Recent decades have witnessed great advancements in multiobjective evolutionary algorithms (MOEAs) for multiobjective optimization problems (MOPs). However, these progressively improved MOEAs have not necessarily been equipped with scalable and learnable problem-solving strategies for new and grand challenges brought by the scaling-up MOPs with continuously increasing complexity from diverse aspects, mainly including expensive cost of function evaluations, many objectives, large-scale search space, time-varying environments, and multi-task. Under different scenarios, divergent thinking is required in designing new powerful MOEAs for solving them effectively. In this context, research studies on learnable MOEAs with machine learning techniques have received extensive attention in the field of evolutionary computation. This paper begins with a general taxonomy of scaling-up MOPs and learnable MOEAs, followed by an analysis of the challenges that these MOPs pose to traditional MOEAs. Then, we synthetically overview recent advances of learnable MOEAs in solving various scaling-up MOPs, focusing primarily on four attractive directions (i.e., learnable evolutionary discriminators for environmental selection, learnable evolutionary generators for reproduction, learnable evolutionary evaluators for function evaluations, and learnable evolutionary transfer modules for sharing or reusing optimization experience). The insight of learnable MOEAs is offered to readers as a reference to the general track of the efforts in this field.

翻译：近几十年来，多目标进化算法（MOEAs）在解决多目标优化问题（MOPs）方面取得了显著进展。然而，这些逐步改进的MOEAs未必具备可扩展和可学习的问题求解策略，以应对由不断复杂化的规模化MOPs带来的全新重大挑战——这些挑战主要来自函数评估的高昂成本、众多目标、大规模搜索空间、时变环境以及多任务场景。在不同场景下，设计新型高性能MOEAs时需要采用差异化思维。在此背景下，结合机器学习技术的可学习MOEAs研究已在进化计算领域受到广泛关注。本文首先提出规模化MOPs与可学习MOEAs的通用分类体系，继而分析这类MOPs对传统MOEAs构成的挑战。随后，我们系统综述可学习MOEAs在解决各类规模化MOPs方面的最新进展，重点聚焦四个引人瞩目的研究方向（即：用于环境选择的可学习进化判别器、用于繁殖的可学习进化生成器、用于函数评估的可学习进化评估器，以及用于共享或重用优化经验的可学习进化迁移模块）。本文为读者提供可学习MOEAs的深刻见解，以作为该领域总体研究方向的参考。