Concurrent function evaluations in local and global optimization (Q1085788)

This paper discusses some basic opportunities for the use of multiprocessing in the solution of optimization problems. We consider two fundamental optimization problems, unconstrained optimization and global optimization, in the important case when function evaluation is expensive and gradients are evaluated by finite differences. First we discuss some simple parallel strategies based upon the use of concurrent function evaluations to evaluate the finite difference gradient. These include the speculative evaluation of the gradient concurrently with the evaluation of the function before it is known whether the gradient value at this point will be required. We present examples that indicate the effectiveness of these parallel strategies for unconstrained optimization. We also give experimental results that show the effect of using these strategies to parallelize each of the multiple local minimizations within a recently proposed concurrent global optimization algorithm. We briefly discuss several parallel optimization strategies that are related to these approaches but make more fundamental changes to standard sequential optimization algorithms.