In this paper we describe a vector and a parallel implementation of a stochastic simulation method to solve optimization problems in the field of many particle systems. We use a case-study where the (energetically) optimal distribution of particles on a closed surface is studied. Crystallization on a closed surface is an interesting sub-domain since such a topology causes lattice defects. To obtain the optimal distribution of particles on a sphere we use the simulated annealing algorithm. Simulated annealing is an application of the Markov chain simulation method which, in principle, guarantees that the minimum in energy of our system of particles is found. However, the time for the algorithm to converge increases rapidly with system size. In order to find the best performing implementation we have made vectorized and parallelized implementations. We parallelize the simulated annealing method in several ways. Here we use two types of parallelization in conjunction, a systolic decomposition of the Markov chains and a functional decomposition of the energy calculations. The sequential nature of the simulated annealing algorithm is hard to parallelize and is therefore an important research topic to study the functional differences between parallel and sequential implementations. Results show that the parallelization influences the accuracy of the iterative process. In this paper we give a comparison between the vectorized and the parallelized implementation. It is shown that the current parallel implementation on the Parsytec GC parallel transputer platform is not capable of outruning our vector implementation on the CRAY Y-MP.
['J.M. Voogd', 'Peter M. A. Sloot', 'R. van Dantzig']
Comparison of vector and parallel implementations of the simulated annealing algorithm