Effects of Objective Normalization on Regions of Interest in Preference-Based Evolutionary Multi-Objective Optimization
2026-06-15 • Neural and Evolutionary Computing
Neural and Evolutionary Computing
AI summaryⓘ
The authors study how to define a decision maker's preferred search area in multi-objective optimization when the objectives have different scales. They find that defining this region in the normalized objective space (adjusted to a common scale) can be very hard to approximate accurately, even when objectives have similar scales. On the other hand, defining this region in the original unnormalized space is easier to approximate, especially when objectives have different scales. Their work highlights that the question of whether to normalize objectives in these problems is important and has been neglected.
Preference-based evolutionary multi-objective optimizationRegion of interest (ROI)Objective normalizationUnnormalized objective spaceNormalized objective spaceIdeal pointNadir pointMulti-objective optimizationDecision maker preferences
Authors
Ryuichi Mogami, Ryoji Tanabe
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.