A new exact method for linear bilevel problems with multiple objective functions at the lower level

•Exact method to optimize semivectorial bilevel linear problems.•The method explores efficient extreme solutions of a multiobjective linear problem.•New heuristic procedure for problems where the global optimum is difficult to reach.•The heuristic can lead to distinct final solutions using different...

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Bibliographic Details
Published in:	European journal of operational research Vol. 303; no. 1; pp. 312 - 327
Main Authors:	Alves, Maria João, Henggeler Antunes, Carlos
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 16.11.2022
Subjects:	Linear bilevel optimization Multiobjective simplex method Multiple objective programming Semivectorial bilevel problem Multiobjective simplex method Linear bilevel optimization Multiple objective programming Semivectorial bilevel problem
ISSN:	0377-2217, 1872-6860
Online Access:	Get full text
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Summary:	•Exact method to optimize semivectorial bilevel linear problems.•The method explores efficient extreme solutions of a multiobjective linear problem.•New heuristic procedure for problems where the global optimum is difficult to reach.•The heuristic can lead to distinct final solutions using different starting points.•Implementation of an effective multiobjective simplex method. In this paper we consider linear bilevel programming problems with multiple objective functions at the lower level. We propose a general-purpose exact method to compute the optimistic optimal solution, which is based on the search of efficient extreme solutions of an associated multiobjective linear problem with many objective functions. We also explore a heuristic procedure relying on the same principles. Although this procedure cannot ensure the global optimal solution but just a local optimum, it has shown to be quite effective in problems where the global optimum is difficult to obtain within a reasonable timeframe. A computational study is presented to evaluate the performance of the exact method and the heuristic procedure, comparing them with an exact and an approximate method proposed by other authors, using randomly generated instances. Our approach reveals interesting results in problems with few upper-level variables.
ISSN:	0377-2217 1872-6860
DOI:	10.1016/j.ejor.2022.02.047