The aim of evolutionary multi/many-objective optimization is to obtain a set of Pareto-optimal solutions with good trade-off among the multiple conflicting objectives. However, the convergence and diversity of multiobjective evolutionary algorithms often seriously decrease with the number of objectives and decision variables increasing. In this paper, we present a decomposition-based evolutionary algorithm for solving scalable multi/many-objective problems. The key features of the algorithm include the following three aspects: (1) a resource allocation strategy to coordinate the utility value of subproblems for good coverage; (2) a multioperator and multiparameter strategy to improve adaptability and diversity of the population; and (3) a bidirectional local search strategy to prevent the decrease in exploration capability during the early stage and increase the exploitation capability during the later stage of the search process. The performance of the proposed algorithm is benchmarked extensively on a set of scalable multi/many-objective optimization problems. The statistical comparisons with seven state-of-the-art algorithms verify the efficacy and potential of the proposed algorithm for scalable multi/many-objective problems.

进化多/多目标优化的目的是获得一组帕累托最优解，并在多个相互冲突的目标之间取得良好的折衷。然而，随着目标数量和决策变量的增加，多目标进化算法的收敛性和多样性往往会严重降低。在本文中，我们提出了一种基于分解的进化算法，用于解决可扩展的多/多目标问题。该算法的主要特征包括以下三个方面：（1）一种资源分配策略，用于协调子问题的效用值以实现良好的覆盖范围；（2）采取多运营商和多参数战略，以提高人口的适应性和多样性；（3）双向局部搜索策略，以防止在搜索过程的早期阶段勘探能力下降，而在搜索过程的后期阶段提高开采能力。提出的算法的性能在一组可缩放的多/多目标优化问题上进行了广泛的基准测试。与七个最新算法的统计比较证明了所提出算法可解决多目标/多目标问题的功效和潜力。