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

TL;DR

This paper introduces a method to improve multi-objective optimization solutions by balancing dispersion in decision space and convergence in a region of interest, leading to more diverse and high-quality Pareto solutions.

Contribution

It proposes a novel approach that combines decision space dispersion with objective space convergence based on decision maker preferences, enhancing solution diversity and quality.

Findings

Improved solution diversity in decision space.

Enhanced convergence towards the region of interest.

Mitigation of clustering bias in solutions.

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.