Analysis of Local Constraint Structures in Real-World Constrained Multi-Objective Optimization Problems

Abstract

Many real-world tasks can be regarded as constrained multi-objective optimization problems (CMOPs), which include multiple objectives and constraints. However, few studies have analyzed the structure of real-world CMOPs and the performance of existing constraint-handling methods. In this study, we focus on the constraint violation (CV), which is commonly used in various constraint-handling methods, and propose Local Constraint Peak Analysis (LCPA) to analyze problem structures where the CV becomes locally minimal. LCPA is a method inspired by Density Peak Clustering, in which the local density is replaced with the CV. It creates a directed graph composed of trees rooted at local CV peaks, representing candidate local optima and pseudo search paths leading to them. In the experiments, we applied the proposed method to solution sets obtained by solving real-world CMOPs using NSGA-II with the Constraint-Dominance Principle (CDP). Then, we clustered the paths using K-medoids based on Dynamic Time Warping distance to visualize the main patterns. The results showed that some infeasible solutions had locally smallest CV values, suggesting that searches using CDP may get stuck in local CV optima.