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On the use of bilevel programming for solving a structural optimization problem with discrete variables

In: Optimization with Multivalued Mappings

Author

Listed:
  • Joaquim J. Júdice

    (Departamento de Matemática da Universidade de Coimbra and Instituto de Telecomunicações)

  • Ana M. Faustino

    (Faculdade de Engenharia da Universidade do Porto)

  • Isabel M. Ribeiro

    (Faculdade de Engenharia da Universidade do Porto)

  • A. Serra Neves

    (Faculdade de Engenharia da Universidade do Porto)

Abstract

Summary In this paper, a bilevel formulation of a structural optimization problem with discrete variables is investigated. The bilevel programming problem is transformed into a Mathematical Program with Equilibrium (or Complementarity) Constraints (MPEC) by exploiting the Karush-Kuhn-Tucker conditions of the follower’s problem. A complementarity active-set algorithm for finding a stationary point of the corresponding MPEC and a sequential complementarity algorithm for computing a global minimum for the MPEC are analyzed. Numerical results with a number of structural problems indicate that the active-set method provides in general a structure that is quite close to the optimal one in a small amount of effort. Furthermore the sequential complementarity method is able to find optimal structures in all the instances and compares favorably with a commercial integer program code for the same purpose.

Suggested Citation

  • Joaquim J. Júdice & Ana M. Faustino & Isabel M. Ribeiro & A. Serra Neves, 2006. "On the use of bilevel programming for solving a structural optimization problem with discrete variables," Springer Optimization and Its Applications, in: Stephan Dempe & Vyacheslav Kalashnikov (ed.), Optimization with Multivalued Mappings, pages 123-142, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-34221-4_7
    DOI: 10.1007/0-387-34221-4_7
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