Complementarity and genetic algorithms for an optimization shell problem

In this paper an optimization thin laminated shallow shell problem is discussed. The existence of a solution for both the linear and nonlinear versions of this problem is firstly studied by exploiting their reductions into variational inequalities. The discretization of these continuous problems by using appropriate finite elements leads into a Mathematical Programming Problem with Equilibrium Constraints (MPEC) in which some of their variables assume integer values and the remaining variables are implicitly defined as the solution of a Mixed Complementarity Problem (MCP). A genetic algorithm incorporating a complementarity path-following technique is proposed for the solution of this MPEC. It is shown that the efficiency of this hybrid problem depends on the problem to be linear or nonlinear. Some computational experience with this algorithm on the solution of special cases of this MPEC has been reported elsewhere and is briefly described to highlight the performance of the proposed methodology.