Abstract

Aims: The main purpose of this paper is to achieve good convergence and distribution in different Pareto fronts.

Background: Research in recent decades has shown that evolutionary multi-objective optimization can effectively solve multi-objective optimization problems with no more than 3 targets. However, when solving MaOPs, the traditional evolutionary multi-objective optimization algorithm is difficult to effectively balance convergence and diversity. In order to solve these problems, many algorithms have emerged, which can be roughly divided into the following three types: decomposition-based, index-based, and dominance relationship-based. In addition, there are many algorithms that introduce the idea of clustering into the environment. However, there are some disadvantages to solving different types of MaOPs. In order to take advantage of the above algorithms, this paper proposes a many-objective optimization algorithm based on two-phase evolutionary selection.

Objective: In order to verify the comprehensive performance of the algorithm on the testing problem of different Pareto front, 18 examples of regular PF problems and irregular PF problems are used to test the performance of the algorithm proposed in this paper.

Method: This paper proposes a two-phase evolutionary selection strategy. The evolution process is divided into two phases to select individuals with good quality. In the first phase, the convergence area is constructed by indicators to accelerate the convergence of the algorithm. In the second phase, the parallel distance is used to map the individuals to the hyperplane, and the individuals are clustered according to the distance on the hyperplane, and then the smallest fitness in each category is selected.

Result: For regular Pareto front testing problems, MaOEA/TPS performed better than RVEA, PREA, CAMOEA and One by one EA in 19, 21, 30, 26 cases, respectively, while it was only outperformed by RVEA, PREA, CAMOEA and One by one EA in 8, 5, 1, and 6 cases. For the irregular front testing problem, MaOEA/TPS performed better than RVEA, PREA, CAMOEA and One by one EA in 20, 17, 25, and 21 cases, respectively, while it was only outperformed by RVEA, PREA, CAMOEA and One by one EA in 6, 8, 1, and 6 cases.

Conclusion: The paper proposes a many-objective evolutionary algorithm based on two phase selection, termed MaOEA/TPS, for solving MaOPs with different shapes of Pareto fronts. The results show that MaOEA/TPS has quite a competitive performance compared with the several algorithms on most test problems.

Other: Although the algorithm in this paper has achieved good results, the optimization problem in the real environment is more difficult, therefore, applying the algorithm proposed in this paper to real problems will be the next research direction.