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

Joaquim J. Júdice (), Ana M. Faustino (), Isabel M. Ribeiro () and A. Serra Neves ()
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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

A chapter in Optimization with Multivalued Mappings, 2006, pp 123-142 from Springer

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.

Keywords: Structural optimization; mixed integer programming; global optimization; complementarity (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-0-387-34221-4_7

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DOI: 10.1007/0-387-34221-4_7

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