Non-dominated sorting methods for multi-objective optimization: Review and numerical comparison

Abstract

<p style='text-indent:20px;'>In multi-objective evolutionary algorithms (MOEAs), non-domina-ted sorting is one of the critical steps to locate efficient solutions. A large percentage of computational cost of MOEAs is on non-dominated sorting for it involves numerous comparisons. By now, there are more than ten different non-dominated sorting algorithms, but their numerical performance comparing with each other is not clear yet. It is necessary to investigate the advantage and disadvantage of these algorithms and consequently give suggestions to specific users and algorithm designers. Therefore, a comprehensively numerical study of non-dominated sorting algorithms is presented in this paper. Firstly, we design a population generator. This generator can generate populations with specific features, such as population size, number of Pareto fronts and number of points in each Pareto front. Then non-dominated sorting algorithms were tested using populations generated in certain structures, and results were compared with respect to number of comparisons and time consumption. Furthermore, In order to compare the performance of sorting algorithms in MOEAs, we embed them into a specific MOEA, dynamic sorting genetic algorithm (DSGA), and use these variations of DSGA to solve some multi-objective benchmarks. Results show that dominance degree sorting outperforms the other methods, fast non-dominance sorting performs the worst and the other sorting algorithms performs equally.