Title: Solving a class of multiobjective bilevel problems by DC programming

Authors: Aicha Anzi; Mohammed Said Radjef

Addresses: Research Unit LaMOS (Modelling and Optimization of Systems), Faculty of Exact Sciences, University of Bejaia, 06000 Bejaia, Algeria ' Research Unit LaMOS (Modelling and Optimization of Systems), Faculty of Exact Sciences, University of Bejaia, 06000 Bejaia, Algeria

Abstract: In this paper, we consider a class of multiobjective bilevel programming problems in which the first level objective function is assumed to be a vector valued DC function and the second level problem is a linear multiobjective program. The problem is transformed into a standard single optimisation problem by using a preference function. We give a characterisation to the induced region and reformulate the problem as a problem of optimising a function over the efficient set. Next, a well-known representation of the efficient set is used which will allow to transform the problem, using an exact penalisation, into a DC program. Finally, we apply the DC algorithm to solve the resulting DC program.

Keywords: bilevel programming; multiobjective optimisation; exact penalty; DC algorithm; DCA; DC programming; preference function.

DOI: 10.1504/IJOR.2020.105364

International Journal of Operational Research, 2020 Vol.37 No.2, pp.157 - 173

Received: 10 Feb 2016
Accepted: 10 Feb 2017

Published online: 20 Feb 2020 *

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