  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.
