High-dimensional Multi-objective Optimization Strategy Based on Decision Space Oriented Search

Traditional multi-objective evolutionary algorithm (MOEA) have sound performance when solving low dimensional continuous multi-objective optimization problems. However, as the optimization problems' dimensions increase, the difficulty of optimization will also increase dramatically. The main reasons are the lack of algorithms' search ability, and the smaller selection pressure when the dimension increases as well as the difficulty to balance convergence and distribution conflicts. In this study, after analyzing the characteristics of the continuous multi-objective optimization problem, a directional search strategy based on decision space (DS) is proposed to solve high dimensional multi-objective optimization problems. This strategy can be combined with the MOEAs based on the dominating relationship. DS first samples solutions from the population and analyzes them, and obtains the controlling vectors of convergence subspace and distribution subspace by analyzing the problem characteristics. The algorithm is divided into convergence search stage and distribution search stage, which correspond to convergent subspace and distributive subspace respectively. In different stages of search, sampling analysis are used results to macroscopically control the region of offspring generation. The convergence and distribution are divided and emphasized in different stages to avoid the difficulty of balancing them. Additionally, it can also relatively focuses the search resources on certain aspect in certain stages, which facilitates the searching ability of the algorithm. In the experiment, NSGA-II and SPEA2 algorithms are compared combining DS strategy with original NSGA-II and SPEA2 algorithms, and DS-NSGA-II is used as an example to compare it with other state-of-the-art high-dimensional algorithms, such as MOEAD-PBI, NSGA-III, Hype, MSOPS, and LMEA. The experimental results show that the introduction of the DS strategy greatly improves the performance of NSGA-II and SPEA2 when addressing high dimensional multi-objective optimization problems. It is also shown that DS-NSGA-II is more competitive when compared the existing classical high dimensional multi-objective algorithms. © Copyright 2019, Institute of Software, the Chinese Academy of Sciences. All rights reserved.