Multi-objective optimization problems (MOPs) necessitate the simultaneous optimization of multiple objectives. Numerous studies have demonstrated that evolutionary computation is a promising paradigm for solving complex MOPs, which involve optimization problems with large-scale decision variables, many objectives, and expensive evaluation functions. However, existing multi-objective evolutionary algorithms (MOEAs) encounter significant challenges in generating high-quality populations when solving diverse complex MOPs. Specifically, the distinct requirements and constraints of the population result in the inefficiency or even incompetence of MOEAs in addressing various complex MOPs. Therefore, this paper proposes the concept of pre-evolving for MOEAs to generate high-quality populations for diverse complex MOPs. Drawing inspiration from the classical transformer architecture, we devise dimension embedding and objective encoding techniques to configure the pre-evolved model (PEM). The PEM is pre-evolved on a substantial number of existing MOPs. Subsequently, when fine-evolving on new complex MOPs, the PEM transforms the population into the next generation to approximate the Pareto-optimal front. Furthermore, it utilizes evaluations on new solutions to iteratively update the PEM for subsequent generations, thereby efficiently solving various complex MOPs. Experimental results demonstrate that the PEM outperforms state-of-the-art MOEAs on a range of complex MOPs.

翻译：多目标优化问题（MOPs）需要同时优化多个目标。大量研究表明，进化计算是解决复杂MOPs（包括大规模决策变量、高维目标及昂贵评估函数的优化问题）的一种有前景的范式。然而，现有的大多数多目标进化算法（MOEAs）在解决各类复杂MOPs时，在生成高质量种群方面面临重大挑战。具体而言，种群的不同需求和约束导致MOEAs在处理各种复杂MOPs时效率低下甚至无法胜任。因此，本文提出了MOEAs的预演化概念，旨在为各类复杂MOPs生成高质量种群。受经典Transformer架构的启发，我们设计了维度嵌入和目标编码技术来配置预演化模型（PEM）。该PEM在大量现有MOPs上进行预演化。随后，在针对新的复杂MOPs进行微调演化时，PEM将种群转化为下一代以逼近帕累托最优前沿。此外，它利用对新解的评估迭代更新PEM以处理后续世代，从而高效求解各种复杂MOPs。实验结果表明，在多种复杂MOPs上，PEM的性能优于最先进的MOEAs。