One for Exploration and Another for Exploitation: A Dual-Population MOEA Framework with Provable Benefits

Abstract

Evolutionary Algorithms (EAs) are currently the most popular tool for solving multi-objective optimization problems. Balancing exploration and exploitation is fundamental to the performance of Multi-Objective EAs (MOEAs). Achieving this requires maintaining a set of high-quality solutions for effective exploitation while simultaneously enabling exploration of diverse regions of the search space. In MOEAs, these two roles are typically fulfilled by a single evolutionary population. However, high-quality solutions that are promising for exploitation may lack the potential to guide the search toward different regions of the search space. Conversely, solutions with high exploratory potential that can lead the search toward more promising regions may themselves be of low quality. To address this issue, this paper proposes a dual-population MOEA with Exploration and Exploitation Decoupled (MOEA/EED): the exploration population uses a simple aging mechanism, while the exploitation population preserves the currently optimal solutions. We theoretically prove the benefits of MOEA/EED, i.e., it achieves the upper bounds, O(n^(k+1) · min{1, (e ln(3e) / k)^k}) and O((5e ln(3e))^(n/5)), on the expected running time for solving two commonly studied bi-objective problems OneJumpZeroJump and bi-objective RealRoyalRoad, which are significantly better (even exponentially smaller) than that of the popular SMS-EMOA, NSGA-II, and their non-elitist variants. Lastly, we empirically show its effectiveness on a wide range of practical optimization problems.