Investigations of Alternative Solution Methodologies for
the 1-Median Location Problem on a Sphere
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Thesis Online (abstract)
Acknowledgements
Chapter One: Introduction
Chapter Two: Problem Background
2.1 The Weber Problem, in general
2.2 Problems in Spherical Geometry: Non-Convex Objective Functions
2.3 Norms for Use in Spherical Weber Problems
2.4 Existing Methodologies for Global Minimization
Chapter Three: Problem Statement and Thesis Objectives
3.1 Existing Methodologies
3.2 'Solutions' in the Weiszfeld's Algorithm Methodology
3.3 Computational Complexity of the Problem
3.4 Problem Statement
3.5 Anticipated Results
3.6 Objectives of Research
3.7 Majority Theorem Implications
Chapter Four: Proposed Methodology
4.1 Development of Stand-Alone Solutions for Testing
4.2 Description of Methodology for Geometric Method
4.3 Proposal for Extension of Possible Solution Bounds
4.4 Surface Coordinate Transformations for Spherical Geometry
4.5 Criteria for Relative Success of Proposed Methodology
Chapter Five: Results and Sample Solutions
5.1 Sample Problem Data Sets
5.2 Results of the Spheresolver Code
5.3 Comparison of Results to Projected Centroid Method
5.4 Results of the Great Circle Arc Norm substitution into the Weiszfeld Algorithm
Chapter Six: Conclusions and Recommendations
6.1 Conclusions drawn from the Spheresolver Code problems
6.2 Conclusions drawn from the Great Circle Arc Norm substitution into the Weiszfeld
Algorithm
6.3 Recommendations for future research
6.4 Final comments
Bibliography and Appendices
Appendix A: Weiszfeld's Algorithm, 2-D Euclidean Minisum SFLP Solver Code in FORTRAN95
Appendix B: Weiszfeld's Algorithm, 3-D Euclidean Minisum SFLP Solver Code in FORTRAN95
Appendix C: Spheresolver Algorithm - 3-D Euclidean Minisum SFLP Solver, R3 Surface Projection, & Sphere Covering Objective Function Solution Code in FORTRAN95
Appendix D: Greatcircle Algorithm - Spherical Surface Great Circle Arc Minisum SFLP Solver Code in FORTRAN 95
Appendix E: Example Data Sets
Vita
Download Word2000 Thesis document (356k)
Executables for Weiszfeld 2D Euclidean Solver, Weiszfeld 3D Euclidean Solver, spheresolver, and greatcircle (381k)
Zip for spheresolver data inputs files (text files) (7k)
Email me if you really, really want the .xls zip for the Excel2000 results of the spheresolver code (13.6Mb).
Now go climb something!!!
