Case Studies in Automatic Design Optimisation using the P-BFGS Algorithm

In this paper we consider a number of real world case studies using an automatic design optimisation system called Nimrod/O. The case studies include a photochemical pollution model, two different simulations of the strength of a mechanical part and the radio frequency properties of a ceramic bead. In each case the system is asked to minimise an objective function that results from the execution of a time consuming computational model. We compare the performance of an exhaustive search technique with a new non-linear gradient descent algorithm called P-BFGS. The exhaustive search results are produced using enFuzion, a commercial version of the parametric execution software Nimrod. P-BFGS is a parallel variant of the well-known BFGS algorithm and has been tested on a 64 processor Pentium cluster. The results show that PBFGS can achieve a speedup when compared to the exhaustive search on 3 out of the 4 problems. In addition, it always uses fewer processors than an exhaustive search.