Simulated Annealing : Comparison of Vector and Parallel Implementations

2 Contents page 1 Introduction 3 1.1 Aim of the research 3 1.2 Background 3 2 Functional Aspects of the S.A. procedure 5 2.1 The sequential version 5 2.2 The vector version 6 2.3 The parallel version 6 3 Implementation Aspects 8 3.1 The vector version 8 3.1.1 Short description of vector processing 8 3.1.2 Description of the implementation 9 3.2 The parallel version 12 4 Time complexities 14 4.1 The sequential version 14 4.2 The vector version 15 4.2.1 Time complexity of the perturbation step 16 4.2.2 Time complexity of the potential energy update 16 4.2.3 Time complexity of the radius update 17 4.2.4 Total timecomplexity of the vector implementation 17 4.3 The parallel version 18 4.3.1 Functional decomposition 18 4.3.2 Systolic and hybrid S.A. 19 5 Results 20 5.1 The vector version 20 5.2 The parallel version 24 5.2.1 The tree decomposition 24 5.2.2 The systolic simulated annealing algorithm 26 5.3 Comparison of the vector and parallel implementations 29 6 Results of the crystallization experiments 31 7 Conclusions 34 7.1 Comparison of the vector and parallel implementations 34 7.2 Crystallization experiments 34 8 Future research 35 Acknowledgements 36 Reference list 36