A DIRECT SEARCH ALGORITHM FOR GLOBAL OPTIMIZATION OF MULTIVARIATE FUNCTIONS

We describe a direct search method for locating the global optimum of a multimodal function. This is an adaptive probabilistic algorithm suitable for any function of many variables subject to arbitrary constraints. The algorithm is based on a simple model for noise reduction and uses an iterative method for averaging random perturbations in the parameter estimates. No prior assumptions are required about the continuity of the search domain, or about the continuity, differentiability and modality of the function. The algorithm is very simple, requiring little preparation and is suitable for application to functions that are nonlinear, noisy and of high dimensionality. The performance of the algorithm is demonstrated by a number of numerical examples, including a highly dimensioned problem in pattern recognition.