An improved NSGA-III algorithm based on distance dominance relation for many-objective optimization

There are two main aspects of research in many-objective optimization algorithm, namely, convergence and diversity. However, it is difficult for original algorithms to maintain the diversity of solutions in the high-dimensional objective space. The NSGA-III algorithm is an advanced algorithm based on Pareto dominance. In the high-dimensional objective space, the diversity maintenance of this algorithm is obviously lacking. In order to enhance the diversity of algorithms in many-objective optimization problems, a new distance dominance relation is proposed in this paper. First, in order to ensure the convergence of the algorithm, the distance dominance relation calculates the distance from the candidate solution to the ideal point as the fitness value, and selects the candidate solution with good fitness value as the non-dominant solution. Then, in order to enhance the diversity of the algorithm, the distance dominance relation sets each candidate solution to have the same niche and ensures that only one optimal solution is retained in the same territory. Finally, the NSGA- III algorithm is improved based on the proposed distance dominance relation. On the DTLZ and MaF test problems with 3, 5, 8, 10, and 15 objectives, the improved algorithm is compared with seven commonly used algorithms. The experimental results show that the improved algorithm is highly competitive and can significantly enhance the diversity of the algorithm.