Computing the Pareto frontier of a bi-objective bi-level linear problem using a multiobjective mixed-integer programming algorithm

In this article, we study the bi-level linear programming problem with multiple objective functions on the upper level (with particular focus on the bi-objective case) and a single objective function on the lower level. We have restricted our attention to this type of problem because the considerati...

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Vydáno v:Optimization Ročník 61; číslo 3; s. 335 - 358
Hlavní autoři: Alves, Maria João, Dempe, Stephan, Júdice, Joaquim J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Taylor & Francis Group 01.03.2012
Taylor & Francis LLC
Témata:
Algorithms
bi-level programming
Decision analysis
Integer programming
Interactive
Linear programming
Mathematical analysis
Mathematical functions
Mathematical models
mixed-integer programming
multiobjective
Optimization
Pareto optimality
Pareto optimum
Programming
Studies
ISSN:0233-1934, 1029-4945
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Shrnutí:In this article, we study the bi-level linear programming problem with multiple objective functions on the upper level (with particular focus on the bi-objective case) and a single objective function on the lower level. We have restricted our attention to this type of problem because the consideration of several objectives at the lower level raises additional issues for the bi-level decision process resulting from the difficulty of anticipating a decision from the lower level decision maker. We examine some properties of the problem and propose a methodological approach based on the reformulation of the problem as a multiobjective mixed 0-1 linear programming problem. The basic idea consists in applying a reference point algorithm that has been originally developed as an interactive procedure for multiobjective mixed-integer programming. This approach further enables characterization of the whole Pareto frontier in the bi-objective case. Two illustrative numerical examples are included to show the viability of the proposed methodology.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2010.511674