Chaos Game Optimization: a novel metaheuristic algorithm

Abstract

In this paper, a novel metaheuristic algorithm called Chaos Game Optimization (CGO) is developed for solving optimization problems. The main concept of the CGO algorithm is based on some principles of chaos theory in which the configuration of fractals by chaos game concept and the fractals self-similarity issues are in perspective. A total number of 239 mathematical functions which are categorized into four different groups are collected to evaluate the overall performance of the presented novel algorithm. In order to evaluate the results of the CGO algorithm, three comparative analysis with different characteristics are conducted. In the first step, six different metaheuristic algorithms are selected from the literature while the minimum, mean and standard deviation values alongside the number of function evaluations for the CGO and these algorithms are calculated and compared. A complete statistical analysis is also conducted in order to provide a valid judgment about the performance of the CGO algorithm. In the second one, the results of the CGO algorithm are compared to some of the recently developed fractal- and chaos-based algorithms. Finally, the performance of the CGO algorithm is compared to some state-of-the-art algorithms in dealing with the state-of-the-art mathematical functions and one of the recent competitions on single objective real-parameter numerical optimization named “CEC 2017” is considered as numerical examples for this purpose. In addition, a computational cost analysis is also conducted for the presented algorithm. The obtained results proved that the CGO is superior compared to the other metaheuristics in most of the cases.