The Global Optimization Algorithm: Newly Updated With Java Implementation And Parallelization (springerbriefs In Optimization)

This book explores the updated version of the GLOBAL algorithm which contains improvements for a local search algorithm and new Java implementations. Efficiency comparisons to earlier versions and on the increased speed achieved by the parallelization, are detailed. Examples are provided for students as well as researchers and practitioners in optimization, operations research, and mathematics to compose their own scripts with ease. A GLOBAL manual is presented in the appendix to assist new users with modules and test functions. GLOBAL is a successful stochastic multistart global optimization algorithm that has passed several computational tests, and is efficient and reliable for small to medium dimensional global optimization problems. The algorithm uses clustering to ensure efficiency and is modular in regard to the two local search methods it starts with, but it can also easily apply other local techniques. The strength of this algorithm lies in its reliability and adaptive algorithm parameters. The GLOBAL algorithm is free to download also in the earlier Fortran, C, and MATLAB implementations.-- Provided by publisher Acknowledgments 5 Contents 6 1 Introduction 9 1.1 Introduction 9 1.2 Problem Domain 10 1.3 The GLOBAL Algorithm 10 2 Local Search 14 2.1 Introduction 14 2.2 Local Search Algorithms 15 2.2.1 Derivative-Free Local Search 15 2.2.2 The Basic UNIRANDI Method 16 2.2.3 The New UNIRANDI Algorithm 16 2.2.4 Reference Algorithms 21 2.3 Computational Investigations 22 2.3.1 Experimental Settings 22 2.3.2 Comparison of the Two UNIRANDI Versions 23 2.3.3 Comparison with Other Algorithms 25 2.3.4 Error Analysis 26 2.3.5 Performance Profiles 29 2.4 Conclusions 32 3 The GLOBALJ Framework 33 3.1 Introduction 33 3.2 Switching from MATLAB to JAVA 34 3.3 Modularization 34 3.4 Algorithmic Improvements 37 3.5 Results 43 3.6 Conclusions 45 4 Parallelization 46 4.1 Introduction 46 4.2 Parallel Techniques 47 4.2.1 Principles of Parallel Computation 47 4.3 Design of PGLOBAL Based on GLOBAL 49 4.4 Implementation of the PGlobal Algorithm 53 4.4.1 SerializedGlobal 53 4.4.2 SerializedClusterizer 56 4.5 Parallelized Local Search 61 4.6 Losses Caused by Parallelization 61 4.7 Algorithm Parameters 61 4.8 Results 62 4.8.1 Environment 62 4.8.2 SerializedGlobal Parallelization Test 63 4.8.3 SerializedGlobalSingleLinkageClusterizer Parallelization Test 66 4.8.4 Comparison of Global and PGlobal Implementations 67 4.9 Conclusions 71 5 Example 73 5.1 Environment 73 5.2 Objective Function 73 5.3 Optimizer Setup 75 5.4 Run the Optimizer 76 5.5 Constraints 77 5.6 Custom Module Implementation 81 Appendix A User's Guide 84 A.1 Global Module 84 A.1.1 Parameters 84 A.2 SerializedGlobal Module 85 A.2.1 Parameters 85 A.3 GlobalSingleLinkageClusterizer Module 86 A.3.1 Parameters 86 A.4 SerializedGlobalSingleLinkageClusterizer Module 87 A.4.1 Parameters 87 A.5 UNIRANDI Module 87 A.5.1 Parameters 87 A.6 NUnirandi Module 88 A.6.1 Parameters 88 A.7 UnirandiCLS Module 88 A.7.1 Parameters 89 A.8 NUnirandiCLS Module 89 A.8.1 Parameters 89 A.9 Rosenbrock Module 90 A.9.1 Parameters 90 A.10 LineSearchImpl Module 90 Appendix B Test Functions 91 Appendix C DiscreteClimber Code 102 References 108 Front Matter ....Pages i-ix Introduction (Balázs Bánhelyi, Tibor Csendes, Balázs Lévai, László Pál, Dániel Zombori)....Pages 1-5 Local Search (Balázs Bánhelyi, Tibor Csendes, Balázs Lévai, László Pál, Dániel Zombori)....Pages 7-25 The GLOBALJ Framework (Balázs Bánhelyi, Tibor Csendes, Balázs Lévai, László Pál, Dániel Zombori)....Pages 27-39 Parallelization (Balázs Bánhelyi, Tibor Csendes, Balázs Lévai, László Pál, Dániel Zombori)....Pages 41-67 Example (Balázs Bánhelyi, Tibor Csendes, Balázs Lévai, László Pál, Dániel Zombori)....Pages 69-79 Back Matter ....Pages 81-111