An Output-Polynomial Time Algorithm to Determine all Supported Efficient Solutions for Multi-Objective Integer Network Flow Problems
Optimization and Control
2025-06-02 v5
Abstract
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.
Cite
@article{arxiv.2305.12867,
title = {An Output-Polynomial Time Algorithm to Determine all Supported Efficient Solutions for Multi-Objective Integer Network Flow Problems},
author = {David Könen and Michael Stiglmayr},
journal= {arXiv preprint arXiv:2305.12867},
year = {2025}
}