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多目标优化问题（涉及大规模决策变量、多个目标以及昂贵的评估函数）的一种有前景的范式。然而，现有的多目标进化算法在求解各类复杂多目标优化问题时，在生成高质量种群方面面临显著挑战。具体而言，种群的不同需求和约束导致多目标进化算法在应对不同复杂多目标优化问题时效率低下甚至无能为力。为此，本文提出了多目标进化算法的预进化概念，旨在为各类复杂多目标优化问题生成高质量种群。受经典transformer架构启发，我们设计了维度嵌入和目标编码技术来构建预进化模型。该模型先在大量已有的多目标优化问题上进行预进化，当在新型复杂多目标优化问题上进行微调进化时，预进化模型将种群转换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结果迭代更新预进化模型用于后续代际，从而高效求解各类复杂多目标优化问题。实验结果表明，预进化模型在多种复杂多目标优化问题上均优于现有最先进的多目标进化算法。