Comparative Analysis of MOGBHS with Other State-of-the-Art Algorithms for Multi-objective Optimization Problems

Abstract

A multi-objective problem must simultaneously satisfy some conditions that may conflict with each other. Some examples of this problem are the design of machines with low power consumption and high power, or the development of software products in a short time and with high quality. Several algorithms have been proposed to solve this type of problems, such as NSGA-II, MOEA/D, SPEA2, and MSOPS. Each of these algorithms is based on different techniques such as the combination of objectives, Pareto efficiency, and prioritization. The selection of the best algorithm for a problem may become a cumbersome task. By its part, MOGBHS is a multi-objective algorithm based on the Global-Best Harmony Search, non-dominated sorting, and crowding distance that has shown great efficiency. This paper presents a comparative analysis of MOGBHS against other state-of-the-art algorithms. The analysis was performed over 21 multi-objective optimization problems from the IEEE CEC competition, 12 without restrictions and 9 with restrictions. The evaluation was performed using several evaluations of the objective function (2000, 5000, 10000 and 20000) and different metrics: Hypervolume, Epsilon, Generational Distance, Inverse Generational Distance, and Spacing. Finally, the analysis of the results was performed using non-parametric statistical tests (Wilcoxon and Friedman). MOGBHS obtained the best results according to the Inverse Generational Distance for 10000 and 20000 evaluations of the objective functions. Likewise, MOGBHS achieved competitive results for 2000 and 5000 evaluations. On the other hand, SPEA2 algorithm reached the best average results in all metrics.