Solving hypervolume scalarizations for MOCO problems

Hypervolume scalarizations have emerged as a promising strategy to find efficient solutions to multiobjective combinatorial optimization problems. Despite their potential, the exact optimization of hypervolume scalarizations remains challenging. This paper introduces exact approaches that exploit particular transformations to compute optimal hypervolume-scalarized solutions efficiently. Extensive experiments on multiobjective knapsack problems show that our methods can improve upon the current state-of-the-art exact approaches that are based on straightforward linearizations, achieving improvements of several orders of magnitude in terms of problem size, number of objectives, and number of reference points.