A Two-stage Evolutionary Framework For Multi-objective Optimization

TL;DR

The paper tackles the challenge of balancing convergence and diversity in multi-objective evolutionary optimization by introducing TEMOF, a two-stage framework that splits the search process and employs an external convergence archive to preserve high-quality Pareto-front members. In stage one, offspring are generated solely from the current population, emphasizing exploration, while in stage two, parents are drawn from either the population or the convergence archive with probability $p$ (default $0.5$), emphasizing exploitation and convergence; EnvironmentalSelection2 ensures only first-front members are retained in the archive. TEMOF is instantiated with three PMOEAs (TEMOF-NSGA-III, TEMOF-GFMMOEA, TEMOF-DWU) and evaluated on MaOPs from the CEC 2024 suite using $N=100$, $maxFEs=100{,}000$, with $M=3$ decision variables and $D=7$ objectives. Results show that TEMOF-NSGA-III frequently achieves superior performance in both $IGD$ and $HV$, demonstrating robustness across problem sets and validating the efficacy of the two-stage framework in enhancing PF coverage while preventing premature convergence. The approach is simple to implement and can be integrated with existing MOEAs to improve Pareto-front approximation, with future work focused on refining environmental selection and reducing dependence on the first stage for broader applicability.

Abstract

In the field of evolutionary multi-objective optimization, the approximation of the Pareto front (PF) is achieved by utilizing a collection of representative candidate solutions that exhibit desirable convergence and diversity. Although several multi-objective evolutionary algorithms (MOEAs) have been designed, they still have difficulties in keeping balance between convergence and diversity of population. To better solve multi-objective optimization problems (MOPs), this paper proposes a Two-stage Evolutionary Framework For Multi-objective Optimization (TEMOF). Literally, algorithms are divided into two stages to enhance the search capability of the population. During the initial half of evolutions, parental selection is exclusively conducted from the primary population. Additionally, we not only perform environmental selection on the current population, but we also establish an external archive to store individuals situated on the first PF. Subsequently, in the second stage, parents are randomly chosen either from the population or the archive. In the experiments, one classic MOEA and two state-of-the-art MOEAs are integrated into the framework to form three new algorithms. The experimental results demonstrate the superior and robust performance of the proposed framework across a wide range of MOPs. Besides, the winner among three new algorithms is compared with several existing MOEAs and shows better results. Meanwhile, we conclude the reasons that why the two-stage framework is effect for the existing benchmark functions.

Figures (2)

• Figure 1: Fridman Ranking of TEMOF-MOEAs
• Figure 2: Fridman Ranking of Comparision Algorithms