Parametric global optimisation for bilevel programming

  • Authors:

  • Nuno P. Faísca;Vivek Dua;Berç Rustem;Pedro M. Saraiva;Efstratios N. Pistikopoulos

  • Affiliations:

  • Centre for Process Systems Engineering, Imperial College London, London, UK SW7 2AZ;Centre for Process Systems Engineering, University College London, London, UK WC1E 7JE;Centre for Process Systems Engineering, Imperial College London, London, UK SW7 2AZ;Gepsi- PSE Group, Department of Chemical Engineering, University of Coimbra, Coimbra, Portugal 3030-290;Centre for Process Systems Engineering, Imperial College London, London, UK SW7 2AZ

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2007

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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 parametric programming algorithms. We first describe how we can recast and solve the inner (follower's) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader's) problem. By inserting the obtained rational reaction sets in the upper level problem 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.