A Multi-Objective Evolutionary Algorithm Based on Uniformity and Diversity to Handle Regular and Irregular Pareto Front Shapes

Abstract

Achieving uniform Pareto front (PF) approximations across various PF geometries and dimensions is a significant challenge. Most multi-objective evolutionary algorithms (MOEAs) that adapt a reference set to guide the evolutionary process, do not prioritize uniformity but the degree of resemblance to the PF shape. Consequently, these MOEAs often require extensive function evaluations to balance uniformity and diversity while representing the PF effectively. To address this issue, we introduce MOEA-UD, a MOEA designed to construct uniformly distributed PF approximations independent of the PF’s geometrical properties. MOEA-UD features a two-stage niching selection process. Initially, it classifies the population into niches using a reference set for uniformity, where the best solution per niche is selected. If additional solutions are needed to reach the population size, it then employs a reference set for diversity to populate any sparse regions. This approach ensures that uniformity is prioritized, while the diversity is used strategically to fill gaps and avoid empty regions. Also, an external archive using an improved selection mechanism based on niching and pair-potential energy function is employed to adapt both reference sets iteratively. We compared MOEA-UD with twelve state-of-the-art MOEAs on a wide range of artificial and real-world multi-objective optimization problems with different PF geometries. Our experimental results show that MOEA-UD consistently exhibits a PF shape invariant performance according to quality indicators, making it a promising option for generating uniform PF approximations.

Keywords

• Multi-objective evolutionary algorithms
• niching selection
• pair-potential energy function
• Pareto front shape invariant performance
• reference sets