Simulation optimization with countably infinite feasible regions

Abstract

This article is concerned with proving the almost sure and global convergence of a broad class of algorithms for solving simulation optimization problems with countably infinite number of feasible points. We first describe the class of simulation optimization algorithms under consideration and discuss how the estimate of the optimal solution should be chosen when the feasible region of the underlying optimization problem is countably infinite. Then, we present a general result that guarantees the global convergence with probability one of the simulation optimization algorithms in this class. The assumptions of this result are sufficiently weak to allow the algorithms under consideration to be efficient, in that they are not required to either allocate the same amount of computer effort to all the feasible points these algorithms visit, or to spend an increasing amount of computer effort per iteration as the number of iterations grows. This article concludes with a discussion of how our assumptions can be satisfied and also generalized.