Stochastic methods for practical global optimization

Engineering design problems often involve global optimization of functions that are supplied as 'black box' functions. These functions may be nonconve x, nondifferentiable and even discontinuous. In addition, the decision vari ables may be a combination of discrete and continuous variables. The functi ons are usually computationally expensive, and may involve finite element m ethods. An engineering example of this type of problem is to minimize the w eight of a structure, while limiting strain to be below a certain threshold . This type of global optimization problem is very difficult to solve, yet design engineers must find some solution to their problem - even if it is a suboptimal one. Sometimes the most difficult part of the problem is findin g any feasible solution. Stochastic methods, including sequential random se arch and simulated annealing, are finding many applications to this type of practical global optimization problem. Improving Hit-and-Run (MR) is a seq uential random search method that has been successfully used in several eng ineering design applications, such as the optimal design of composite struc tures. A motivation to IHR is discussed as well as several enhancements. Th e enhancements include allowing both continuous and discrete variables in t he problem formulation. This has many practical advantages, because design variables often involve a mixture of continuous and discrete values. IHR an d several variations have been applied to the composites design problem. So me of this practical experience is discussed.