Since more than thirty years mathematical programming has become a standard tool for structural optimization. Initially, methods which used only local information the functions and which required no gradients were favoured. Grid- and tabu-search were proposed and in connection with chance-constrained design problems, the Monte-Carlo-Method was applied. These zero-order and direct methods were followed in the seventies by first- and second-order methods, which required the analytical or numerical computation of first- and second-order gradients. The restriction to the class of differentiable optimization problems was honoured by faster and even superlinear convergence. Due to the high non-linearity and because of the non-convexity of most engineering problems, these gradient-based methods ended up at best at, a local optimal design point. Furtheron, their lack of robustness for problems with hundreds of design variables and constraints became apparent. A decomposition of the engineering problems which preserved the superlinear convergence proved to be difficult: The decomposability decreases with the complexity of the problems and the complexity increases wit h the realistic modelling of the problems. For this reason, the zero-order and direct methods gained renewed interest in the early eighties. This tendency was further enhanced by the availability of high-speed parallel computing. Influenced by this development, stochastic search methods and Darwinian methods have been the subject of many publications during the past fifteen years. Grid search and the Monte-Carlo-Method will be discussed first, followed by the basic Darwinian methods and their generalizations for integer, mixed discrete-continuous problems and parallelization. Similarities between the different Darwinian techniques are discussed and applications to realistic problems are presented.

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