Computational Methods for Decision Making
Bruns, Morgan Chase
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In this paper, we investigate computational methods for decision making based on imprecise information in the context of engineering design. The goal is to identify the subtleties of engineering design problems that impact the choice of computational solution methods, and to evaluate some existing solution methods to determine their suitability and limitations. Although several approaches for propagating imprecise probabilities have been published in the literature, these methods are insufficient for practical engineering analysis. The dependency bounds convolution approach of Williamson and Downs and the distribution envelope determination approach of Berleant work sufficiently well only for open models (that is, models with known mathematical operations). Both of these approaches rely on interval arithmetic and are therefore limited to problems with few repeated variables. In an attempt to overcome the difficulties faced by these deterministic methods, we propose an alternative approach that utilizes both Monte Carlo simulation and optimization. The Monte Carlo/optimization hybrid approach has its own drawbacks in that it assumes that the uncertain inputs can be parameterized, that it requires the solution of a global optimization problem, and that it assumes independence between the uncertain inputs.