Robust optimization of a quartic multimodal nonlinear function - Methods and results

Abstract

Mathematical functions are often used to define an engineering design problem and these models are also used to find an optimal solution for the problem. The optimal solutions thus achieved are deterministic in nature and often neglect aberrations in design data as well as in design variables themselves. These uncertainties can manifest in a variety of forms including manufacturing errors, mechanical inaccuracies, and stochasticity in design parameters. This paper presents different robust design optimization methodologies followed by their application on a numerical optimization problem. Some modifications on the existing methods will also be presented. It will be shown that robust design optimization provides a strong framework for handling uncertainty since actual environments parameters are subject to these uncertainties. The methodologies will present robust optimization techniques that will result in designs that are minimally sensitive to input variations making them suitable for problems with uncertain parameters. Ten different robust optimal design methodologies will be briefly discussed and implemented on a quartic multimodal nonlinear test objective - chosen to be Himmelblau’s function. Since many problems arising in engineering design are nonlinear and multimodal, the methodologies discussed can be applied to similar design and quality engineering problems. It will be seen that different robust optimization methodologies vary substantially not only in terms of requirements but also in terms of the solutions they achieve. A summary of these results will be presented at the end.