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.

Constructing Synthetic Samples

We consider the problem of constructing a synthetic sample from a population of interest which cannot be sampled from but for which the population means of some of its variables are known. In addition, we assume that we have in hand samples from two similar populations. Using the known population means, we will select subsamples from the samples of the other two populations which we will then combine to construct the synthetic sample. The synthetic sample is obtained by solving an optimization problem, where the known population means, are used as constraints. The optimization is achieved through an adaptive random search algorithm. Simulation studies are presented to demonstrate the effectiveness of our approach. We observe that on average, such synthetic samples behave very much like actual samples from the population of interest. As an application we consider constructing a one-percent synthetic sample for the missing 1890 decennial sample of the United States.