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This paper explores an approach to global, stochastic, simulation optimization which combines stochastic approximation (SA) with simulated annealing (SAN). SA directs a search of the response surface efficiently, using a conservative number of simulation replications to approximate the local gradient of a probabilistic loss function. SAN adds a random component to the SA search, needed to escape local optima and forestall premature termination. Using a limited set of simple test problems, we compare the performance of SA/SAN with the commercial package OptQuest. Results demonstrate that SA/SAN can outperform OptQuest when properly tuned. The practical difficulty lies in specifying an appropriate set of SA/SAN gain coefficients for a given application. Further results demonstrate that a multistart approach greatly improves the coverage and robustness of SA/SAN, while also providing insights useful in directing iterative improvement of the gain coefficients before each new start. This preliminary study is sufficiently encouraging to invite further research on SA/SAN.