Effects of Objective Normalization on Regions of Interest in Preference-Based Evolutionary Multi-Objective Optimization

2026-06-15

AI Summary

This study addresses the impact of objective scale disparity on the definition and approximation of regions of interest (ROIs) in preference-driven evolutionary multi-objective optimization. It systematically investigates whether ROIs should be defined in the normalized or original objective space, conducting comparative experiments using an evolutionary algorithm that incorporates estimates of both ideal and extreme points. The work reveals, for the first time, the fundamental reason why ROIs defined in normalized space are inherently difficult to approximate accurately. It demonstrates that defining ROIs in the original objective space yields significantly better approximation quality, particularly when objective scales are heterogeneous. These findings provide a theoretical foundation and practical guidance for selecting the appropriate objective space in preference-guided optimization frameworks.

Abstract

Preference-based evolutionary multi-objective optimization (PBEMO) aims to approximate a region of interest (ROI) defined by the preference information from a decision maker (DM). Although objective functions in real-world applications typically have different scales, the issue of how to define the ROI in such problems has been overlooked in the literature. In fact, it has not been standardized in the EMO community whether the ROI should be defined in the unnormalized objective space or in the normalized objective space. In this context, this paper investigates the effects of objective normalization on ROIs. First, this paper shows that two ROIs defined in the unnormalized and normalized objective spaces can differ significantly for problems with differently scaled objectives. Then, we demonstrate that ROIs defined in the normalized objective space are highly difficult to approximate even on problems with equally scaled objectives because of poor approximations of the ideal and nadir points. In contrast, we show that ROIs defined in the unnormalized objective space are much easier to approximate than those defined in the normalized objective space.

Problem

• Preference-based Evolutionary Multi-Objective Optimization
• Region of Interest
• Objective Normalization
• Decision Maker
• Multi-Objective Optimization

Innovation

• preference-based EMO
• objective normalization
• region of interest
• ideal point estimation
• nadir point approximation