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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| Veröffentlicht in: | Discrete Applied Mathematics Jg. 376; S. 1 - 14 |
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| Sprache: | Englisch |
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15.12.2025
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| ISSN: | 0166-218X |
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| 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. |
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| AbstractList | 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. |
| Author | Stiglmayr, Michael Könen, David |
| Author_xml | – sequence: 1 givenname: David orcidid: 0000-0003-1747-8791 surname: Könen fullname: Könen, David email: koenen@uni-wuppertal.de – sequence: 2 givenname: Michael surname: Stiglmayr fullname: Stiglmayr, Michael email: stiglmayr@uni-wuppertal.de |
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| Cites_doi | 10.1016/j.cor.2017.01.004 10.1007/s10898-019-00745-6 10.1016/S0377-2217(99)00191-5 10.1002/mcda.1603 10.1016/j.dam.2022.07.007 10.1002/net.20407 10.1016/0020-0190(88)90065-8 10.1016/j.ejor.2008.10.031 10.1002/mcda.1574 10.1007/s10898-011-9709-y 10.1287/mnsc.18.7.401 10.1016/0377-2217(77)90063-7 10.1023/A:1008258310679 10.1016/j.ejor.2005.09.033 10.1111/j.1475-3995.2010.00761.x 10.1287/opre.22.1.189 10.1016/j.cor.2014.02.009 10.1016/S0305-0548(99)00095-7 10.1016/j.cor.2008.11.001 |
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| Keywords | Minimum cost flow Multi-objective network flow Weakly supported Complexity theory Multi-objective integer linear programming Output-polynomial algorithm |
| Language | English |
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| SubjectTerms | Complexity theory Minimum cost flow Multi-objective integer linear programming Multi-objective network flow Output-polynomial algorithm Weakly supported |
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