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Metaheuristic Algorithms for the Vehicle Routing Problem with Time Window and Skill Set Constraints

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Metaheuristic Algorithms for the Vehicle Routing Problem with Time Window and Skill Set Constraints METAHEURISTIC ALGORITHMS FOR THE VEHICLE ROUTING PROBLEM WITH TIME WINDOW AND SKILL SET CONSTRAINTS by Lu Han Submitted in partial fulfilment of the requirements for the degree of Master of Applied Science at Dalhousie University Halifax, Nova Scotia December 2016 © Copyright by Lu Han, 2016 Table of Contents List of Tables .............................................................................................................................. iv List of Figures .............................................................................................................................. v Abstract ....................................................................................................................................... vi List of Abbreviations Used ..................................................................................................... vii Acknowledgements ................................................................................................................. viii Chapter 1 Introduction .............................................................................................................. 1 Chapter 2 Literature Review ................................................................................................... 5 2.1 General VRP .................................................................................................................................... 5 2.1.1 Exact Algorithms .................................................................................................................................. 5 2.1.2 Heuristic and Metaheuristic Algorithms ........................................................................................ 7 2.2 Variants of Vehicle Routing Problem ..................................................................................... 12 2.2.1 The Travelling Salesman Problem (TSP) .................................................................................... 12 2.2.2 The Capacitated Vehicle Routing Problem (CVRP) ................................................................ 13 2.2.3 The Inventory Routing Problem (IRP) ......................................................................................... 14 2.2.4 The Period Vehicle Routing Problem (PVRP) .......................................................................... 15 2.2.5 The Split Delivery Vehicle Routing Problem (SDVRP) ........................................................ 16 2.2.6 Vehicle Routing Problem with Time Windows (VRPTW) ................................................... 16 2.2.7 Vehicle Routing Problem with Skill Sets (VRPSS) ................................................................. 19 2.2.8 Travelling Repairman Problem (TRP) ......................................................................................... 21 Chapter 3 Problem Context and Assumptions.................................................................. 23 3.1 Problem Definition ...................................................................................................................... 23 3.2 Problem Assumptions and Requirements ............................................................................. 24 Chapter 4 Methodology .......................................................................................................... 26 4.1 MILP Model ................................................................................................................................. 26 4.1.1 Sets and Parameters ............................................................................................................................ 26 4.1.2 Variables ................................................................................................................................................ 27 4.1.3 Objective Function.............................................................................................................................. 28 4.1.4 Constraints ............................................................................................................................................. 28 ii 4.1.5 Preprocessing Phase ........................................................................................................................... 31 4.2 Heuristic Algorithm .................................................................................................................... 31 4.2.1 Initialization .......................................................................................................................................... 32 4.2.2 Local Improvement ............................................................................................................................ 38 4.3 Metaheuristic Algorithms .......................................................................................................... 48 4.3.1 Tabu Search .......................................................................................................................................... 49 4.3.2 Simulated Annealing .......................................................................................................................... 51 Chapter 5 Results and Discussions ...................................................................................... 55 5.1 Data Simulation ........................................................................................................................... 55 5.1.1 Customer data ....................................................................................................................................... 55 5.1.2 Technician data .................................................................................................................................... 57 5.1.3 Travel time ............................................................................................................................................ 58 5.2 Selection of parameters for metaheuristic algorithms ....................................................... 60 5.2.1 Tabu Search parameters .................................................................................................................... 60 5.2.2 Simulated Annealing parameters ................................................................................................... 62 5.3 Comparison between two neighborhood heuristics ............................................................ 66 5.4 Comparison among different methods ................................................................................... 67 5.5 Tests on Large-Scale Examples ................................................................................................ 71 5.6 Conclusion and Future Research............................................................................................. 73 5.6.1 Future Research ............................................................................................................................... 74 Bibliography .............................................................................................................................. 75 Appendix A Solomon’s Insertion Heuristic ..................................................................... 84 Appendix B Average cost of running different numbers of replications in SA algorithm .......................................................................................................... 86 Appendix C Comparisons of different neighborhood structure by algorithms ...... 87 Appendix D Comparisons of applying different methods ............................................ 89 iii List of Tables Table 5.1 Comparison of Tabu Search parameter combinations………………………60 Table 5.2 Comparison of different Tabu Size………………………………………….62 Table 5.3 Comparison of Simulated Annealing parameter combinations...……….…...64 Table 5.4 Number of optimal solutions of four methods………………………………69 Table 5.5 Average computation time of four methods…………………………………69 Table 5.6 Results of tabu search with different tabu size in 100- and 150-customer examples……………………………………………………………………..72 Table 5.7 Comparison among heuristic and metaheuristic algorithms on large-scale examples………………………………………………………………….….72 iv List of Figures Figure 1.1 Overall process……………………………………………………………...1 Figure 2.1 Or-opt heuristic……………………………………………………………..10 Figure 2.2 Relocate (Transfer) heuristic………………………………………………..11 Figure 2.3 Exchange (Swap) heuristic………………………………………………….11 Figure 2.4 2-opt* heuristic……………………………………………………………...18 Figure 4.1 Process of checking the eligibility of a technician for a specific customer....33 Figure 4.2 Process of pre-allocation…………………………………………………….36 Figure 4.3 Process of selecting a technician and inserting customers…………………..38 Figure 4.4 Sub-tour reversal……….…….…….…….…….…….…...…….…….……...41 Figure 4.5 Waiting time improvement when feasible delay is less than waiting time......42 Figure 4.6 Waiting time improvement when feasible delay is greater than waiting time…….…….…….…….…….…...……….…….…….…….……..………42 Figure 4.7 The transfer of customer C………………………………………………..…45 Figure 4.8 The swap of customer C………………………………………………….….47 Figure 4.9 Searching for the best solution…………………………..………………..…48 Figure 4.10 Process of tabu search…………………………………..……………….…51 Figure 4.11 Process of simulated annealing…………………..…………..………….…54 Figure 5.1 Probability density function of Pareto distribution (Danvildanvil (2014))….56 Figure 5.2 One standard of the Mean for 1, 3, 5 replications…………………………...64 Figure 5.3 Mean, Std, and Optimality
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