Optimization of constrained mathematical and engineering design problems using chaos game optimization

In the past few decades, many different metaheuristic algorithms have been developed for optimization purposes each of which have specific advantages and disadvantages due to multiple applications in different optimization fields. The Chaos Game Optimization (CGO) is proposed in this paper as a new metaheuristic algorithm for optimization of constrained mathematical and engineering design problems. The proposed CGO method is formulated based on some principles of chaos theory in which the fractals configuration by chaos game methodology alongside the fractals self-similarity issues are in perspective. A total number of 34 constrained mathematical problems are collected which have been benchmarked and proposed in the Competitions on Evolutionary Computation (CEC) and 15 constrained engineering design problems are selected in order to evaluate the overall performance of the proposed novel CGO method. In order to validate the results of the novel CGO algorithm, the best results of different standard, improved and hybrid metaheuristic algorithms in dealing with the considered constrained problems are selected from the literature for comparative purposes. In addition, the statistical results of the CGO algorithm including the minimum, mean, maximum and the standard deviation values are all calculated and compared to the results of other metaheuristics. The obtained results proved that the proposed algorithm is capable of providing very competitive results and outperforms the other metaheuristics in most of the cases.