Application of genetic algorithms in response surface optimization problems.

摘要

In many areas of science and engineering, the choice of a good experimental design is very important. The performance of an experimental design for estimating a specific type of response surface model depends on the levels of the design variables selected from the design region of interest. Therefore, these design points should be carefully chosen so that the experimental design results in desirable statistical properties. Generally, response surface methodology is the framework used for these types of experiments.; It is possible to construct good experimental designs through the use of various optimization techniques and different design optimality criteria. However, these techniques may not guarantee the optimality of a design as the number of factors increases; that is, one may find a locally optimal design rather than a globally optimal design because of the complex combinatorial aspects of the optimal design problem. A solution technique based on the general principle of local improvement is the Genetic Algorithm (GA). This technique consisting of various random transformation processes that modify the forms of solutions and fitness measure of solutions associated with a level of optimality searches an optimal solution in huge solution spaces.; This research investigates how Genetic Algorithms (GAs) are used in generating good experimental designs for several different situations. In particular, this research focuses on three problems in the field of response surface methodology: G-optimal designs with a small number of runs, model-robust G-efficient designs, and cost-constrained G-efficient designs. These three problems have complex combinatorial aspects, and the search process for finding G-efficiency for each created design requires a moderately large amount of computation when compared to methods for the other alphabetical-efficient design problems such as the D-optimal design problem. An efficient GA procedure is developed for finding optimal or highly efficient solutions (designs) to these experimental design problems. Applications to several examples that are reflective of practical situations are presented.