Stochastic annealing for synthesis under uncertainty

Simulated annealing is a recently developed combinatorial optimization technique based upon ideas in statistical mechanics. This paper presents the concept of stochastic annealing to handle the effect of uncertainties on the objective function. Most implementations of the simulated annealing algorithm are used for discrete, deterministic problems and do not take into consideration the associated uncertainties in the input variables. The stochastic annealing is an algorithm designed to efficiently optimize a probabilistic objective function. That is, for each solution examined, there is not a single cost value but a distribution of costs based on uncertainties in the problem inputs. We choose to optimize over expected cost. The simulated annealing algorithm is modified to select not only the design variables, but also the number of samples to be taken in calculating the expected cost. This strategy essentially allows for an increased number of samples as one approaches the optimum. As the system gets ‘cooler’, the accuracy of the expected cost is higher. At high temperatures, however, there is no need for high accuracy and the algorithm uses small samples. This concept improves the computational efficiency significantly, which can otherwise be a major bottleneck in solving stochastic combinatorial optimization problems. The applicability of this new algorithm is illustrated in the context of synthesis of a multistage compression system.