Pareto Optima of Multicriteria Integer Linear Programs

We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct: (1) polynomial-time algorithms to determine exactly the num...

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Veröffentlicht in:INFORMS journal on computing Jg. 21; H. 1; S. 39
Hauptverfasser: De Loera, Jesús A, Hemmecke, Raymond, Köppe, Matthias
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Linthicum Institute for Operations Research and the Management Sciences 22.12.2009
Schlagworte:
Hierarchies
Integer programming
Mathematical models
Pareto optimum
Studies
ISSN:1091-9856, 1091-9856
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Zusammenfassung:We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct: (1) polynomial-time algorithms to determine exactly the number of Pareto optima and Pareto strategies; (2) a polynomial-space polynomial-delay prescribed-order enumeration algorithm for arbitrary projections of the Pareto set; (3) a polynomial-time algorithm to minimize the distance of a Pareto optimum from a prescribed comparison point with respect to arbitrary polyhedral norms; and (4) a fully polynomial-time approximation scheme for the problem of minimizing the distance of a Pareto optimum from a prescribed comparison point with respect to the Euclidean norm. [PUBLICATION ABSTRACT]
Bibliographie:SourceType-Scholarly Journals-1
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ISSN:1091-9856
1091-9856
DOI:10.1287/ijoc.1080.0277