  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.
