A Generalized Scalarization Method for Evolutionary Multi-Objective Optimization

• URL: http://arxiv.org/abs/2212.01545v2
• Date: Tue, 7 Nov 2023 00:46:59 GMT
• Title: A Generalized Scalarization Method for Evolutionary Multi-Objective Optimization
• Authors: Ruihao Zheng and Zhenkun Wang
• Abstract summary: This paper uses the global replacement algorithm (GR) as the backbone. We find that the $L_p$-based ($1leq pinfty$) subproblems have inconsistently large preference regions. We propose a generalized $L_p$ (G$L_p$) scalarization to ensure that the subproblem's direction vector passes through its preference region.
• Score: 6.902116920364312
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The decomposition-based multi-objective evolutionary algorithm (MOEA/D) transforms a multi-objective optimization problem (MOP) into a set of single-objective subproblems for collaborative optimization. Mismatches between subproblems and solutions can lead to severe performance degradation of MOEA/D. Most existing mismatch coping strategies only work when the $L_{\infty}$ scalarization is used. A mismatch coping strategy that can use any $L_{p}$ scalarization, even when facing MOPs with non-convex Pareto fronts, is of great significance for MOEA/D. This paper uses the global replacement (GR) as the backbone. We analyze how GR can no longer avoid mismatches when $L_{\infty}$ is replaced by another $L_{p}$ with $p\in [1,\infty)$, and find that the $L_p$-based ($1\leq p<\infty$) subproblems having inconsistently large preference regions. When $p$ is set to a small value, some middle subproblems have very small preference regions so that their direction vectors cannot pass through their corresponding preference regions. Therefore, we propose a generalized $L_p$ (G$L_p$) scalarization to ensure that the subproblem's direction vector passes through its preference region. Our theoretical analysis shows that GR can always avoid mismatches when using the G$L_p$ scalarization for any $p\geq 1$. The experimental studies on various MOPs conform to the theoretical analysis.

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