To search for an optimal design in a large search space, Wu, Mao, Ma (1990) suggested the SEL-method to find an optimal setting. Genetic algorithms (GA) can be used to improve upon this method. To make the search procedure more efficient, new ideas of forbidden array and weighted mutation are introduced. Relaxing the condition of orthogonality, GA is able to accommodate a variety of design points which allows more flexibility and enhances the chance of getting the best setting in fewer runs, particularly in the presence of interactions. The search procedure is enriched by a Bayesian method for identifying the important main effects and two-factor interactions. Illustration is given with the optimization of three functions, one of which is from Shekel's family.