Optimal Engineering Design Under Uncertainty by Geometric Programming

This paper presents an application of stochastic (posynomial) geometric programming to an optimal engineering design problem. A theory developed by Avriel and Wilde for calculating and bounding the expected value of the objective function is summarized. Moreover, a method known as the statistical error propagation method is used to calculate approximate confidence intervals for the cost function. Stochastic geometric programming is applied to the design of a conventional “once-through” condensing system for a steam power plant in the presence of uncertainty (e.g., fuel costs can vary with market conditions). It is shown how the design engineer can extract a considerable amount of information from the solution of merely one small optimization problem. If tighter bounds on the expected cost value are desired, knowledge of discrete probability distributions for the individual random parameters is required and additional optimization problems must be solved.