Levy Flight and Chaos Theory-Based Gravitational Search Algorithm for Global Optimization: LCGSA for Global Optimization

Levy Flight and Chaos Theory-Based Gravitational Search Algorithm for Global Optimization: LCGSA for Global Optimization

Sajad Ahmad Rather, P. Shanthi Bala
Copyright: © 2022 |Pages: 58
DOI: 10.4018/IJAMC.292496
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Abstract

The Gravitational Search Algorithm (GSA) is one of the highly regarded population-based algorithms. It has been reported that GSA has a powerful global exploration capability but suffers from the limitations of getting stuck in local optima and slow convergence speed. In order to resolve the aforementioned issues, a modified version of GSA has been proposed based on levy flight distribution and chaotic maps (LCGSA). In LCGSA, the diversification is performed by utilizing the high step size value of levy flight distribution while exploitation is carried out by chaotic maps. The LCGSA is tested on well-known 23 classical benchmark functions. Moreover, it is also applied to three constrained engineering design problems. Furthermore, the analysis of results is performed through various performance metrics like statistical measures, convergence rate, and so on. Also, a signed Wilcoxon rank-sum test has also been conducted. The simulation results indicate that LCGSA provides better results as compared to standard GSA and most of the competing algorithms.
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1. Introduction

Optimization is the process of finding the best solution to the problem from the already available pool of solutions. Basically, a problem whether in engineering, business, science, or management can be considered as an optimization task. To solve an optimization problem, the researchers have used both deterministic methods and population-based algorithms. In the former case, the optimization algorithm depends on the gradient information of the problem. However, they have the drawbacks of unimodality, entrapment in local minima, and so on. In contrast, population-based algorithms treat an optimization problem as a black box meaning non-dependability on the design of the given problem. Moreover, they have the advantages of stochasticity, simplicity of design, flexibility, information interchange, parallelism, and less complexity.

All population-based algorithms are heuristic in nature which means finding the optimal solution from the feasible candidate solutions. Basically, the optimization process starts with the initialization of searcher agents in the solution space. Then, the iteration process creates rapid changes in the values of candidate solutions. After the maximum number of iterations, the optimization process stops and provides an optimal solution. Furthermore, it has been seen that all population-based algorithms consist of two fundamental processes namely exploration and exploitation. The exploration (diversification) is defined as the lower and upper limits of the solution space where searcher agents can move during the optimization process. Moreover, searcher agents change values more often during the exploration phase. In contrast, exploitation (intensification) is the process of finding an optimal solution from the rich pool of feasible candidate solutions. Meanwhile, the searcher agents undergo less number of changes during this phase. According to Eiben and Schippers (1998), exploration and exploitation are inversely proportional to each other. So, a proper balance between them during the optimization process is necessary for getting the best solutions.

It is a fact that most of the population-based algorithms are inspired by nature. The researchers have proposed a number of heuristic algorithms to solve real-world problems. Examples of some of the famous HAs include GA (Holland, 1992), PSO (Kennedy and Eberhart,1995), ACO (Dorigo et al., 2006), DE (Storn and Price, 1995), BBO (Simon, 2008), and many more. Moreover, the recent inclusions into the list of HAs include GWO (Mirjalili et al., 2014), ALO (Mirjalili, 2015), SCA (Mirjalili, 2016), SSA (Mirjalili et al., 2017), AFO (Cheng et al., 2018), SRO (Shabani et al., 2019), BWO (Hayyolalam, 2020), CSO (Ahmed et al., 2020), and BMO (Suliman et al., 2020).

In the hierarchy of HAs, Gravitational Search Algorithm (GSA) is one of the efficient, highly used, and popular optimization technique designed by Rashedi et al. (2009). It is a physics-based algorithm inspired by Newton’s laws of universal gravitation and motion. In GSA, the searcher agents are in the form of masses which get attracted towards heavy masses. The position of heavy mass provides the optimal solution. It has been reported that GSA has a powerful global exploration capability which is crucial for solving complex optimization problems.

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