A novel algorithm for many-objective dimension reductions: Pareto-PCA-NSGA-II

Many-objective problem has more than 3 objectives. Because of the extraordinary difficulty of acquiring their Pareto optimal solutions directly, traditional methods will be out of operation for such problems. In recent years, many researchers have turned their attention to the study of this area. They are interested in two areas: acquiring some part of Pareto front which is useful to the researchers (Preferred Solutions) and reducing redundant objectives. In this paper, we combine two dimension reduction methods: the method based on Pareto optimal solution analysis and the method based on correlation analysis, to form a novel algorithm for dimension reduction. Firstly, the Pareto optimal solutions are acquired through NSGA-II. Then the objectives who contribute little to the number of non-dominated solutions are removed. At last, the dimension of objectives is reduced further according to their contribution to the principal component in PCA analysis. In this way, we can acquire the right non-redundant objectives with low time complexity. Simulation results show that the proposed algorithm can effectively reduce redundant objectives and keep the non-redundant objectives with low time.