IJPAM: Volume 47, No. 4 (2008)


Manjula A. Iyer$^1$, Rhonda D. Phillips$^2$,
Michael W. Trosset$^3$, Layne T. Watson$^4$
$^{1,2,4}$Department of Computer Science
Virginia Polytechnic Institute and State University
Mail Code 0106, Blacksburg, VA 24061, USA
$^1$e-mail: manjula@vt.edu
$^2$e-mail: rdphllps@vt.edu
$^4$e-mail: ltw@cs.vt.edu
$^3$Department of Statistics
Indiana University
Bloomington, IN 47405, USA
e-mail: mtrosset@indiana.edu

Abstract.Robust design optimization (RDO) uses statistical decision theory and optimization techniques to optimize a design over a range of uncertainty (introduced by the manufacturing process and unintended uses). Since engineering objective functions tend to be costly to evaluate and prohibitively expensive to integrate (required within RDO), surrogates are introduced to allow the use of traditional optimization methods to find solutions. This paper explores the suitability of radically different (deterministic and stochastic) optimization methods to solve prototypical robust design problems. The algorithms include a genetic algorithm using a penalty function formulation, the simultaneous perturbation stochastic approximation (SPSA) method, and two gradient-based constrained nonlinear optimizers (method of feasible directions and sequential quadratic programming). The results show that the fully deterministic standard optimization algorithms are consistently more accurate, consistently more likely to terminate at feasible points, and consistently considerably less expensive than the fully nondeterministic algorithms.

Received: August 20, 2008

AMS Subject Classification: 65C20, 65K05, 68U99

Key Words and Phrases: design under uncertainty, genetic algorithm, multidisciplinary design optimization, stochastic optimization

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 4