On the computation of all supported efficient solutions in multi-objective integer network flow problems

This paper presents a new algorithm for identifying all supported non-dominated vectors (or outcomes) in the objective space, as well as the corresponding efficient solutions in the decision space, for multi-objective integer network flow problems. Identifying the set of supported non-dominated vect...

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Bibliographic Details
Published in:European journal of operational research Vol. 199; no. 1; pp. 68 - 76
Main Authors: Eusébio, Augusto, Figueira, José Rui
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.11.2009
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Algorithms
Applied sciences
Approximation
Decision theory. Utility theory
Exact sciences and technology
Flows in networks. Combinatorial problems
Multi-objective linear and integer programming
Multi-objective linear and integer programming Multi-objective network flows Negative-cycle algorithms Parametric programming
Multi-objective network flows
Negative-cycle algorithms
Network flow problem
Operational research and scientific management
Operational research. Management science
Parametric programming
Studies
Negative-cycle algorithms
Multi-objective linear and integer programming
Multi-objective network flows
Parametric programming
Network flow
Efficiency
Multiobjective programming
Vector support machine
Multi-objective linear and integer
Connectedness
programming
Multiple decision
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:This paper presents a new algorithm for identifying all supported non-dominated vectors (or outcomes) in the objective space, as well as the corresponding efficient solutions in the decision space, for multi-objective integer network flow problems. Identifying the set of supported non-dominated vectors is of the utmost importance for obtaining a first approximation of the whole set of non-dominated vectors. This approximation is crucial, for example, in two-phase methods that first compute the supported non-dominated vectors and then the unsupported non-dominated ones. Our approach is based on a negative-cycle algorithm used in single objective minimum cost flow problems, applied to a sequence of parametric problems. The proposed approach uses the connectedness property of the set of supported non-dominated vectors/efficient solutions to find all integer solutions in maximal non-dominated/efficient facets.
Bibliography:SourceType-Scholarly Journals-1
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content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2008.10.031