Comparison of Vector and Parallel Implementations of the Simulated Annealing Algorithm J.M. Voogd*, P.M.A. Sloot*, R. v. Dantzig** *Parallel Scientific Computing and Simulation group University of Amsterdam, Kruislaan 403 1098 SJ Amsterdam, The Netherlands **NIKHEF, PO Box 41882 1009 DB Amsterdam, The Netherlands 1 Introduction The Parallel Scientific Computing and Simulation group at the University of Amsterdam is pursuing research in the field of parallel natural solvers. Natural solvers are algorithms that are inspired by processes from nature. In parallel computing especially the class of natural solvers provides a very promising approach, since the characteristics of the original physical phenomenon remain visible in the solving method and the implicit and explicit parallelism of the problem remains conserved. One of the natural solvers is an optimisation algorithm called Simulated Annealing (SA) which is the topic of this paper. Because of the inherent sequential nature of the algorithm, this particular method however, turns out to be hard to parallellize. The SA algorithm is applied to a case study where simulation of crystallisation with spherical boundary conditions is studied. Since this is a problem that requires an enormous amount of computing power, even for modest problem sizes, we started looking for methods to speed up the simulations. In this report we compare a vector implementation of SA on a super computer (CRAY Y- MP 4/464) with parallel implementations on a transputer platform (Parsytec GCel with 512 nodes). We have investigated the scalability of the parallel implementations with the number of particles (N) and the number of processors (P) and compared it with the scalability of the vector implementation. In section 2 we explain the background of our study, in section 3 we discuss the algorithms and time complexities for the sequential, vector and parallel implementations. Section 4 contains the conclusions. 2 Background Particle dynamics simulations with spherical boundary conditions for large numbers ( ≥ 10 3 ) of particles with Lennard-Jones or similar interactions at high density, provide an important testing ground for the study of closed 2D systems. Crystallisation with this type of constraints is poorly understood. As a model for such (bio)physically relevant systems, we started with particles, e.g. molecules, confined to a spherical surface. Examples of actual systems are buckyballs, viruses and membrane vesicles. Particle simulations on a spherical surface are also an alternative to simulations with periodic boundary conditions to approximate bulk systems in