Mean square error criteria to multiresponse process optimization by a new genetic algorithm

The recent push for quality in industry has brought response surface methodology to the attention of many users. Most of the published literature on robust design methodology is basically concerned with optimization of a single response or quality characteristic which is often most critical to consumers. For most products, however, quality is multidimensional, so it is common to observe multiple responses in an experimental situation. In this paper, we present a methodology for analyzing several quality characteristics simultaneously using the mean square error (MSE) criterion when data are collected from a combined array. Problems with highly nonlinear, or multimodal, objective functions are extremely difficult to solve and are further complicated by the presence of multiple objectives. An alternative approach is to use a heuristic search procedure such as a genetic algorithm (GA). The GA generates a string of solutions using genetics-like operators such as selection, crossover and mutation. In this paper, a genetic algorithm based on arithmetic crossover for the multiresponse problem is proposed. The string of solutions highlight the trade-offs that one needs to consider in order to obtain a compromise solution. A numerical example has been presented to illustrate the performance and the applicability of the proposed method.