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

J. Júdice, A. Faustino, I. Ribeiro and A. Serra Neves

Abstract

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 analysed. 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 favourably with a commercial integer program code for the same purpose.