Global Optimization by Parallel Constrained Biased Random Search

The main purpose of this paper is to demonstrate that even a very minimal cooperation between multiple processors (each executing the same general purpose probabilistic global optimization algorithm) can significantly improve the computational efficiency as compared to executing the algorithm without cooperation. We describe one such cooperative general purpose algorithm for global optimization and its implementation on a parallel computer. The algorithm, called Parallel Constrained Biased Random Search (PCBRS), can be classified as a probabilistic random search method. It needs just one user supplied parameter which is related to the accuracy of the solution. Comparisons to several algorithms using the Dixon-Szego test functions are presented. PCBRS has been implemented on a multiprocessor system and on a distributed system of workstations following a Multiple Instruction Multiple Data model. Its parallel performance is evaluated using an eight-dimensional pattern classification problem. Our results make apparent that the PCBRS algorithm is computationally efficient for large problems and especially for functions with many local minima. It is shown that the cooperative work of several processors ensures an efficient solution to the global optimization problem.