Multimodal multiobjective optimization problems (MMOPs) widely exist in real-world applications, which have multiple equivalent Pareto-optimal solutions that are similar in the objective space but totally different in the decision space. While some evolutionary algorithms (EAs) have been developed to find the equivalent Pareto-optimal solutions in recent years, they are ineffective to handle large-scale MMOPs having a large number of variables. This article thus proposes an EA for solving large-scale MMOPs with sparse Pareto-optimal solutions, i.e., most variables in the optimal solutions are 0. The proposed algorithm explores different regions of the decision space via multiple subpopulations and guides the search behavior of the subpopulations via adaptively updated guiding vectors. The guiding vector for each subpopulation not only provides efficient convergence in the huge search space but also differentiates its search direction from others to handle the multimodality. While most existing EAs solve MMOPs with 2–7 decision variables, the proposed algorithm is shown to be effective for benchmark MMOPs with up to 500 decision variables. Moreover, the proposed algorithm also produces a better result than state-of-the-art methods for the neural architecture search.

中文翻译：

---

一种求解大规模多模态多目标优化问题的多种群进化算法

多模态多目标优化问题 (MMOP) 广泛存在于现实世界的应用中，其具有多个等价的帕累托最优解，这些解在目标空间中相似但在决策空间中完全不同。虽然近年来已经开发了一些进化算法 (EA) 来寻找等效的帕累托最优解，但它们对于处理具有大量变量的大规模 MMOP 是无效的。因此，本文提出了一种用稀疏帕累托最优解来解决大规模 MMOP 的 EA，即最优解中的大多数变量为 0。所提出的算法通过多个子种群探索决策空间的不同区域，并指导该算法的搜索行为。通过适应性更新的指导向量划分亚群。每个子群的引导向量不仅可以在巨大的搜索空间中提供有效的收敛，而且可以区分其搜索方向以处理多模态。虽然大多数现有的 EA 解决具有 2-7 个决策变量的 MMOP，但所提出的算法被证明对于具有多达 500 个决策变量的基准 MMOP 是有效的。此外，所提出的算法还产生了比最先进的神经架构搜索方法更好的结果。