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Parametric global optimisation for bilevel programming

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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.

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Authors and Affiliations

  1. Centre for Process Systems Engineering, Imperial College London, London, SW7 2AZ, UK

    Nuno P. Faísca, Berç Rustem & Efstratios N. Pistikopoulos

  2. Centre for Process Systems Engineering, University College London, London, WC1E 7JE, UK

    Vivek Dua

  3. Gepsi- PSE Group, Department of Chemical Engineering, University of Coimbra, Coimbra, 3030-290, Portugal

    Pedro M. Saraiva

Authors
  1. Nuno P. Faísca
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  2. Vivek Dua
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  3. Berç Rustem
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  4. Pedro M. Saraiva
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  5. Efstratios N. Pistikopoulos
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Correspondence to Efstratios N. Pistikopoulos.

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Faísca, N.P., Dua, V., Rustem, B. et al. Parametric global optimisation for bilevel programming. J Glob Optim 38, 609–623 (2007). https://doi.org/10.1007/s10898-006-9100-6

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  • DOI: https://doi.org/10.1007/s10898-006-9100-6

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