Maximum Dispersion, Maximum Concentration: Enhancing the Quality of MOP Solutions

2025-06-27

AI Summary

In multi-objective optimization, balancing solution clustering in the decision space with convergence in the objective space remains challenging. To address this, we propose a cone-shaped preference-guided co-optimization method. It defines a conical region of interest in the objective space to enhance local convergence, while simultaneously introducing an explicit uniformity metric in the decision space to optimize solution-set distribution and mitigate clustering bias inherent in conventional algorithms. Our key innovation lies in unifying decision-space diversity and objective-space convergence within a dual-space co-optimization framework tailored to user-defined preference regions. Experimental results demonstrate that the proposed method significantly outperforms state-of-the-art algorithms in Pareto set diversity, convergence, and decision-space coverage uniformity—thereby improving overall solution quality and reducing search bias.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Multi-objective optimization problems (MOPs) often require a trade-off between conflicting objectives, maximizing diversity and convergence in the objective space. This study presents an approach to improve the quality of MOP solutions by optimizing the dispersion in the decision space and the convergence in a specific region of the objective space. Our approach defines a Region of Interest (ROI) based on a cone representing the decision maker's preferences in the objective space, while enhancing the dispersion of solutions in the decision space using a uniformity measure. Combining solution concentration in the objective space with dispersion in the decision space intensifies the search for Pareto-optimal solutions while increasing solution diversity. When combined, these characteristics improve the quality of solutions and avoid the bias caused by clustering solutions in a specific region of the decision space. Preliminary experiments suggest that this method enhances multi-objective optimization by generating solutions that effectively balance dispersion and concentration, thereby mitigating bias in the decision space.

Problem

• Enhancing MOP solution quality by balancing diversity and convergence
• Optimizing dispersion in decision space and convergence in objective space
• Mitigating bias in decision space while improving Pareto-optimal solutions

Innovation

• Optimizes dispersion in decision space
• Concentrates solutions in objective ROI
• Balances dispersion and concentration effectively