Parameter Sensitivity Measures for Single Objective, Multi-Objective, and Feasibility Robust Design Optimization

Abstract

Uncontrollable variations are unavoidable in engineering design. If ignored, such variations can seriously deteriorate performance of an optimum design. Robust optimization is an approach that optimizes performance of a design and at the same time reduces its sensitivity to variations. The literature reports on numerous robust optimization techniques. In general, these techniques have three main shortcomings: (i) they presume probability distributions for parameter variations, which might be invalid, (ii) they limit parameter variations to a small (linear) range, and (iii) they use gradient information of objective/constraint functions. These shortcomings severely restrict applications of the techniques reported in the literature. The objective of this dissertation is to present a robust optimization method that addresses all of the above-mentioned shortcomings. In addition to being efficient, the robust optimization method of this dissertation is applicable to both single and multi-objective optimization problems. There are two steps in our robust optimization method. In the first step, the method measures robustness for a design alternative. The robustness measure is developed based on a concept that associated with each design alternative there is a sensitivity region in parameter variation space that determines how much variation a design alternative can absorb. The larger the size of this region, the more robust the design. The size of the sensitivity region is estimated by a hyper-sphere, using a worst-case approach. The radius of this hyper-sphere is obtained by solving an inner optimization problem. By comparing this radius to an actual range of parameter variations, it is determined whether or not a design alternative is robust. This comparison is added, in the second step, as an additional constraint to the original optimization problem. An optimization technique is then used to solve this problem and find a robust optimum design solution. As a demonstration, the robust optimization method is applied to numerous numerical and engineering examples. The results obtained are numerically analyzed and compared to nominal optimum designs, and to optimum designs obtained by a few well-known methods from the literature. The comparison study verifies that the solutions obtained by our method are indeed robust, and that the method is efficient.