1. 1 Applying Simulated Annealing Approach in Truck & Trailer Routing Problem and Location Routing Problem 報告人：長庚大學資訊管理系 林詩偉教授 TTRP: Co-authors with Prof. Vincent Yu, and Shuo-Yan Chou LRP: Co-authors with Prof. Vincent Yu, Wenyih Lee, and Ching-Jung Ting

2. 2 Two Major Topics Part 1: 卡車拖車途程問題 ( Truck and Trailer Routing Problem, TTRP ) Part 2: 區位途程問題 ( Location Routing Problem, LRP ) TTRP: Co-authors with Prof. Vincent Yu and Shuo-Yan Chou LRP: Co-authors with Prof. Vincent Yu, Wenyih Lee, and Ching-Jung Ting

3. 3 Outline (Part 1: TTRP) 1. Introduction 2.1 Description of the VRP 2.2 Truck and trailer routing problem (TTRP) 3. Solution method 4. Computational study 5. Conclusion and Future Research

4. 4 1. Introduction Truck and trailer routing problem (TTRP) is a variant of the vehicle routing problem (VRP). TTRP considers a commonly neglected feature in the VRP, i.e., the use of trailers. Taking into account the use of trailer makes the problem more difficult to solve than the VRP, which is NP-hard.

5. 5 1. Introduction TTRP is difficult to solve because There are two types of customers. Some customer can only be serviced by a single truck due to various reasons. There are three different types of routes, one of them contains a main tour and one or more sub- tours. Determining the location of the starting point of a subtour is not trivial. An node may be traveled more than twice, etc.

6. 6 1. Introduction (cond.) However, it is an important and practical routing problem that arises in logistics management. By using trailers, the capacity of each route may be doubled, and thus distribution costs may be reduced. Therefore, an efficient solution approach to tackle this problem is needed. Moreover, it is also a very interesting problem that attracts little attention from the academics.

7. 7 2.1 Problem Description - VRP Definition Given a fleet of identical vehicles with capacity Q, and an undirected network G = (N, E, c) where N = {0, 1, 2, …, n} = set of customers where 0 is the depot. E = {(i, j) : i, j N} = set of edges connecting depot and customers. c = {c ij : (i, j) E} = distance or cost associated with each edge in E Each customer i N \{0} has a positive demand q i. Each customer is serviced exactly once. Each route starts and ends at the depot.

8. 8 2.1 Problem Description - Example of VRP

9. 9 2.2 Problem Description - TTRP Definition

10. 10 2. 2 Problem Description - TTRP Definition Two types of customers: truck customer, TC vehicle customer, VC Three types of routes: pure truck route (PTR): traveled by a truck alone. pure vehicle route (PVR): traveled by a complete vehicle. (Trailer is never dropped.) complete vehicle route (CVR): contains a main tour traveled by a complete vehicle and one or more sub-tours traveled by a truck alone. Each sub-tour starts and ends at a customer site, where the trailer is temporarily parked.

11. 11 2. 2 Problem Description - Example of TTRP

12. 12 2. 2 Problem Description -Relationship between VRP and TTRP TTRP can be reduced to the VRP if there are no truck customers (Chao, 2002). Therefore, it is at least as difficult as the VRP, which is known to be NP-hard. It is unlikely to and an exact solution approach that is capable of solving large TTRP instances to optimality. We propose a simulated annealing (SA) heuristic for the TTRP that proves to be highly effective and efficient.

13. 13 3. Solution method -Background of Simulated Annealing Motivated by the physical annealing process. Material is heated and slowly cooled into a uniform structure. Simulated annealing (SA) mimics this process. Compared to hill climbing the main difference is that SA allows downwards steps. Simulated annealing also differs from hill climbing in that a move is selected at random and then decides whether to accept it. In SA better moves are always accepted. Worse moves are not. It has probability to accept worse moves.

14. 14 3. Solution method -Background of Simulated Annealing A local search algorithm capable of escaping from local optima. Popular due to its ease of implementation convergence properties use of hill-climbing moves to escape local optima Typically used to solve discrete optimization problems. Few applications on continuous optimization problems.

15. 15 3. Solution method -Solution Representation In our algorithm, each solution is represented as a string of the n customers and N dummy 0s, followed by a 0-1 string whose length equals the number of VCs. The j th nonzero entry in the first n + N dummy positions indicates that the j th customer being visited. An 1 in position i of the 0-1 string indicates that the i th VC is serviced by a truck alone, while a 0 indicates that the VC is serviced by a complete vehicle.

16. 16 3. Solution method -Example of Solution Representation

17. 17 3. Solution method -Neighborhood Swap Insert Change service type

18. 18 3. Solution method -Pseudo-code of the proposed SA

19. 19 3. Solution method -Pseudo-code of the proposed SA ≦

20. 20 3. Solution method -Pseudo-code of the proposed SA

21. 21 4. Computational Study The SA heuristic was coded in C++ and compiled using Microsoft Visual C++ 6.0. It was then applied to the 21 TTRP benchmark instances created by Chao (2002) on a Pentium IV 1.5 GHz PC with 1 GB RAM under Microsoft Windows XP operating system In the initial experiments, the following combinations of parameters were tested. α = 0.965, 0.975; P = 25, 50, 75, 100, 125; I iter = 3000, 5000, 70000, 90000, 120000, 150000, 200000; K = 1/1, 1/2, …,1/9. T 0 =100; T f =1;

22. 22 4. Computational Study Setting T 0 =100, T f =1, α= 0.965, I iter =150000, P = 50, and K = 1/3 seemed to give best results. All the experiments were terminated after 130 reductions (temperature reductions) or when X best is not improved in 30 successive reductions in temperature.

23. 23 4. Computational Study

24. 24 4. Computational Study The proposed SA heuristic obtained best solutions to 17 out of the 21 TTRP benchmark problems, 11 of them are new best solutions, while Scheuerer (2006) remained the best known for 10 of the 21 problems (tied on 6 problems).

25. 25

26. 26 5. Conclusion and Future Research The proposed SA heuristic found 17 best solutions to 21 TTRP benchmark problems, including 11 new best solutions 6 previously reported best solutions The main characteristics of the SA are The combination of a two-level solution representation and the use of dummy depots/roots Random neighborhood structure which utilizes four different types of moves.

27. 27 5. Conclusion and Future Research The computational study shows that our algorithm is competitive with other known solution approaches for the TTRP. Moreover, the algorithm is very efficient as it takes less time to obtain the best or near-best solutions.

28. 28 5. Conclusion and Future Research There are several potential topics for consideration in continued research. Application of the proposed SA to TTRP with time window constraints, TTRP with split deliveries, and other variants of the TTRP. Application of the proposed SA to other combinatorial problems. Experiment with other meta-heuristics for solving the TTRP.

29. 29 Outline (Part 2: LRP) 1. Introduction 2. Problem Definition 3. The Proposed Approach 4. Experimental Result 5. Conclusion and Future Research

30. 30 1. Introduction The location routing problem (LRP) is a relatively new field which takes into account two key components of a logistics system, namely the facility location and vehicle routing. In various settings, these components are interdependent; therefore it is beneficial to consider the two components simultaneously.

31. 31 1. Introduction LRP is applicable to a wide variety of fields such as food and drink distribution blood bank location newspapers delivery waste collection bill delivery military application parcel delivery various consumer goods distribution

32. 32 1. Introduction The LRP belongs to the class of NP-hard problems since it combines two difficult sub- problems: the facility location problem (FLP) and the vehicle routing problem (VRP), both of them are shown to be NP-hard As the problem size grows larger, heuristic approaches become the only viable alternative.

33. 33 2. Problem Definition

34. 34 2. Problem Definition Each route must start and terminate at the same depot, and its total load must not exceed vehicle capacity. The total load of the routes assigned to a depot must fit the capacity of the depot. The objective is to determine which depots should be opened and which routes should be constructed to minimize the total cost.

35. 35 2. Problem Definition Blue circle: depot Red circle: customer Open Cost for depot Vehicle Cost for each route Traveling cost between customers Depot capacity Vehicle capacity

36. 36 3. The Proposed Approach -Solution Representation A solution is represented by a string of numbers consisting of a permutation of n customers denoted by the set, m potential depots denoted by the set {n+1, n+2, …, n+m}, and N dummy zeros. The i th number in denotes the i th customer to be serviced. The first number in a solution is always in {n+1, n+2, …, n+m} indicating the first depot under consideration.

37. 2016/7/837 3. Solution method -Example of Solution Representation

38. 38 3. Solution method -Example of Solution Representation

39. 39 3. Solution method -Initial Solution Step 1: Choose the unused depot with the most unassigned customers closest to it. Step 2: For all unassigned customers, assigned them to the chosen depot one by one in the increasing order of the distance between the customer and the chosen depot. Stop when the capacity of the depot is violated. Step 3: Construct a TSP route which starts from and ends at the depot using the Lin and Kernighan’s heuristic (1973). Step 4: Split the TSP route constructed by the Lin and Kernighan’s heuristic into several routes so that the route capacity constraint mentioned is not violated. Step 5: If there are still unassigned customers, go to Step 1; otherwise, terminate the procedure.

40. 40 3. Solution method -Neighborhood Swap Insert Inversion

41. 41 3. Solution method -Pseudo-code of the proposed SA

42. 42 4. Experimental Result Implemented in C language and run on a PC with an Intel Core 2 Quad CPU (2.6 GHz) CPU and 2GB memory. Two well-known LRP problem sets are selected as test problems. In the initial experiments, the following combinations of parameters were tested. α = 0.96, 0.97, 0.98, 0.99; P = 100, 200, …, 2000; I iter = 1000L, 2000L, 3000L, 4000L, 5000L, 6000L, where L denotes the length of solution representation; K = 1/1, 1/2, …, 1/15. T 0 =30; T f =0.1;

43. 43 4. Experimental Result Two benchmark datasets are. (1) Barreto’s dataset (19 problems) (2) Prins et al.’s dataset (30 problems) T 0 =100, T f =1, α=0.98, I iter =5000L, P=400, and K=1/9 were used for computational study. For each instance, only one run of the proposed approach is executed in order to have a fair comparison with other approaches.

44. 44 4. Experimental Result

45. 45 4. Experimental Result

46. 46 4. Experimental Result

47. 47 4. Experimental Result

48. 48 4. Experimental Result For problem set 1 (19 problems). Using the proposed parameter 9 new best solution and 9 the same solution (BKS). In the parameter analysis phase 10 new best solution and 9 the same solution (BKS). For problem set 2 (30 problems). Using the proposed parameter 7 new best solution and 9 the same solution (BKS). In the parameter analysis phase 20 new best solution and 10 the same solution (BKS).

49. 49 5. Conclusion and Future Research The proposed SALRP algorithm was tested on three well-known benchmark problem sets that contain a wide variety of LRP instances. Computational results and comparisons of the SALRP algorithm with various promising LRP heuristics are presented. The results of the comparative study are very encouraging: the proposed SALRP algorithm not only performs better than the other heuristics on many instances, but its computational time requirement is also quite reasonable for realistic size problems.

50. 50 5. Conclusion and Future Research The encouraging results suggest that the proposed SALRP algorithm may be applied to other combinatorial problems that contain multiple levels of decision making. In this application (LRP), there are two decision components (facility location and vehicle routing) where the decisions made for one component affect the other. Thus, an integrated approach similar to the proposed SALRP may be used for other combinatorial problem with more than one component of interdependent decisions, such as multi-level location problems, hub- and-spoke network design problems, and multi-modal transportation problems.