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Domination-based multi-objective (MO) evolutionary algorithms (EAs) are todayarguably the most frequently used type of MOEA. These methods however stagnatewhen the majority of the population becomes non-dominated, preventingconvergence to the Pareto set. Hypervolume-based MO optimization has shownpromising results to overcome this. Direct use of the hypervolume howeverresults in no selection pressure for dominated solutions. The recentlyintroduced Sofomore framework overcomes this by solving multiple interleavedsingle-objective dynamic problems that iteratively improve a singleapproximation set, based on the uncrowded hypervolume improvement (UHVI). Itthereby however loses many advantages of population-based MO optimization, suchas handling multimodality. Here, we reformulate the UHVI as a quality measurefor approximation sets, called the uncrowded hypervolume (UHV), which can beused to directly solve MO optimization problems with a single-objectiveoptimizer. We use the state-of-the-art gene-pool optimal mixing evolutionaryalgorithm (GOMEA) that is capable of efficiently exploiting the intrinsicallyavailable grey-box properties of this problem. The resulting algorithm,UHV-GOMEA, is compared to Sofomore equipped with GOMEA, and thedomination-based MO-GOMEA. In doing so, we investigate in which scenarioseither domination-based or hypervolume-based methods are preferred. Finally, weconstruct a simple hybrid approach that combines MO-GOMEA with UHV-GOMEA andoutperforms both.

Uncrowded Hypervolume-based Multi-objective Optimization with Gene-pool Optimal Mixing