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A greedy hypervolume polychotomic scheme for multiobjective combinatorial optimization

Computers & Operations Research 2025年 183卷

作者： Gonçalo Lopes Kathrin Klamroth Luís Paquete CISUC Department of Informatics Engineering University of Coimbra Pólo II 3030-290 Coimbra Portugal School of Mathematics and Natural Sciences University of Wuppertal 42119 Wuppertal Germany

The usual goal in multiobjective combinatorial optimization is to find the complete set of nondominated points. However, in general, the nondominated set may be too large to be enumerated under a tight time budget. In these cases, it is preferable to rapidly obtain a concise representation of the nondominated set that satisfies a given property of interest. This work describes a generic greedy approach to compute a representation of the nondominated set for multiobjective combinatorial optimization problems that approximately maximizes the dominated hypervolume. The representation is built iteratively by solving a sequence of hypervolume scalarized problems, each of which with respect to k reference points, which is a parameter of our approach. We present a mixed-integer formulation of the hypervolume scalarization function for k reference points as well as a combinatorial branch-and-bound for the m -objective knapsack problem. We empirically analyse the functional relationship between k and its running-time and representation quality. Our results indicate that the branch-and-bound is a much more efficient approach and that increasing k does not directly translate into much better representation quality.

关键词： Multiobjective combinatorial optimization hypervolume scalarization Representation of the nondominated set greedy hypervolume algorithm Local bounds

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