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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Optimization Jg. 61; H. 3; S. 335 - 358
Hauptverfasser: Alves, Maria João, Dempe, Stephan, Júdice, Joaquim J.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Taylor & Francis Group 01.03.2012
Taylor & Francis LLC
Schlagworte:
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
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-2
content type line 23
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2010.511674