A Generalized Scalarization Method for Evolutionary Multi-Objective Optimization

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∞ scalarization is used. A mismatch coping strategy that can use any Lp 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∞ is replaced by another Lp with p ∈ [1, ∞), and find that the Lp-based (1 ≤ p < ∞) 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 Lp (GLp) 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 GLp scalarization for any p ≥ 1. The experimental studies on various MOPs conform to the theoretical analysis.