Generator sets for the Minkowski sum problem

This paper develops a new theoretical framework for generator sets in the context of Minkowski Sum Problems (MSPs) arising in multi-objective optimization. In MSPs, the nondominated set of the global problem equals the nondominated set of the Minkowski sum of several local nondominated sets. We intr...

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Bibliographic Details
Published in:European journal of operational research Vol. 328; no. 3; pp. 912 - 924
Main Authors: Lyngesen, Mark, Gadegaard, Sune Lauth, Nielsen, Lars Relund
Format: Journal Article
Language:English
Published: Elsevier B.V 01.02.2026
Subjects:
Decomposition
Minkowski sum
Multiple criteria analysis
Multiple objective programming
Decomposition
Minkowski sum
Multiple criteria analysis
Multiple objective programming
ISSN:0377-2217
Online Access:Get full text
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Summary:This paper develops a new theoretical framework for generator sets in the context of Minkowski Sum Problems (MSPs) arising in multi-objective optimization. In MSPs, the nondominated set of the global problem equals the nondominated set of the Minkowski sum of several local nondominated sets. We introduce the concept of generator sets: subsets of local nondominated vectors that are sufficient to construct the global nondominated set. We present novel theoretical results that characterize conditions for vectors to belong to a generator set or to be redundant. Moreover, we develop algorithms for finding generator sets and identifying redundant local vectors. Finally, we conduct extensive numerical experiments to test the impact of varying characteristics of the instances on the resulting global nondominated set and the number of redundant vectors. •Minkowski sum problems relate to additively-separable multi-objective problems.•Analysis of necessary local solutions for generating the nondominated sum.•Algorithms for finding minimum generator sets given known local sets.•Empirical study showing properties resulting in many redundant local solutions.
ISSN:0377-2217
DOI:10.1016/j.ejor.2025.07.005