Stochastic search in discrete structural optimization simulated annealing, genetic algorithms and neural networks

A number of structural optimization problems are characterized by the presence of discrete and integer design variables, over and beyond the more traditional continuous variable problems. In some applications, the number of design variables may be quite large. Additionally, the design space in such problems may be nonconvex, and in some situations, even disjointed. The use of conventional mathematical programming methods in such problems is fraught with hazards. First, these gradient-based methods cannot be used directly in the presence of discrete variables. Their use is facilitated by creating multiple equivalent continuous variable problems (branch and bound techniques); in the presence of high-dimensionality, the number of branched problems that may have to be solved can be quite large. In some problems, the analysis can be computationally demanding, thereby further limiting the effective use of these methods. Finally, it must be borne in mind that these methods have a propensity to convergence to a relative optimum closest to the starting point, and this is a major weakness in the presence of multimodality in the design space. This chapter focusses on the application of recently emergent computational paradigms such as simulated annealing, genetic algorithms, and neural networks in structural optimization problems with mixed variables. These methods illustrate an extremely effective exploitation of stochastic methods for search and numerical modeling.