Why Dominance Is Not Enough: Lessons from Practical Evolutionary Multi-Objective Algorithms
Duc-Cuong Dang, Andre Opris, Dirk Sudholt · Algorithmica · 2025
Abstract Practical evolutionary multi-objective (EMO) algorithms like NSGA-II, NSGA-III, and SMS-EMOA combine the dominance relation with diversity criteria to identify promising solutions. Despite many success stories, their theoretical foundation remains underdeveloped, with key questions still unanswered–such as which information obtained during evolution is critical for their success. In this work, we explore the limitations of the information provided by the dominance relation between search points encountered so far. We present a large class of bi-objective problems whose Pareto-optimal set is small, while almost all pairs of search points are incomparable. On such problems, we prove that any black-box EMO algorithm that only relies on the dominance relation for making decisions fails spectacularly, requiring exponential time with high probability. In stark contrast, NSGA-II, NSGA-III, and SMS-EMOA efficiently cover the Pareto front in at most expected quadratic time by incorporating additional information from the objective values, such as crowding distances or hypervolume contributions of search points. Experiments conducted on randomly generated problems complement our theoretical findings. Our results highlight the superiority of practical EMO algorithms and the necessity of using information beyond dominance for effective multi-objective optimisation.