A Model Reference Adaptive Search Method for Stochastic Global Optimization

Abstract

We propose a randomized search method called Stochastic Model Reference Adaptive Search (SMRAS) for solving stochastic optimization problems in situations where the objective functions cannot be evaluated exactly, but can be estimated with some noise (or uncertainty), e.g., via simulation. The method generalizes the recently proposed Model Reference Adaptive Search (MRAS) method for deterministic optimization, and is based on sampling from an underlying probability distribution "model" on the solution space, which is updated iteratively after evaluating the performance of the samples at each iteration. We prove global convergence of SMRAS in a general stochastic setting, and carry out numerical studies to illustrate its performance. An emphasis of this paper is on the application of SMRAS for solving static stochastic optimization problems with either continuous or discrete domains; its various applications for solving dynamic decision making problems can be found in [6].

On the performance of the Cross-Entropy method

“…where { ηk } is the sequence of mean vectors generated by Algorithm 2 when applied to simulation optimization. A large deviations approach similar to that of Hu et al (2008) can be used to determine the conditions on the allocation rule…”

“…The Cross-Entropy (CE) method (Rubinstein and Kroese 2004), when viewed in an optimization context, is typical of a class of sampling-based algorithms known as model-based methods (Zolchin et al 2004, Fu et al 2006. The basic idea of CE is to work with a parameterized probability distribution on the solution space and randomly generate at each iteration a group of candidate solutions.…”