Multimodal Multi-objective Optimization Problems (MMOPs) refer to the problems that have multiple Pareto-optimal solution sets in decision space corresponding to the same or similar Pareto-optimal front in objective space. These problems require the optimization algorithm to locate multiple Pareto Sets (PSs). This paper proposes a differential evolution algorithm based on the clustering technique and an elite selection mechanism to solve MMOPs. In this algorithm, a Clustering-based Special Crowding Distance (CSCD) method is designed to calculate the comprehensive crowding degree in decision and objective spaces. Subsequently, a distance-based elite selection mechanism (DBESM) is introduced to determine the learning exemplars of various individuals. New individuals are generated around the exemplars to obtain a well-distributed population in both decision and objective spaces. To test the performance of the proposed algorithm, extensive experiments on the suit of CEC'2019 benchmark functions have been conducted. The results indicate that the proposed method has superior performance compared with other commonly used algorithms.

多峰多目标优化问题（MMOP）是指在决策空间中具有多个帕累托最优解集的问题，这些问题集对应于目标空间中相同或相似的帕累托最优前沿。这些问题需要优化算法来定位多个Pareto集（PS）。提出了一种基于聚类技术和精英选择机制的MMOP差分进化算法。该算法设计了一种基于聚类的特殊拥挤距离（CSCD）方法来计算决策空间和目标空间的综合拥挤度。随后，引入了基于距离的精英选择机制（DBESM），以确定各种个人的学习范例。在样本周围产生新的个体，以在决策空间和目标空间中获得分布良好的种群。为了测试所提出算法的性能，已经针对CEC'2019基准函数进行了广泛的实验。结果表明，与其他常用算法相比，该方法具有更好的性能。