Publications Details
A two-level parallel direct search implementation for arbitrarily sized objective functions
In the past, many optimization schemes for massively parallel computers have attempted to achieve parallel efficiency using one of two methods. In the case of large and expensive objective function calculations, the optimization itself may be run in serial and the objective function calculations parallelized. In contrast, if the objective function calculations are relatively inexpensive and can be performed on a single processor, then the actual optimization routine, itself may be parallelized. In this paper, a scheme based upon the Parallel Direct Search (PDS) technique is presented which allows the objective function calculations to be done on an arbitrarily large number (p2) of processors. If, p, the number of processors available, is greater than or equal to 2p{sub 2} then the optimization may be parallelized as well. This allows for efficient use of computational resources since the objective function calculations can be performed on the number of processors that allow for peak parallel efficiency and then further speedup may be achieved by parallelizing the optimization. Results are presented for an optimization problem which involves the solution of a PDE using a finite-element algorithm as part of the objective function calculation. The optimum number of processors for the finite-element calculations is less than p/2. Thus, the PDS method is also parallelized. Performance comparisons are given for a nCUBE 2 implementation.