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Parametric global optimisation for bilevel programming

by Nuno P. Faísca, Vivek Dua, Berç Rustem, Pedro M. Saraiva, Efstratios N. Pistikopoulos
Journal of Global Optimization ()
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Abstract

We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed para- metric programming algorithms. We first describe how we can recast and solve the inner (follower’s) problem of the bilevel formulation as a multi-parametric program- ming problem, with parameters being the (unknown) variables of the outer (leader’s) problem. By inserting the obtained rational reaction sets in the upper level prob- lem the overall problem is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global optimisation strategy.

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