Simulated Annealing in Bayesian Decision Theory

Abstract

Since the seminal paper by Kirkpatrick, Gelatt and Vechhi (1983), a number of papers in the scientific literature refer to simulated annealing as a powerful random optimization method which promises to deliver, within reasonable computing times, optimal or nearly optimal solutions to complex decision problems hitherto forbidding. The algorithm, which uses the physical process of annealing as a metaphor, is special in that, at each iteration, one may move with positive probability to solutions with higher values of the function to minimize, rather than directly jumping to the point with the smallest value within the neighborhood, thus drastically reducing the chances of getting trapped in local minima. This paper describes a variation of this algorithm within the Bayesian context of minimizing the expected loss in complex decision problems. The procedure is then applied to the identification of good designs for political sample surveys, aimed at predicting the behaviour of the electorate in future elections.