An output-polynomial time algorithm to determine all supported efficient solutions for multi-objective integer network flow problems

This paper addresses the problem of enumerating all supported efficient solutions for a linear multi-objective integer minimum cost flow problem (MOIMCF). It derives an output-polynomial time algorithm to determine all supported efficient solutions for MOIMCF problems. This is the first approach to...

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Bibliographic Details
Published in:	Discrete Applied Mathematics Vol. 376; pp. 1 - 14
Main Authors:	Könen, David, Stiglmayr, Michael
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 15.12.2025
Subjects:	Complexity theory Minimum cost flow Multi-objective integer linear programming Multi-objective network flow Output-polynomial algorithm Weakly supported Minimum cost flow Multi-objective network flow Weakly supported Complexity theory Multi-objective integer linear programming Output-polynomial algorithm
ISSN:	0166-218X
Online Access:	Get full text
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Summary:	This paper addresses the problem of enumerating all supported efficient solutions for a linear multi-objective integer minimum cost flow problem (MOIMCF). It derives an output-polynomial time algorithm to determine all supported efficient solutions for MOIMCF problems. This is the first approach to solve this general problem in output-polynomial time. Moreover, we prove that the existence of an output-polynomial time algorithm to determine all weakly supported nondominated vectors (or all weakly supported efficient solutions) for a MOIMCF problem with a fixed number of d≥3 objectives can be excluded unless P=NP.
ISSN:	0166-218X
DOI:	10.1016/j.dam.2025.06.001