Many-objective evolutionary algorithm with multi-strategy selection mechanism and adaptive reproduction operation

Many-objective optimization problem is one of the most important and widely faced optimization problems in the real world. To solve many-objective optimization problems (MaOPs), numerous multi-objective evolutionary algorithms (MOEAs) have been developed to find a good convergence and well-distributed Pareto front. However, with the increase of dimensions, the distribution of solutions obtained by MOEAs becomes more complex and tends to be orthogonal, which significantly reduces the effectiveness of the algorithms. In this paper, we propose an improved many-objective evolutionary algorithm (MaOEA-MSAR), which incorporates a multi-strategy selection mechanism into an existing MOEA, and develops an adaptive reproduction operation to produce promising offspring individuals. Firstly, the selection strategy based on the angle-penalized distance is used to improve the coverage of the solutions in the objective space. Then, the selection strategy based on convergence rate is employed to strengthen the balance between diversity and convergence. Finally, an adaptive reproduction operation is used to select different reproduction strategies for the gene-level global exploration or local exploitation. A series of experiments are carried out against seven state-of-the-art many-objective optimization algorithms. Experimental results on commonly used 31 benchmark test problems with up to 15 objectives and a multi-objective vehicle routing problem have demonstrated that MaOEA-MSAR is competitive in handling various kinds of MaOPs.