This dissertation contains the first proof of convergence of a genetic algorithm in the context of stochastic optimization. The class of stochastic optimization problems includes formulations in which the objective is an expected value, which can be evaluated using Monte Carlo methods. Growing computer power combined with methods presented here and elsewhere makes feasible the solution of many stochastic optimization problems with applications ranging from process design to facility location.
The dissertation also describes the proposed stochastic optimization method that combines a sequential ranking and selection procedure with an elitist genetic algorithm. A batching procedure is included to assure that batch means of solutions achieve approximate normality. The proposed method is proven under the normality assumption to converge in the long run to identify and maintain solutions with objective values within an acceptable difference, D, from the global optimal solution with probability greater than an acceptable probability, P*. Computational results illustrate that the proposed algorithm achieves promising performance compared with alternatives for a variety of problems with minimal changes.
The first application is on the stochastic optimization for “robust” engineering process design decisions making. By robust we mean designs that maximize the expected utility taking into account variation of “noise factors”.
A methodology for robust process design is presented based on direct minimization of the expected loss in some cases using the proposed optimization heuristics. The proposed methods are compared with alternatives including methods based on Taguchi’s signal-to-noise ratios. Several formulations of the loss are explored. The method is illustrated through its application to the design of robotic gas metal arc-welding parameter settings.
The second application is a simulation optimization method applied to decision making about where to locate facilities and how to transport products in a supply chain. This problem is shown to be a stochastic generalized assignment problem for which a bound is presented. We also propose a genetic algorithm, for cases in which bounds are available, that offers the possibility of stopping while guaranteeing that a solution with objective value within an acceptable difference, Δ, of the optimal value is found with probability greater than P*.