Reliability of the weight vector generation method of the multi-objective evolutionary algorithm and application

The decomposition-based multi-objective evolutionary algorithm first generates a set of weight vectors in advance, and it is very important to select a set of appropriate weight vectors for the decomposition-based algorithm. A variety of weight vector generation methods have been proposed in the existing algorithms, but in most algorithms, a pre-defined weight vector generation method is still used, the pre-defined weight vector is too specialized for the simplex-like front surface, which results in poor performance on the front surface with irregularities. At the same time, most of the existing algorithms have proposed many new adaptive strategies for weight vectors, but if you generate a set of more suitable weight vectors at the beginning, and then use the update strategy, it can make the algorithm achieve a better balance between diversity and convergence. In order to select a suitable weight vector, this paper proposes a multi-stage MOEA to select a suitable weight vector. The algorithm is divided into multiple stages according to the evolution process, first of all, in the early stage of evolution, the reliability of multiple weight vector generation methods was evaluated according to the spearman correlation coefficient in statistics, choose the most suitable weight generation method; Secondly, this method can be applied to the search for high-quality solutions in the middle of evolution; Finally, a weight vector adaptive strategy is adopted in the overall evolution process. In the experiment, the proposed algorithm was analyzed in the benchmark test problem, mechanical bearing and light aircraft gear reducer. The experimental results show the effectiveness of the proposed algorithm.