Setting the control parameters of a genetic algorithm to obtain good results is a long-standing problem. We define an experiment design and analysis method to determine relative importance and effective settings for control parameters of any evolutionary algorithm, and we apply this method to a classic binary-encoded genetic algorithm (GA). Subsequently, as reported elsewhere, we applied the GA, with the control parameter settings determined here, to steer a population of cloud-computing simulators toward behaviors that reveal degraded performance and system collapse. GA-steered simulators could serve as a design tool, empowering system engineers to identify and mitigate low-probability, costly failure scenarios. In the existing GA literature, we uncovered conflicting opinions and evidence regarding key GA control parameters and effective settings to adopt. Consequently, we designed and executed an experiment to determine relative importance and effective settings for seven GA control parameters, when applied across a set of numerical optimization problems drawn from the literature. This paper describes our experiment design, analysis, and results. We found that crossover most significantly influenced GA success, followed by mutation rate and population size and then by rerandomization point and elite selection. Selection method and the precision used within the chromosome to represent numerical values had least influence. Our findings are robust over 60 numerical optimization problems.