Accelerating the convergence of the stochastic ruler method for discrete stochastic optimization

Abstract

Two variants of the stochastic ruler method for solving discrete stochastic optimization problems are presented. These two variants use the same mechanism for moving around the state space as the modified stochastic ruler method. However, these variants use different approaches for estimating the optimal solution. In particular, the modified stochastic rule method uses the number of visits to each state by the embedded chain of the Markov chain generated by the algorithm to estimate the optimal solution, while the variant methods use the feasible solution with the best average estimated objective function value to estimate the optimal solution. These two methods are guaranteed to converge almost surely to the set of global solutions.