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Real-world optimisation problems that are not endowed in mathematical characteristics like differentiability, convexity etc. require non-traditional optimisation approaches that explore the promising regions of the search space stochastically to achieve the optima of the problem. Grey Wolf Optimizer (GWO) is one of the efficient and recently developed approaches in the area of Swarm Intelligence to solve real-world optimisation problems over continuous space. However, in some cases, due to the insufficient diversity, GWO still suffers from the problem of stagnation in local optimums. Therefore, this article presents the novel algorithm OCS-GWO that enhances the performance of original GWO by introducing the opposition-based learning to approximate the closer search candidate solution to the global optima and chaotic local search for the exploitation of the search regions efficiently. In OCS-GWO, a chaotic local search is used for balancing the exploration and exploitation operators that are the underlying features of any stochastic search algorithm. The performance of the proposed algorithm OCS-GWO has been evaluated on a set of 23 standard benchmark test problems and on three engineering application problems – gear train, cantilever beam and speed reducer design problems. The experimental results on test problems and engineering applications confirm the efficiency and reliability of the proposed algorithm over original GWO. [ABSTRACT FROM AUTHOR]

Abstract Grey Wolf Optimizer (GWO) algorithm is a relatively new algorithm in the field of swarm intelligence for solving continuous optimization problems as well as real world optimization problems. The Grey Wolf Optimizer is the only algorithm in the category of swam intelligence which is based on leadership hierarchy. This paper has three important aspects- Firstly, for improving the search ability by grey wolf a modified algorithm RW-GWO based on random walk has been proposed. Secondly, its performance is exhibited in comparison with GWO and state of art algorithms GSA, CS, BBO and SOS on IEEE CEC 2014 benchmark problems. A non-parametric test Wilcoxon and Performance Index Analysis has been performed to observe the impact of improving the leaders in the proposed algorithm. The results presented in this paper demonstrate that the proposed algorithm provide a better leadership to search a prey by grey wolves. The third aspect of the paper is to use the proposed algorithm and GWO on real life application problems. It is concluded from this article that RW-GWO algorithm is an efficient and reliable algorithm for solving not only continuous optimization problems but also for real life optimization problems. [ABSTRACT FROM AUTHOR]

Grey Wolf Optimiser (GWO) is a recently developed optimisation approach to solve complex non-linear optimisation problems. It is relatively simple and leadership-hierarchy based approach in the class of SwarmIntelligence based algorithms. For solving complex real-world non-linear optimisation problems, the search equation provided in GWO is not of sufficient explorative behaviour. Therefore, in the present paper, an attempt has been made to increase the exploration capability along with the exploitation of a search space by proposing an improved version of classical GWO. The proposed algorithm is named as Cauchy-GWO. In Cauchy-GWO Cauchy operator has been integrated in which first two new wolves are generated with the help of Cauchy distributed random numbers and then another new wolf is generated by taking the convex combination of these new wolves. The performance of Cauchy-GWO is exhibited on standard IEEE CEC 2014 benchmark problem set. Statistical analysis of the results on CEC 2014 benchmark set and popular evaluation criteria, Performance Index (PI) proves that Cauchy-GWO outperforms GWO in terms of error values defined in IEEE CEC 2014 benchmarks collection. Later on in the paper, GWO and Cauchy-GWO algorithms have been used to solve three well-known engineering application problems and two problems of reliability. From the analysis conducted in the present paper, it can be concluded that the proposed algorithm, Cauchy-GWO is reliable and efficient algorithm to solve continuous benchmark test problems, as well as real-life applications problems. [ABSTRACT FROM AUTHOR]

Swarm intelligence is one of the most promising area of numerical optimization to solve real‐world optimization problems. Grey wolf optimizer (GWO), which is based on leadership hierarchy of grey wolves, is one of the relatively new algorithm in the field of swarm intelligence–based algorithms. In order to solve constrained real‐world optimization problems, in this paper, a constrained version of GWO has been proposed by incorporating a simple constraint handling technique in GWO, and then an attempt is made to improve the ability of the leaders in original GWO by proposing random walk GWO (RW‐GWO) by pointing out some drawbacks in their process of searching prey. (To the best of the knowledge of the authors, a constrained version of GWO has not been developed yet. The unconstrained version of RW‐GWO has been proposed in the authors' earlier work.) The efficiency of both these proposed algorithms have been tested on the Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation 2006 benchmark problems and on 3 engineering application problems to observe their comparative performance. It is concluded from the results that the proposed improved version of GWO, namely, RW‐GWO, has better potential to solve these constraint problems compared to GWO very efficiently as a constrained optimizer. [ABSTRACT FROM AUTHOR]

This study addresses the traffic light scheduling problem for pedestrian–vehicle mixed-flow networks. A macroscopic model, which strikes an appropriate balance between pedestrians' needs and vehicle drivers' needs, is employed to describe the traffic light scheduling problem in a scheduling framework. The objective of this problem is to minimize the total network-wise delay time of vehicles and pedestrians within a given finite-time window, which is crucial to avoid traffic congestion in urban road networks. To achieve this objective, the present study first uses a well-known optimization solver called GUROBI to obtain the optimal solution by converting the problem into mixed-integer linear programming. The obtained results indicate the computational inefficiency of the solver for large network sizes. To overcome this computational inefficiency, three novel metaheuristic methods based on the sine–cosine algorithm are proposed. These methods are denoted by discrete sine–cosine algorithm, discrete sine–cosine algorithm with local search operator, and discrete sine–cosine algorithm with local search operator and memory utilization inspired by harmony search. Each of these methods is developed hierarchically by taking the advantages of previously developed method(s) in terms of a better search process to provide more accurate solutions and a better convergence rate. To validate all these proposed metaheuristics, extensive computational experiments are carried out using the real traffic infrastructure of Singapore. Moreover, various performance measures such as statistical optimization results, relative percentage deviation, computational time, statistical analysis, and convergence behavior analysis have been employed to evaluate the performance of algorithms. The comparison of the proposed SCA variants is done with GUROBI solver and other metaheuristics namely, harmony search, firefly algorithm, bat algorithm, artificial bee colony, genetic algorithm, salp swarm algorithm, and harris hawks optimization. Overall comparison analysis concludes that the proposed methods are very efficient to solve the traffic light scheduling problem for pedestrian–vehicle mixed-flow networks with different network sizes and prediction time horizons. • A macroscopic model for urban traffic light scheduling problem (PV-TLSP). • PV-TLSP considers pedestrian–vehicle mixed-flow networks. • Discrete sine–cosine algorithm is proposed for solving PV-TLSP. • Enhanced DSCA variants are proposed using local search and memory utilization. • Extensive experiments are carried out to verify the efficacy of proposed algorithms. [ABSTRACT FROM AUTHOR]

• Nine recent meta-heuristics are used to optimize eight mechanical design problems. • Theoretical and numerical comparisons are extensively investigated. • The results show the merits of the methods used in solving the case studies. Determining the solution for real mechanical design problems is a challenging task when using the newly developed and efficient swarm intelligence algorithms. There are so many difficulties to be addressed, including but not limited to mixed decision variables, diverse constraints, inherent errors, conflicting objectives, and numerous locally optimal solutions. This work analyzes the behavior of nine metaheuristic algorithms, namely, salp swarm algorithm (SSA), multi-verse optimizer (MVO), moth-flame optimizer (MFO), atom search optimization (ASO), ecogeography-based optimization (EBO), queuing search algorithm (QSA), equilibrium optimizer (EO), evolutionary strategy (ES) and hybrid self-adaptive orthogonal genetic algorithm (HSOGA). The efficiency of these algorithms is evaluated on eight mechanical design problems using the solution quality and convergence analysis, which verifies the wide applicability of these algorithms to real-world application problems. [ABSTRACT FROM AUTHOR]

Grey Wolf Optimizer (GWO) is a new nature-inspired metaheuristic algorithm based on the leadership and social behaviour of grey wolves in nature. It has shown potential to solve several real-life applications, but still for some complex optimization tasks, it may face the problem of getting trapped at local optima and premature convergence. Therefore, in this study, to prevent from these drawbacks and to get a more stable sense of balance between exploitation and exploration, a new modified GWO called memory-based Grey Wolf Optimizer (mGWO) is proposed. In the mGWO, the search mechanism of the wolves is modified based on the personal best history of each individual wolves, crossover and greedy selection. These strategies help to enhance the global exploration, local exploitation and an appropriate balance between them during the search procedure. To investigate the effectiveness of the proposed mGWO, it has been tested on standard and complex benchmarks given in IEEE CEC 2014 and IEEE CEC 2017. Furthermore, some real engineering design problems and multilevel thresholding problem are also solved using the mGWO. The results analysis and its comparison with other algorithms demonstrate the better search-efficiency, solution accuracy and convergence rate of the proposed mGWO in performing the global optimization tasks. • A modified Grey Wolf Optimizer (mGWO) is proposed for global optimization. • The mGWO is validated on standard IEEE CEC 2014 and IEEE CEC 2017 benchmark problems. • The mGWO algorithm is used for solving engineering design and thresholding problems. • Comparison with other algorithms illustrate the effectiveness of the mGWO. [ABSTRACT FROM AUTHOR]