Many multimodal multiobjective optimization algorithms aim to find as many Pareto optimal solutions as possible while the performance in the objective space is despised. More seriously, some algorithms even overemphasize the diversity of solution set in the decision space at the cost of convergence. How to improve convergence and diversity simultaneously is an important issue when solving multimodal multiobjective optimization problems. In this paper, we propose an evolutionary multiobjective optimization algorithm with a decomposition strategy in the decision space (EMO-DD). A decision subregion allocation and diversity archive preservation methods are proposed to promote the diversity of solutions in the decision space. Meanwhile, a bi-objective optimization problem is formulated for screening for solutions with great convergence and diversity. Combining a modified mating selection method, well-performed solutions both on the convergence and diversity are preserved and inherited. The performance of EMO-DD is compared with five state-of-the-art algorithms on fifteen test problems. The experimental results show that EMO-DD can solve multimodal multiobjective optimization problems, and can improve the performance of the solution set in both the decision and objective spaces.

许多多模态多目标优化算法旨在在不考虑目标空间性能的情况下，找到尽可能多的帕累托最优解。更严重的是，某些算法甚至以收敛为代价过分强调了决策空间中解决方案集的多样性。解决多峰多目标优化问题时，如何同时提高收敛性和多样性是一个重要问题。在本文中，我们提出了一种具有决策空间分解策略的进化多目标优化算法（EMO-DD）。提出了决策子区域分配和多样性档案保存方法，以促进决策空间中解决方案的多样性。同时，提出了一种双目标优化问题，用于筛选具有极大收敛性和多样性的解决方案。结合改进的匹配选择方法，可以保留和继承性能优良的收敛性和多样性解决方案。在15个测试问题上，将EMO-DD的性能与五种最新算法进行了比较。实验结果表明，EMO-DD可以解决多模态多目标优化问题，并且可以提高决策空间和目标空间中解集的性能。