A Model Reference Adaptive Search Method for Global Optimization

We introduce a new randomized method called Model Reference Adaptive Search (MRAS) for solving global optimization problems. The method works with a parameterized probabilistic model on the solution space and generates at each iteration a group of candidate solutions. These candidate solutions are then used to update the parameters associated with the probabilistic model in such a way that the future search will be biased toward the region containing high quality solutions. The parameter updating procedure in MRAS is guided by a sequence of implicit reference models. We provide a particular instantiation of the sequence of reference models and describe an algorithm that implements the idea. We prove global convergence of the proposed algorithm in both continuous and combinatorial domains. In addition, we show that the model reference framework can also be used to describe the recently proposed cross-entropy (CE) method for optimization and study its properties. Numerical studies are also carried out to illustrate the performance of the algorithm.