Work

A greedy hypervolume polychotomic scheme for multiobjective combinatorial optimization

Year: 2025

Type: article

Abstract: 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 multi-objective 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.

Source: Computers & Operations Research

DOI: 10.1016/j.cor.2025.107140

Authors: Gonçalo Lopes, Kathrin Klamroth, Luís Paquete

Institutions: University of Coimbra, University of Wuppertal

Language: English

Topic: Advanced Multi-Objective Optimization Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,570

Funders: European Cooperation in Science and Technology, Deutscher Akademischer Austauschdienst, Deutsche Forschungsgemeinschaft, Fundação para a Ciência e a Tecnologia