Advanced metaheuristic algorithms on solving multimodal functions: Experimental analyses and performance evaluations

Abstract

Optimization problems encountered in real-world have multiple local minimums. Multimodal functions can well represent many real-world applications as they include two or more local minimum points in nature. Numerous metaheuristic algorithms aim to find the best balance between exploration and exploitation, and better algorithms have been developed during the search for such a balance. Therefore, it becomes necessary to answer the question: Which metaheuristic algorithm is the best-suited algorithm among the metaheuristics that have been developed? This study presents a comprehensive and fair investigation of the seven metaheuristic algorithms developed in the last five years on twenty multimodal functions with a wide range of dimensions commonly used in literature. Each is subject to the same initial conditions but with three different performance criteria. The strengths and weaknesses of the each algorithm were demonstrated for each criterion and the experimental results were analyzed statistically by using the Friedman test. Furthermore, to the best of our knowledge, this is the first attempt to address these challenging problems, in combination with these algorithms and performance metrics, which can also give a further insight to the researchers for choosing appropriate algorithms in the context of global optimization.