Discrete stochastic optimization via a modification of the stochastic ruler method

In this paper, we present a modification of the stochastic ruler method for solving discrete stochastic optimization problems. Our method generates a stationary Markov chain sequence taking values in the feasible set of the underlying discrete optimization problem. The number of visits to every state by this Markov chain is used to estimate the optimal solution. Unlike the original stochastic ruler method, our method is guaranteed to converge almost surely to a global optimal solution. We present empirical results that illustrate the performance of our method, and we show that these results compare favorably with empirical results obtained using the original stochastic ruler method.