Exploration of the effectiveness of physical programming in robust design

Computational optimization for design is effective only to the extent that the aggregate objective function adequately captures designer's preference. Physical programming is an optimization method that captures the designer's physical understanding of the desired design outcome in forming the aggregate objective function. Furthermore, to be useful, a resulting optimal design must be sufficiently robust/insensitive to known and unknown variations that to different degrees affect the design's performance. This paper explores the effectiveness of the physical programming approach in explicitly addressing the issue of design robustness. Specifically, we synergistically integrate methods that had previously and independently been developed by the authors, thereby leading to optimal - robust - designs. We show how the physical programming method can be used to effectively exploit designer preference in making tradeoffs between the mean and variation of performance, by solving a bi-objective robust design problem. The work documented in this paper establishes the general superiority of physical programming over other conventional methods (e.g., weighted sum) in solving multiobjective optimization problems. It also illustrates that the physical programming method is among the most effective multi-criteria mathematical programming techniques for the generation of Pareto solutions that belong to both convex and non-convex efficient frontiers.