The performance of the decomposition-based multi-objective optimization algorithm (MOEA/D) is dependent on the consistency of the Pareto front and the distribution of the weight vectors . Uniformly distributed weight vectors have a great advantage in solving Pareto fronts with simplex-like shapes. However, the fronts of real-world problems to be solved are often irregular, and fixed weight vectors are likely to cause deterioration of the solution. To obtain a set of solution sets that are uniformly distributed in the objective space, a MOEA/D-based weight adaptive updating algorithm (called MOEA/D-AWS) is proposed. First, the subproblem evolutionary matrix similarity is used to determine when to adjust the weight vectors. Second, the objective space is divided by creating a subspace of weight vectors to increase population diversity. Third, partial weights are given a second chance to be selected based on the subspace size. Experimental tests are conducted with seven representative algorithms on benchmark functions DTLZ1-7, IDTLZ1-2, MaF1-7, and WFG1-5 (with objective numbers of 3, 5, 8, 10, and 15). The results show that MOEA/D-AWS is more effective for irregular Pareto fronts, especially discontinuous, degenerate, and sharp-tailed Pareto front problems.

In the field of evolutionary algorithms, Pareto-based algorithms are less effective when more than three objectives are encountered, due to the lack of sufficient selection pressure. In this paper, a Pareto-based many-objective evolutionary algorithm with reference direction and coordinated selection strategy, abbreviated as SPEACSS, is proposed. The algorithm inherits the fitness calculation strategy of the strength Pareto evolutionary algorithm, while it applied an efficient reference direction-based density estimator and a novel selection strategy. Moreover, mating selection and environmental selection are complementary and coordinated in the evolutionary process and have better performance than be used alone. In the criteria of mating selection, a method is given to improve the effectiveness of the parent combination. Experimental results on benchmark functions show that the proposed algorithm is superior to several state-of-the-art designs, and demonstrate the effectiveness of the improved algorithm in balancing diversity and convergence.