Robust Design of Structural Beams via Nondominated Sorting Genetic Algorithm

The design of structural beams involves the presence of uncertainties in minimizing the cross-sectional area subject to constraints on bending stress, deflection, and bounds. This is a case of robust optimization problem in which solutions are sampled around the neighborhood of a given solution and the mean and variance of this sample are taken as the objective functions. In this paper, we present robust optimization using Nondominated Sorting Genetic Algorithm (NSGA) which does not involve a-priori weights on the objective functions. The robust solution is finally taken from the optimum Pareto front of solutions based on the priority of the manufacturer. We study the cases when the uncertainties assume a uniform and normal distributions. Although an increased cross-sectional area is expected, a greater increase is found from the case of normally distributed uncertainties than that of uniformly distributed uncertainties. T-beam is observed to be more sensitive to uncertainties than the I-beam. Finally, we remark that the solutions found from the case of uniformly distributed uncertainties for both beams suffer if the uncertainties are actually normally distributed, which is not the case vice-versa.