On the use of bilevel programming for solving a structural optimization problem with discrete variables
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 th...
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| Outros Autores: | , , |
| Formato: | book |
| Idioma: | eng |
| Publicado em: |
2006
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| Assuntos: | |
| Texto completo: | https://hdl.handle.net/10216/102028 |
| País: | Portugal |
| Oai: | oai:repositorio-aberto.up.pt:10216/102028 |
| Resumo: | 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. |
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