Self-Organizing Map-Based Weight Design for Decomposition-Based Many-Objective Evolutionary Algorithm

Many-objective optimization problems (MaOPs), in which the number of objectives is greater than three, are undoubtedly more challenging compared with the bi- and tri-objective optimization problems. Currently, the decomposition-based evolutionary algorithms have shown promising performance in dealing with MaOPs. Nevertheless, these algorithms need to design the weight vectors, which has significant effects on the performance of the algorithms. In particular, when the Pareto front of problems is incomplete, these algorithms cannot obtain a set of uniformly distribution solutions by using the conventional weight design methods. In the literature, it is well-known that the self-organizing map (SOM) can preserve the topological properties of the input data by using the neighborhood function, and its display is more uniform than the probability density of the input data. This phenomenon is advantageous to generate a set of uniformly distributed weight vectors based on the distribution of the individuals. Therefore, we will propose a novel weight design method based on SOM, which can be integrated with most of the decomposition-based algorithms for solving MaOPs. In this paper, we choose the existing state-of-the-art decomposition-based algorithms as examples for such integration. This integrated algorithms are then compared with some state-of-the-art algorithms on eleven redundancy problems and eight nonredundancy problems, respectively. The experimental results show the effectiveness of the proposed approach.