A Methodology for Trading-Off Performance and Robustness Under Uncertainty

Abstract

Mathematical optimization plays an important role in engineering design, leading to greatly improved performance. Deterministic optimization, however, may result in undesired choices because it neglects uncertainty. Reliability-based design optimization (RBDO) and robust design can improve optimization by considering uncertainty. This paper proposes an efficient design optimization method under uncertainty, which simultaneously considers reliability and robustness. A mean performance is traded-off against robustness for a given reliability level of all performance targets. This results in a probabilistic multiobjective optimization problem. Variation is expressed in terms of a percentile difference, which is efficiently computed using the advanced mean value method. A preference aggregation method converts the multiobjective problem to a single-objective problem, which is then solved using an RBDO approach. Indifference points are used to select the best solution without calculating the entire Pareto frontier. Examples illustrate the concepts and demonstrate their applicability.