Adaptive decomposition-based evolutionary algorithm for many-objective optimization with two-stage dual-density judgment

In order to better balance the convergence and diversity of MOEA/D for many objective optimization problems (MaOPs) with various Pareto fronts (PFs), an adaptive decomposition-based evolutionary algorithm for MaOPs with two-stage dual-density judgment is proposed. To solve the problem that weighted Tchebycheff decomposition may produce weakly Pareto optimal solutions when the solution is not unique or the uniqueness is difficult to guarantee, an augmented weighted Tchebycheff decomposition is adopted. To balance the convergence and diversity of non-dominated solutions in the external archive, different sparsity-level evaluations using vector angles or Euclidean distances are used to measure the distribution of solutions at different stages. To improve the diversity of solution sets obtained by MOEA/D for various PFs, an adaptive weight vector adjustment method based on two-stage dual-density judgment is presented. For weight vector addition, the potential search area is found according to the two-stage density judgment, and then a two-stage sparsity level judgment on the solutions of this area is performed for a second density judgment. For weight vector deletion, the degree of crowding is used to delete the weight vectors with a high crowding degree. Compared with nine advanced multi-objective optimization algorithms on DTLZ and WFG problems, the results demonstrate that the performance of the proposed algorithm is significantly better than other algorithms.