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April  2012, 8(2): 469-484. doi: 10.3934/jimo.2012.8.469

A metaheuristic method for vehicle routing problem based on improved ant colony optimization and Tabu search

Mingyong Lai 1, and  Xiaojiao Tong 2,

1. 

Key Laboratory of Logistics Information and Simulation Technology, Hunan University, Changsha 410082, China
2. 

Department of Mathematics and Computing Science, Hengyang Normal University, Hengyang 421002, China

Received  October 2011 Revised  January 2012 Published  April 2012

A mixed integer programming mathematical formulation of vehicle routing problem with simultaneous pickups and deliveries, and time window constraints (VRP-SPDTW) is presented in this paper. The proposed model aims at minimizing the vehicle number and the overall travel cost. A novel two-stage hybrid metaheuristic method for VRP-SDPTW is also proposed. The first stage adopts improved ant colony optimization (IACO) to determine the minimum number of used vehicles. The second stage employs improved Tabu search to optimize the total travel cost, in which the initial solutions are obtained by IACO in the first stage. Experimental results demonstrate the effectiveness of the proposed metaheuristic method.
Keywords: improved Tabu search, time window constraints., Improved ant colony optimization, vehicle routing problem, simultaneous pickups and deliveries.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Mingyong Lai, Xiaojiao Tong. A metaheuristic method for vehicle routing problem based on improved ant colony optimization and Tabu search. Journal of Industrial & Management Optimization, 2012, 8 (2) : 469-484. doi: 10.3934/jimo.2012.8.469
References:
[1]

A. Alshamrani, K. Mathur and R. H. Ballou, Reverse logistics: Simultaneous design of delivery routes and returns strategies, Computers & Operations Research, 34 (2007), 595-619. doi: 10.1016/j.cor.2005.03.015.  Google Scholar

[2]

E. Angelelli and R. Mansini, The vehicle routing problem with time windows and simultaneous pick-up and delivery, in "Quantitative Approaches to Distribution Logistics and Supply Chain Management" (eds. M. G. Speranza, A. Klose and L. N. Van Wassenhove), Springer, Berlin, (2002), 249-267. doi: 10.1007/978-3-642-56183-2_15.  Google Scholar

[3]

R. Battiti, Reactive search: Toward self-tuning heuristics, Keynote talk at Applied Decision Technologies, Brunel, UK, (1995), 3-4. Google Scholar

[4]

R. Bent and P. Van Hentenryck, A two-stage hybrid local search for the vehicle routing problem with time windows, Transportation Science, 38 (2004), 515-530. doi: 10.1287/trsc.1030.0049.  Google Scholar

[5]

R. Bent and P. Van Hentenryck, A two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows, Computers & Operations Research, 33 (2006), 875-893. doi: 10.1016/j.cor.2004.08.001.  Google Scholar

[6]

G. Berbeglia, J.-F. Cordeau, I. Gribkovskaia and G. Laporte, Static pickup and delivery problems: A classification scheme and survey, TOP, 15 (2007), 1-31. doi: 10.1007/s11750-007-0009-0.  Google Scholar

[7]

P. Bieganski, J. Riedl, J. Carlis and E. F. Retzel, Generalized suffix trees for biological sequence data: Applications and implementation, in "The Twenty-Seventh Hawaii International Conference on System Sciences," (1994), 35-44. Google Scholar

[8]

A. Colorni, M. Dorigo and V. Maniezzo, Distributed optimization by ant colonies, in "European Conference of Artificial Life," (1991), 134-142. Google Scholar

[9]

G. Dan, "Algorithms on Strings, Trees, and Sequences," Computer Science and Computational Biology, Cambridge University Press, Cambridge, 1997.  Google Scholar

[10]

M. Dell'Amico, G. Righini and M. Salani, A branch-and-price approach to the vehicle routing problem with simultaneous distribution and collection, Transportation Science, 40 (2006), 235-247. doi: 10.1287/trsc.1050.0118.  Google Scholar

[11]

J. Dethloff, Vehicle routing and reverse logistics: The vehicle routing problem with simultaneous delivery and pick-up. Operations research in environmental management, OR Spektrum, 23 (2001), 79-96. doi: 10.1007/PL00013346.  Google Scholar

[12]

J. Homberger and H. Gehring, Two evolutionary metaheuristics for the vehicle routing problem with time windows, INFOR, 37 (1999), 297-318. Google Scholar

[13]

M. Lai and E. Cao, An improved differential evolution algorithm for vehicle routing problem with simultaneous picks and deliveries and time windows, Engineering Applications of Artificial Intelligence, 23 (2010), 188-195. Google Scholar

[14]

M. Lai, C. Liu and X. Tong, A two-stage hybrid meta-heuristic for pickup and delivery vehicle routing problem with time windows, Journal of Industrial and Management Optimization, 6 (2010), 435-451. doi: 10.3934/jimo.2010.6.435.  Google Scholar

[15]

H. C. Lau and Z. Liang, Pickup and delivery with time windows: Algorithms and test case generation, International Journal on Artificial Intelligence Tools (Architectures, Languages, Algorithms), 11 (2002), 455-472. Google Scholar

[16]

H. Min, The multiple vehicle routing problem with simultaneous delivery and pickup points, Transportation Research A, 23 (1989), 377-386. doi: 10.1016/0191-2607(89)90085-X.  Google Scholar

[17]

F. Alfredo Tang Montané and R. D. Galvão, A tabu search algorithm for the vehicle routing problems with simultaneous pick-up and delivery service, Computer & Operation Research, 33 (2006), 595-619. doi: 10.1016/j.cor.2004.07.009.  Google Scholar

[18]

W. P. Nanry and W. J. Barnes, Solving the pickup and delivery problem with time windows using reactive tabu search, Transportation Research Part B, 34 (2000), 107-121. doi: 10.1016/S0191-2615(99)00016-8.  Google Scholar

[19]

B. Nicola and R. Giovanni, Heuristic algorithms for the vehicle routing problem with simultaneous pick-up and delivery, Computers & Operations Research, 34 (2007), 578-594. doi: 10.1016/j.cor.2005.03.014.  Google Scholar

[20]

H. N. Psarafis, A dynamic programming solution to the single vehicle many-to-many immediate request dial-a-ride problem, Transportation Science, 14 (1980), 130-154. doi: 10.1287/trsc.14.2.130.  Google Scholar

[21]

S. Ropke, J.-F. Cordeau and G. Laporte, Models and a branch-and-cut algorithm for pickup and delivery problems with time windows, Networks, 49 (2007), 258-272. doi: 10.1002/net.20177.  Google Scholar

[22]

S. Ropke and D. Pisinger, An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows, Transportation Science, 40 (2006), 455-472. doi: 10.1287/trsc.1050.0135.  Google Scholar

show all references

References:
[1]

A. Alshamrani, K. Mathur and R. H. Ballou, Reverse logistics: Simultaneous design of delivery routes and returns strategies, Computers & Operations Research, 34 (2007), 595-619. doi: 10.1016/j.cor.2005.03.015.  Google Scholar

[2]

E. Angelelli and R. Mansini, The vehicle routing problem with time windows and simultaneous pick-up and delivery, in "Quantitative Approaches to Distribution Logistics and Supply Chain Management" (eds. M. G. Speranza, A. Klose and L. N. Van Wassenhove), Springer, Berlin, (2002), 249-267. doi: 10.1007/978-3-642-56183-2_15.  Google Scholar

[3]

R. Battiti, Reactive search: Toward self-tuning heuristics, Keynote talk at Applied Decision Technologies, Brunel, UK, (1995), 3-4. Google Scholar

[4]

R. Bent and P. Van Hentenryck, A two-stage hybrid local search for the vehicle routing problem with time windows, Transportation Science, 38 (2004), 515-530. doi: 10.1287/trsc.1030.0049.  Google Scholar

[5]

R. Bent and P. Van Hentenryck, A two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows, Computers & Operations Research, 33 (2006), 875-893. doi: 10.1016/j.cor.2004.08.001.  Google Scholar

[6]

G. Berbeglia, J.-F. Cordeau, I. Gribkovskaia and G. Laporte, Static pickup and delivery problems: A classification scheme and survey, TOP, 15 (2007), 1-31. doi: 10.1007/s11750-007-0009-0.  Google Scholar

[7]

P. Bieganski, J. Riedl, J. Carlis and E. F. Retzel, Generalized suffix trees for biological sequence data: Applications and implementation, in "The Twenty-Seventh Hawaii International Conference on System Sciences," (1994), 35-44. Google Scholar

[8]

A. Colorni, M. Dorigo and V. Maniezzo, Distributed optimization by ant colonies, in "European Conference of Artificial Life," (1991), 134-142. Google Scholar

[9]

G. Dan, "Algorithms on Strings, Trees, and Sequences," Computer Science and Computational Biology, Cambridge University Press, Cambridge, 1997.  Google Scholar

[10]

M. Dell'Amico, G. Righini and M. Salani, A branch-and-price approach to the vehicle routing problem with simultaneous distribution and collection, Transportation Science, 40 (2006), 235-247. doi: 10.1287/trsc.1050.0118.  Google Scholar

[11]

J. Dethloff, Vehicle routing and reverse logistics: The vehicle routing problem with simultaneous delivery and pick-up. Operations research in environmental management, OR Spektrum, 23 (2001), 79-96. doi: 10.1007/PL00013346.  Google Scholar

[12]

J. Homberger and H. Gehring, Two evolutionary metaheuristics for the vehicle routing problem with time windows, INFOR, 37 (1999), 297-318. Google Scholar

[13]

M. Lai and E. Cao, An improved differential evolution algorithm for vehicle routing problem with simultaneous picks and deliveries and time windows, Engineering Applications of Artificial Intelligence, 23 (2010), 188-195. Google Scholar

[14]

M. Lai, C. Liu and X. Tong, A two-stage hybrid meta-heuristic for pickup and delivery vehicle routing problem with time windows, Journal of Industrial and Management Optimization, 6 (2010), 435-451. doi: 10.3934/jimo.2010.6.435.  Google Scholar

[15]

H. C. Lau and Z. Liang, Pickup and delivery with time windows: Algorithms and test case generation, International Journal on Artificial Intelligence Tools (Architectures, Languages, Algorithms), 11 (2002), 455-472. Google Scholar

[16]

H. Min, The multiple vehicle routing problem with simultaneous delivery and pickup points, Transportation Research A, 23 (1989), 377-386. doi: 10.1016/0191-2607(89)90085-X.  Google Scholar

[17]

F. Alfredo Tang Montané and R. D. Galvão, A tabu search algorithm for the vehicle routing problems with simultaneous pick-up and delivery service, Computer & Operation Research, 33 (2006), 595-619. doi: 10.1016/j.cor.2004.07.009.  Google Scholar

[18]

W. P. Nanry and W. J. Barnes, Solving the pickup and delivery problem with time windows using reactive tabu search, Transportation Research Part B, 34 (2000), 107-121. doi: 10.1016/S0191-2615(99)00016-8.  Google Scholar

[19]

B. Nicola and R. Giovanni, Heuristic algorithms for the vehicle routing problem with simultaneous pick-up and delivery, Computers & Operations Research, 34 (2007), 578-594. doi: 10.1016/j.cor.2005.03.014.  Google Scholar

[20]

H. N. Psarafis, A dynamic programming solution to the single vehicle many-to-many immediate request dial-a-ride problem, Transportation Science, 14 (1980), 130-154. doi: 10.1287/trsc.14.2.130.  Google Scholar

[21]

S. Ropke, J.-F. Cordeau and G. Laporte, Models and a branch-and-cut algorithm for pickup and delivery problems with time windows, Networks, 49 (2007), 258-272. doi: 10.1002/net.20177.  Google Scholar

[22]

S. Ropke and D. Pisinger, An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows, Transportation Science, 40 (2006), 455-472. doi: 10.1287/trsc.1050.0135.  Google Scholar

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