DECISION GUIDANCE QUERY LANGUAGE (DGQL), ALGORITHMS AND SYSTEM by Nathan E. Egge A Dissertation Submitted to the Graduate Faculty of George Mason University in Partial Fulfillment of The Requirements for the Degree of Doctor of Philosophy Computer Science Committee: Dr. Alexander Brodsky, Dissertation Director Dr. Amihai Motro, Committee Member Dr. Larry Kerschberg, Committee Member Dr. Igor Griva, Committee Member Dr. Sanjeev Setia, Department Chair Dr. Kenneth S. Ball, Dean, Volgenau School of Engineering Date: Summer Semester 2014 George Mason University Fairfax, VA Decision Guidance Query Language (DGQL), Algorithms and System A Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at George Mason University by Nathan E. Egge Master of Science Virginia Tech, 2001 Bachelor of Science Virginia Tech, 1999 Director: Alexander Brodsky, Associate Professor Department of Computer Science Summer Semester 2014 George Mason University Fairfax, VA Copyright © 2014 by Nathan E. Egge All Rights Reserved ii ACKNOWLEDGEMENTS I would like to thank my advisor Dr. Alexander Brodsky for his ongoing support throughout this process, my PhD committee, Dr. Amihai Motro, Dr. Larry Kerschberg and Dr. Igor Griva for pushing me to extend my research in new directions, and finally Dr. X. Sean Wang and Mr. Hadon Nash for inspiration on early DGQL prototypes. I would also like to recognize the many people who have been instrumental in my academic career over the past 35 years. The teachers, parents, friends, coworkers, colleagues and mentors who have encouraged and nurtured my curiosity. I am standing in the shade today because long ago someone planted a tree. iii TABLE OF CONTENTS Page List of Tables ..................................................................................................................... vi List of Figures ................................................................................................................... vii List of Mathematical Programming Problems ................................................................. viii List of Algorithms .............................................................................................................. ix List of Abbreviations .......................................................................................................... x Abstract .............................................................................................................................. xi 1. Introduction ................................................................................................................. 1 1.1 Motivation and Background ................................................................................. 1 1.2 Research Gap........................................................................................................ 3 1.3 Thesis and Summary of Contributions ................................................................. 7 1.4 Thesis Structure .................................................................................................. 11 2. Related Work ............................................................................................................. 12 3. DGQL Syntax and Semantics .................................................................................... 17 3.1 A Running Example ........................................................................................... 17 3.2 DGQL by Example............................................................................................. 19 3.3 Formal Syntax and Semantics ............................................................................ 23 4. Algorithms for DGQL Reduction to MP and CP ...................................................... 29 4.1 MP and its Computational Complexity .............................................................. 29 4.2 Reduction Procedure .......................................................................................... 31 4.3 Detailed Reduction Example .............................................................................. 37 4.4 Formal Reduction ............................................................................................... 43 4.5 Proof of Correctness ........................................................................................... 46 4.6 Experimental Evaluation for Reduction Overhead ............................................ 52 5. Online Optimization Based on Offline Preprocessing .............................................. 58 5.1 A Motivating Example ....................................................................................... 58 5.2 Distributed Manufacturing Network as DGQL Query ....................................... 61 iv 5.3 Problem Formulation and Complexity ............................................................... 65 5.4 Principles of Preprocessing and Decomposition ................................................ 70 5.5 Online-Decomposition Algorithm...................................................................... 73 5.6 Experimental Evaluation for Online Speed-Up ................................................. 77 6. Adaptive Pre-processing Algorithm .......................................................................... 85 6.1 Efficient Offline Pre-processing Algorithm ....................................................... 85 6.2 Experimental Evaluation for Adaptive Speed-Up .............................................. 89 7. Proof of Concept Prototype. ...................................................................................... 94 8. Conclusions and Future Research .............................................................................. 99 Appendix: Resulting Publications................................................................................... 102 Publications Directly Related to Dissertation ............................................................. 102 Other Publications ....................................................................................................... 103 References ....................................................................................................................... 105 v LIST OF TABLES Table Page Table 1: High-level comparison between the OR approach and the DB approach ............ 6 Table 2: List of implemented DGQL commands in research prototype ........................... 96 vi LIST OF FIGURES Figure Page Figure 1: Multi-stage Production Network ......................................................................... 2 Figure 2: Scatter plot of solution time (DGQL v. AMPL) ............................................... 55 Figure 3: Scatter plot of total number of variables (DGQL v. AMPL) ............................ 56 Figure 4: Distributed Manufacturing Network ................................................................. 59 Figure 5: Cost functions of different size machines in one assembly............................... 79 Figure 6: Preprocessed cost function with linear approximation...................................... 80 Figure 7: Comparison of solution convergence of B&B and ODA with 120 variables ... 82 Figure 8: Comparison of solution convergence of B&B and ODA with 180 variables ... 83 Figure 9: Comparison cost functions using different preprocessing budget allocations .. 91 Figure 10: Comparison cost functions using different tradeoff weights T ....................... 93 Figure 11: High-level diagram describing client interaction with DGQL backend .......... 95 vii LIST OF MATHEMATICAL PROGRAMMING PROBLEMS Problem Page Problem 1: AMPL implementation of Procurement Example .......................................... 53 Problem 2: Distributed Manufacturing Network implemented in AMPL ........................ 66 Problem 3: Equivalent objective implementation in AMPL............................................. 67 Problem 4: Reformulation of Distributed Manufacturing Network ................................. 69 Problem 5: AMPL implementation of assembly subproblem ........................................... 74 viii LIST OF ALGORITHMS Algorithm Page Algorithm 1: Constraint Reduction ................................................................................... 34 Algorithm 2: DGQL Computation .................................................................................... 36 Algorithm 3: Subproblem Preprocessing .......................................................................... 74 Algorithm 4: Heuristic Search .......................................................................................... 76 Algorithm 5: Online-Decomposition Algorithm .............................................................. 77 Algorithm 6: Subdivision Heuristic .................................................................................. 87 Algorithm 7: Adaptive Pre-processing Algorithm ............................................................ 88 ix LIST OF ABBREVIATIONS A Mathematical Programming Language .................................................................. AMPL Adaptive Pre-processing Algorithm ..............................................................................APA Branch & Bound ........................................................................................................... B&B Constraint Programming ................................................................................................... CP Constraint Satisfaction Problem ...................................................................................