysis on a set of 23 standard benchmark problems. Later, the proposed ECr-SCA is compared with seventeen other algorithms including improved versions of the SCA and state-of-the-art algorithms. Furthermore, the ECr-SCA is used to train multi-layer perceptron and the results are compared with variants of SCA and other metaheuristics. Overall comparison based on several different metrics illustrates the significant improvement in the search strategy of the SCA by the proposal of the ECr-SCA. • The enhanced sine cosine algorithm (ECr-SCA) is proposed for global optimization. • A greedy search and modified transition parameter are used to increase exploitation. • The multi-parent crossover is embedded to enhance diversity and global search. • The excellent performance of the ECr-SCA is validated on benchmark problems. • The ECr-SCA is also used to train multilayer perceptron. [ABSTRACT FROM AUTHOR]

The main role of the optimal Generator Maintenance Scheduling (GMS) problem in power systems is to develop an optimal preventive maintenance scheduling of the generation part units. An optimal GMS provides power systems with higher operational reliability, extends the generators lifetime and reduces the cost of generators maintenance. The GMS problem is formulated as an optimisation problem. This problem should satisfy both load's power demand and workforce constraints with ensuring the reliability of power systems at economical operation cost. The GMS problem has been studied for many years when exact mathematical methods have been used in the past to reach exact solutions for small-scale problems. However, these conventional mathematical approaches have many limitations and they suffer from unreasonable computational efforts as system dimension increases. Traditional approximate methods have been adopted to overcome the limitations of exact methods for medium-scale power systems. However, they provide approximate solutions and they require a large computational effort for wide-area systems of big dimensions. Recently, modern methods based on metaheuristics optimisation have taken a long part to solve the GMS problem and to overcome the limitations of approximate methods. In this paper, a proposed Discrete Chaotic Jaya Optimisation (DCJO) algorithm is employed to perform the preventive maintenance scheduling of electric power systems generators. The proposed algorithm is based on a cooperation between the discrete Jaya optimisation algorithm and a proposed move rule based on Chaotic Local Search (CLS) technique to improve both exploration and exploitation phases. The GMS problem is modelled based on the reliability criterion of an objective function of a sum of the squares of the reserves of generation. The optimisation process is performed through minimising an evaluation function of a weighted sum of the objective function and the penalty function for violations of the constraints. The proposed approach has been tested in a 21-unit test system over a planned horizon of 52 weeks in which the peak load is 4739 MW and the maximum generation is 5688 MW and there is a total number of 35 workforce available per week to perform the maintenance tasks. The proposed method has been compared through several statistical tests with recent algorithms of the related works. The obtained results show the effectiveness of the proposed algorithm for solving the GMS problem as compared to other recent algorithms. This approach can be relied at the present upon to solve maintenance scheduling problems of generation units in power systems. • A discrete chaotic Jaya algorithm is proposed to solve the generator maintenance scheduling problem in power systems. • The Chaotic Local Search (CLS) has been incorporated into the Discrete Jaya Optimisation (DJO) algorithm. • The DJO algorithm has been used for global optimisation and CLS has been designed for local optimisation. • The local and global optimisations have been improved through CLS and DJO algorithm respectively. • Statistical validity of obtained results has been tested using various statistical tests. [ABSTRACT FROM AUTHOR]

In the crowded environment of bio-inspired population-based metaheuristics, the Salp Swarm Optimization (SSO) algorithm recently appeared and immediately gained a lot of momentum. Inspired by the peculiar spatial arrangement of salp colonies, which are displaced in long chains following a leader, this algorithm seems to provide an interesting optimization performance. However, the original work was characterized by some conceptual and mathematical flaws, which influenced all ensuing papers on the subject. In this manuscript, we perform a critical review of SSO, highlighting all the issues present in the literature and their negative effects on the optimization process carried out by this algorithm. We also propose a mathematically correct version of SSO, named Amended Salp Swarm Optimizer (ASSO) that fixes all the discussed problems. We benchmarked the performance of ASSO on a set of tailored experiments, showing that it is able to achieve better results than the original SSO. Finally, we performed an extensive study aimed at understanding whether SSO and its variants provide advantages compared to other metaheuristics. The experimental results, where SSO cannot outperform simple well-known metaheuristics, suggest that the scientific community can safely abandon SSO. • Critical analysis of the widely-used salp optimization algorithm (SSO). • Definition of an amended version of SSO that fixed SSO's structural bias. • Extensive experimental phase using the CEC 2017 benchmark suite. • Results show that SSO does not provide any advantage w.r.t. existing heuristics. • Metaphor-based approach to design metaheuristics may introduce bias. [ABSTRACT FROM AUTHOR]

In this paper, a new parameter for population management is implemented in the Differential Evolution algorithm. The new scheme integrates a set of operators that analyze the exploration and exploitation effects during its operation. With these operators, the new method obtains important knowledge about its population diversity during its evolution. Under such conditions, the proposed method can reduce its population when the diversity is too low in order to reduce its computational cost and improve its search capacities simultaneously. To test the new additions, the proposed algorithm has been tested in a set of 29 complex functions and two interplanetary trajectory design problems. The outcome of the tests demonstrates a greatly improved performance when compared to the original Differential Evolution algorithm, a few of its most successful variants, and other algorithms. • A novel population reduction technique for population based Metaheuristics. • A way to measure population diversity has been added to the original DE algorithm. • New operators have been designed to use the population diversity value as metric to adjust the algorithm. • Designed operators have been included in the original DE scheme to improve its search abilities. • Experimental results demonstrate the superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

• A new optimization algorithm based on Lichtenberg figure pattern is presented. • Difussion Limited Aggregation is formulated to create new agents in search space. • Lichtenberg figure pattern presents exploration–exploitation balance. • Tested on complex functions and problems and compared with renowned metaheuristics. This paper proposes a novel global optimization algorithm called Lichtenberg Algorithm (LA), inspired by the Lichtenberg figures patterns. Optimization is an essential tool to minimize or maximize functions, obtaining optimal results on costs, mass, energy, gains, among others. Actual problems may be multimodal, nonlinear, and discontinuous and may not be minimized by classical analytical methods that depend on the gradient. In this context there are metaheuristics algorithms inspired by natural phenomena to optimize real problems. There is no algorithm that is the worst or the best, but more efficient for a given type of problem. Thus, an unprecedented metaheuristic algorithm was created inspired by the physical phenomenon of radial intra-cloud lightning and Lichtenberg figures, successfully exploiting the fractal power and it is different from many in the literature as it is a hybrid algorithm composed of methods of search based on population and trajectory. Several test functions, including a design problem in a welded beam, were used to verify the robustness and to validate the Lichtenberg Algorithm. In all cases, the results were satisfactory when compared to those in the literature. LA shown to be a powerful optimization tool for both unconstraint optimizations and real problems with linear and nonlinear constraints. [ABSTRACT FROM AUTHOR]

This paper proposes a novel population-based metaheuristic optimization algorithm, called Adolescent Identity Search Algorithm (AISA), which is inspired by the process of identity development/search of adolescents. AISA simulates the identity formation behavior of adolescents in the peer group. This behavior is modeled mathematically to solve optimization problems. The proposed algorithm is evaluated on thirty-nine well-known unimodal, multimodal, fixed-dimensional multimodal, composite and CEC 2019 benchmark functions to test exploration, exploitation, local optima avoidance, and convergence properties. The results are verified by an extensive comparative study with thirteen state-of-art metaheuristic algorithms. Furthermore, AISA has been used to solve IIR system identification and inverse kinematics problem of a seven Degrees Of Freedom (7-DOF) robot manipulator considered as the real-life engineering applications. The overall optimization results demonstrate that AISA possesses a strong and robust capability to produce superior performance over other competitor metaheuristic algorithms in solving various complex numerical optimization problems. • A novel metaheuristic algorithm named as Adolescent Identity Search Algorithm (AISA) is proposed. • The AISA has been tested on thirty-nine benchmark problems, IIR system identification and inverse kinematics problem of a seven Degrees Of Freedom (7-DOF) robot manipulator. • The AISA is compared with thirteen well-known optimization algorithms. • Experimental results confirm the performance and effectiveness of the AISA in practice. [ABSTRACT FROM AUTHOR]

Many real-life systems in production and transportation logistics are complex, large-scale, and stochastic in nature. As a consequence, simheuristic approaches – which integrate simulation inside a metaheuristic framework – are becoming increasingly popular in the optimization and simulation communities. In a simheuristic algorithm, time-consuming simulation runs are required in order to: (i) obtain accurate results on the stochastic performance of solutions generated by the metaheuristic; and (ii) provide feedback that can be useful to better guide the metaheuristic search. If the underlying system is complex, discrete-event simulation might be needed, and then the simulation component could easily overrun the computational time of the metaheuristic component. Thus, for each new solution generated by the metaheuristic, several related questions arise: (i) should the simulation component be applied to that solution? – i.e., is that solution 'promising' enough to invest additional computational time on retrieving information about its performance in a stochastic environment?; and (ii) if so, how many simulation runs are needed in order to obtain useful information (i.e., statistics with a minimum level of accuracy)? This paper discusses these issues and proposes several concepts that allow to improve the efficiency (in terms of computational time) of simheuristic algorithms. A case study, based on a typical manufacturing system, is introduced. In order to illustrate and test different speeding-up techniques, the system is optimized by using a simheuristic that integrates a genetic algorithm with discrete-event simulation. [ABSTRACT FROM AUTHOR]

Given a fixed set of rectangular items and a single rectangular object of fixed width and unlimited height, the two-dimensional strip packing problem consists of packing all the items into the object in a non-overlapping manner, such that the resulting packing height is a minimum. Two improved strip packing metaheuristics are proposed in this paper. The first algorithm is a hybrid approach in which the method of simulated annealing is combined with a heuristic construction algorithm, while the second algorithm involves application of the method of simulated annealing directly in the space of completely defined packing layouts, without an encoding of solutions. These two algorithms are compared with a representative sample of metaheuristics from the literature in terms of solution quality achieved in the context of a large set of 1 718 benchmark instances, clustered into four sets of test problems, each with differing characteristics. It is found that the new algorithms indeed compare favourably with, and in some cases outperform, existing strip packing metaheuristics in the literature. • Application of metaheuristic techniques to solve the strip packing problem. • Approaches involving the method of simulated annealing yields favourable results. • The characteristics of the test data employed affect the performances of the algorithms. [ABSTRACT FROM AUTHOR]

This paper introduces a bio-inspired metaheuristic optimization algorithm named Tunicate Swarm Algorithm (TSA). The proposed algorithm imitates jet propulsion and swarm behaviors of tunicates during the navigation and foraging process. The performance of TSA is evaluated on seventy-four benchmark test problems employing sensitivity, convergence and scalability analysis along with ANOVA test. The efficacy of this algorithm is further compared with several well-regarded metaheuristic approaches based on the generated optimal solutions. In addition, we also executed the proposed algorithm on six constrained and one unconstrained engineering design problems to further verify its robustness. The simulation results demonstrate that TSA generates better optimal solutions in comparison to other competitive algorithms and is capable of solving real case studies having unknown search spaces. Note that the source codes of the proposed TSA algorithm are available at [ABSTRACT FROM AUTHOR]