Simulation Optimization Using Multi-Time-Scale Adaptive Random Search

We propose a random search algorithm for seeking the global optimum of an objective function in a simulation setting. The algorithm can be viewed as an extension of the MARS algorithm proposed in Hu and Hu (2011) for deterministic optimization, which iteratively finds improved solutions by modifying and sampling from a parameterized probability distribution over the solution space. However, unlike MARS and many other algorithms in this class, which are often population-based, our method only requires a single candidate solution to be generated at each iteration. This is primarily achieved through an effective use of past sampling information by means of embedding multiple nested stochastic approximation type of recursions into the algorithm. We prove the global convergence of the algorithm under general conditions and discuss two special simulation noise cases of interest, in which we show that only one simulation replication run is needed for each sampled solution. A preliminary numerical study is also carried out to illustrate the algorithm.