Solving a class of multiobjective bilevel problems by DC programming

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.