Non-Gradient Based Parameter Sensitivity Estimation for Single Objective Robust Design Optimization

Abstract

We present a method for estimating the parameter sensitivity of a design alternative for use in single objective robust design optimization. The method is non-gradient based: it is applicable even when the objective function of an optimization problem is non-differentiable and/or discontinuous with respect to the parameters. Also, the method does not require a presumed probability distribution for parameters, and is still valid when parameter variations are large. The sensitivity estimate is developed based on the concept that associated with each design alternative there is a region in the parameter variation space whose properties can be used to predict that design’s sensitivity. Our method estimates such a region using a worst-case scenario analysis and uses that estimate in a bi-level robust optimization approach. We present a numerical and an engineering example to demonstrate the applications of our method.

A multi-objective genetic algorithm for robust design optimization

“…3.2) with respect to ∆p over the radius of the exterior hyper-sphere of normalized tolerance region [18]. It is used as a robustness measure in our method.…”

“…In this section, we first briefly discuss the sensitivity estimation proposed by Gunawan and Azarm [18][19][20][21], based on which, the measures for robustness and performance of solutions are defined. We then present our two-objective RMOGA approach.…”

“…In this paper, we present a new deterministic approach to investigate the trade-off between the performance and robustness of optimum solutions, based on a Multi-Objective Genetic Algorithm (MOGA). The goal of our approach is to simultaneously optimize: i) a measure of the optimum solutions' performance, i.e., the fitness value, that accounts for objective and constraint values in the original optimization problem (defined in Section 2), and ii) a measure of the optimum solutions' robustness, the robustness index, originally proposed by Gunawan and Azarm [18][19][20][21], extended in this paper with the use of two additional distance norms. This approach is a deterministic method using non-gradient based parameter sensitivity estimation, which can be applied to optimization problems having objective and/or constraint functions that are non-differentiable with respect to the parameters.…”

“…Deterministic approaches, on the other hand, obtain robust optimum design solutions using gradient information of the parameters (e.g., Balling et al [11], Sundaresan et al [12,13], Zhu and Ting [14], Lee and Park [15], Su and Renaud [16], Messac and Yahaya [17]) or using a non-gradient based parameter sensitivity estimation (Gunawan and Azarm [18][19][20][21]). The aim of the Gunawan and Azarm's approach [18][19][20][21] is to obtain optimum solutions which essentially satisfy an additional robustness constraint that is prescribed by the decision maker (DM). In this paper, we present a new deterministic approach to investigate the trade-off between the performance and robustness of optimum solutions, based on a Multi-Objective Genetic Algorithm (MOGA).…”

“…Any MOGA in the literature can be applied to this approach. In Gunawan and Azarm's approach [18][19][20][21], the authors tried to obtain optimum solutions that are insensitive to the parameter variation. In other words, the robustness requirement was considered as a constraint in their approach.…”