The decomposition-based multi-objective optimization algorithm MOEA/D (multi-objective evolutionary algorithm based on decomposition) introduces the concept of neighborhood, where each sub-problem requires optimization through solutions within its neighborhood. Due to the comparison being only with solutions in the neighborhood, the obtained set of solutions is not sufficiently diverse, leading to poorer convergence properties. In order to adequately acquire a high-quality set of solutions, this algorithm requires a large number of population iterations, which in turn results in relatively low computational efficiency. To address this issue, this paper proposes an algorithm termed MOEA/D-NRD, which is based on neighborhood region domination in the MOEA/D framework. In the improved algorithm, domination relationships are determined by comparing offspring solutions against neighborhood ideal points and neighborhood worst points. By selecting appropriate solution sets within these comparison regions, the solution sets can approach the ideal points more and faster, thereby accelerating population convergence and enhancing the computational efficiency of the algorithm.

The penalty-based boundary cross-aggregation (PBI) method is a common decomposition method of the MOEA/D algorithm, but the strategy of using a fixed penalty parameter in the boundary cross-aggregation function affects the convergence of the populations to a certain extent and is not conducive to the maintenance of the diversity of boundary solutions. To address the above problems, this paper proposes a penalty boundary crossing strategy (DPA) for MOEA/D to adaptively adjust the penalty parameter. The strategy adjusts the penalty parameter values according to the state of uniform distribution of solutions around the weight vectors in the current iteration period, thus helping the optimization process to balance convergence and diversity. In the experimental part, we tested the MOEA/D-DPA algorithm with several MOEA/D improved algorithms on the classical test set. The results show that the MOEA/D with the DPA has better performance than the MOEA/D with the other decomposition strategies.