An Electromagnetism-like Mechanism for Solving the Multiple Depot Vehicle Routing Problem

1. 1 Talk at Department of Industrial Engineering & Management,I-Shou University. July. 21, 2006 B.Y. Huang Committees: Dr. Chin-Shiuh Shieh & Dr. Nai-Chie Wei Research Advisers: Dr. Peitsang Wu & Dr. I-Ming Chao An Electromagnetism-like Mechanism for Solving the Multiple Depot Vehicle Routing Problem My background PhD UiO in reactive factory scheduling Stay at Robotics Institute CMU, Steve Smith, Mark Fox, Norman Sadeh Worked with contract research at SINTEF/SI for > 20 years My background PhD UiO in reactive factory scheduling Stay at Robotics Institute CMU, Steve Smith, Mark Fox, Norman Sadeh Worked with contract research at SINTEF/SI for > 20 years

2. 2 Outline Introduction Routing Problems Motivation Research Objectives Literature Review Solution Methods Methodologies The Mathematical Formulation of the MDVRP The Electromagnetism-like Mechanism Illustrated Examples & Analyses Conclusions & Future Research

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5. 5 Traveling Salesman Problem

6. 6 Vehicle Routing Problem

7. 7 Multiple Depot VRP

8. 8 Motivation Exciting Problem Practical Applications Industrial Relevance Importance to Society

9. 9 Research Objectives Objectives Solve the MDVRP Good performance & be investigated Tool The EM algorithm Execution C++ program language

10. 10 Research Scope and Restrictions Network non-directional and symmetrical network corresponding to Euclidian Space Depot limitless volume of stock needless to consider the vehicle loading time Customer demand quantity, place coordinate, and merchandise categories, etc., are all already known and fixed Vehicle needless to consider driving speed, drivers state limited carries capacity

11. 11 Thesis Architecture

12. 12 Literature Review The MDVRP is NP-hard (Lenstra et al, 1981) Current Methods in VRP Exact Methods Dynamic Programming Langrangean relaxation Branch & bound Approximate Algorithms and Heuristics Savings Algorithm (Clarke and Wright, 1964) Route first, cluster second ; Cluster first, route second Tabu search Genetic algorithm Simulated annealing Threshold accepting, etc.

13. 13 Solution Methods for MDVRP Exact Procedure Branch and bound Laporte et al. (1984) customers ? 50; depots ? 8 Laporte et al. (1988) customers ? 80; depots ? 3

14. 14 Solution Methods for MDVRP Heuristic Algorithms Savings Algorithm Tillman (1971) Two-Phase-Approaches Wren and Holliday (1972) applied �cluster first, route second� way for two depots and up to 176 cities Raft (1982) introduced 2-opt exchange procedure Chao et al. (1993) used the "record-to-record" Giosa et al. (1999) described the �Assignment Algorithms� Meta-Heuristic Algorithms Renaudl et al. (1994) introduced the tabu search heuristic

15. 15 The Mathematical Formulation of the MDVRP

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17. 17 Birbil and Fang (2003) constructed a mechanism that likes the attraction-repulsion mechanism of the electromagnetism theory. Chiang (2005) used the EM to solve the traveling salesman problem (TSP) and the results corresponded to his expected Yu (2005) in his thesis described the EM could suitable for the �Object Sequencing� and �Grouping Problems� Electromagnetism-like Mechanism

18. 18 Electromagnetism-like Mechanism General Scheme

19. 19 General Scheme Initialize

20. 20 General Scheme Local search

21. 21 General Scheme Total force calculation

22. 22 General Scheme Move along the total force

23. 23 The Activity-List (AL) The Random-Key (RK) The EM for MDVRP

24. 24 An AL form of the EM algorithm

25. 25 The three types of the EM algorithms The prototype EM Algorithm: the original type of the EM algorithm; The improved EM Algorithm: add a swap mechanism (The 2-Opt method) to the EM algorithm; The intensification EM Algorithm: construct initial solutions for the improved EM algorithm.

26. 26 Characteristics of test problems

27. 27 Parameters of the EM Algorithm

28. 28 The Prototype EM Algorithm

29. 29 Results in the Prototype EM algorithm

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31. 31 The Improved EM Algorithm

32. 32 Results in the Improved EM Algorithm

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34. 34 The Intensification EM Algorithm

35. 35 Results in the Intensification EM Algorithm

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37. 37 Summary of computational results

38. 38 Summary of computational results

39. 39 Summary of computational results

40. 40 Conclusions In our researches, The improved EM algorithm is better than the original (prototype) EM algorithm. When the improved EM algorithm accedes to the initial solutions construction method, we can improve the results. The EM algorithm is possible to solve the MDVRP because the transportation cost is close to the best known cost.

41. 41 Future Researches Combine other meta-heuristic algorithms with the EM algorithm, the performance of the new integration may be better. Apply other local search methods to improve the efficiency of the EM algorithm might produce better results and spend less time.

42. 42 Future Researches We can apply this method for other problems, e.g., the VRP, and VRPTW, have not be solved by this new meta-heuristic algorithm. Combine other meta-heuristic algorithms with the EM algorithm, the performance of the new integration may be better.

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