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.

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