Automated, Parallel Optimization of Stochastic Functions Using a Modified Simplex Algorithm

This paper proposes a framework and new parallel algorithm for optimization of stochastic functions based on a downhill simplex algorithm. The function to be optimized is assumed to be subject to random noise, the variance of which decreases with sampling time, this is the situation expected for many real-world and simulation applications where results are obtained from sampling, and contain experimental error or random noise. The proposed optimization method is found to be comparable to previous stochastic optimization algorithms. The new framework is based on a master-worker architecture where each worker runs a parallel program. The parallel implementation allows the sampling to proceed independently on multiple processors, and is demonstrated to scale well to over 100 vertices. It is highly suitable for clusters with an ever increasing number of cores per node. The new method has been applied successfully to the reparameterization of the TIP4P water model, achieving thermodynamic and structural results for liquid water that are as good as or better than the original model, with the advantage of a fully automated parameterization process.