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研究生: 宋仁鈞
Jen-Chun Song
論文名稱: 改良式帝國主義競爭演算法於物流管理之動態車輛運途問題研究
An Improved Imperialist Competitive Algorithm to Solve the Dynamic Vehicle Routing Problem in Logistics Management
指導教授: 羅士哲
Shih-Che Lo
口試委員: 蔡鴻旭
Hung-Hsu Tsai
郭伯勳
Po-Hsun Kuo
羅士哲
Shih-Che Lo
學位類別: 碩士
Master
系所名稱: 管理學院 - 工業管理系
Department of Industrial Management
論文出版年: 2018
畢業學年度: 106
語文別: 英文
論文頁數: 83
中文關鍵詞: 智慧物流管理帝國主義競爭演算法動態車輛運途問題掃描法
外文關鍵詞: Intelligent logistics management, Imperialist Competition Algorithm, Dynamic vehicle routing problem, Sweep method
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任何企業在現今激烈的競爭環境下不外乎都是將增加其獲利視為主要的目的,除了降低生產成本及提高銷售量之外,最重要的不外乎就是提升物流的效率。在工業4.0的架構之下,智慧物流系統的建構與整合將更為的重要。因此,企業必須使用有效率的物流運籌網路來因應快速的顧客回應需求,而導入智慧物流的概念是為了有效的派遣車輛進而降低公司的固定與變動成本的新思維。
本研究提出以帝國主義競爭演算法(Imperialist Competitive Algorithm)結合掃描法(Sweep Method)的啟發式演算法,稱為sICA 演算法,對在不同時間片段下的動態車輛運途問題(Dynamic Vehicle Routing Problem, DVRP)快速提出一個近似最佳解,主要目標在於滿足所有限制條件下,達到總成本(運輸及營運)的最小化。為了驗證所提出的sICA 演算法之效能,本研究與基因演算法(Genetic Algorithm, GA)做比較,以60組動態車輛運途問題(DVRP)進行運輸成本最佳化分析。實驗結果顯示,相較於處理離散型問題的基因演算法而言,sICA 演算法在組合型最佳化問題上有著不錯的效能。


In today's fierce competitive environment, any enterprise considers increasing its profitability as main purpose. Apart from reducing production costs and increasing sales, the most important thing is to increase the efficiency of logistics. After the fourth industrial revolution, the construction and integration of the intelligent logistics system will be even more important. Therefore, companies must use efficient logistics networks to rapid respond customer’s requests. The concept of intelligent logistics is a new way of thinking to effectively dispatch vehicles to reduce the company's fixed and various costs.
This thesis proposed a method based on the Imperialist Competition Algorithm combined with the sweep method, called the sICA, to generate a near optimal solution quickly to the dynamic vehicle routing problem (DVRP) at different time segments. The main goal is to satisfy all constraints while minimizing the total cost (transportation and operation). In order to verify the effectiveness of the proposed sICA algorithm, we compared the sICA to the genetic algorithm (GA). Experimental results from 60 DVRP problems show that the sICA algorithm has better performance compared with GA in combinatory optimization problems.

摘要 i ABSTRACT ii ACKNOWLEDGEMENTS iii CONTENTS iv FIGURES vi TABLES viii CHAPTER 1 INTRODUCTION 1 1.1 Research Motivation 1 1.2 Research Objectives 2 1.3 Research Structure 2 CHAPTER 2 LITERATURE REVIEW 4 2.1 Logistics Management 4 2.2 Vehicle Routing Problem 7 2.3 Dynamic Vehicle Routing Problem 9 2.4 VRP Solving Algorithm 10 2.5 Genetic Algorithm 12 2.6 Imperialist Competitive Algorithm 14 CHAPTER 3 PROBLEM FORMULATION AND IMPERIALIST COMPETITIVE ALGORITHM 16 3.1 Problem Proposition 16 3.1.1 The Capacitated Vehicle Routing Problem (CVRP) 16 3.1.2 The Dynamic Vehicle Routing Problem (DVRP) 18 3.2 The Sweep Method 20 3.3 The General Imperialist Competitive Algorithm Procedure 23 3.3.1 Solution Representation 23 3.3.2 Evaluate Power 25 3.3.3 Generating Initial Empire 25 3.3.4 Moving the Colonies to its Relevant Imperialist 26 3.3.5 Exchange Position of the Imperialist and Colony 27 3.3.6 Calculate Entire Power of an Empire 28 3.3.7 Eliminating the Powerless Empire 29 3.3.8 Convergence 29 3.4 The Proposed sICA for the CVRP 31 3.4.1 Solution Representations 32 3.4.2 Assimilation 33 CHAPTER 4 COMPUTATIONAL EXPERIMENTS 35 4.1 Preliminary Test 35 4.2 Computational Results 38 4.2.1 Efficiency of the Two Methods in the Small Scale DVRP 38 4.2.2 sICA Perform in the Large Scale DVRP 42 CHAPTER 5 COCLUSIONS AND FUTURE RESEARCH 49 5.1 Conclusion 49 5.2 Future Research 49 REFERENCES 51 Appendix A. The Solution of the sICA for DVRP Instance 50D1 64 Appendix B. The Solution of the sICA for DVRP Instance 50D7 67 Appendix C. The Solution of the sICA for DVRP Instance 50D13 70

AbdAllah, A. M. F. M., Essam, D. L., and Sarker, R. A. (2017). On solving periodic re-optimization dynamic vehicle routing problems. Applied Soft Computing, 55, 1-12.
Abdechiri, M., Faez, K., and Bahrami, H. (2010). Adaptive imperialist competitive algorithm (AICA). Paper presented at the 2010 9th IEEE International Conference on Cognitive Informatics (ICCI).
Abdollahi, M., Isazadeh, A., and Abdollahi, D. (2013). Imperialist competitive algorithm for solving systems of nonlinear equations. Computers & Mathematics with Applications, 65(12), 1894-1908.
Akpinar, S. (2016). Hybrid large neighbourhood search algorithm for capacitated vehicle routing problem. Expert Systems with Applications, 61, 28-38.
Albareda-Sambola, M., Fernández, E., and Laporte, G. (2014). The dynamic multiperiod vehicle routing problem with probabilistic information. Computers & Operations Research, 48, 31-39.
Alvarado-Iniesta, A., Garcia-Alcaraz, J. L., Rodriguez-Borbon, M. I., and Maldonado, A. (2013). Optimization of the material flow in a manufacturing plant by use of artificial bee colony algorithm. Expert Systems with Applications, 40(12), 4785-4790.
Amous, M., Toumi, S., Jarboui, B., and Eddaly, M. (2017). A variable neighborhood search algorithm for the capacitated vehicle routing problem. Electronic Notes in Discrete Mathematics, 58, 231-238.
Arakaki, R. K., and Usberti, F. L. (2018). Hybrid genetic algorithm for the open capacitated arc routing problem. Computers & Operations Research, 90, 221-231.
Ardalan, Z., Karimi, S., Poursabzi, O., and Naderi, B. (2015). A novel imperialist competitive algorithm for generalized traveling salesman problems. Applied Soft Computing, 26, 546-555.
Atashpaz-Gargari, E., and Lucas, C. (2007). Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. Paper presented at the 2007 IEEE Congress on Evolutionary Computation.
Bădică, A., Bădică, C., Leon, F., and Luncean, L. (2017). Declarative representation and solution of vehicle routing with pickup and delivery problem. Procedia Computer Science, 108, 958-967.
Belenguer, J.-M., Benavent, E., Prins, C., Prodhon, C., and Wolfler Calvo, R. (2011). A branch-and-cut method for the capacitated location-routing problem. Computers & Operations Research, 38(6), 931-941.
Berbeglia, G., Cordeau, J.-F., and Laporte, G. (2010). Dynamic pickup and delivery problems. European Journal of Operational Research, 202(1), 8-15.
Beuchat, P. N., and Lygeros, J. (2017). Approximate dynamic programming via penalty functions. IFAC-PapersOnLine, 50(1), 11814-11821.
Biesinger, B., Hu, B., and Raidl, G. (2016). An integer l-shaped method for the generalized vehicle routing problem with stochastic demands. Electronic Notes in Discrete Mathematics, 52, 245-252.
Çatay, B. (2010). A new saving-based ant algorithm for the vehicle routing problem with simultaneous pickup and delivery. Expert Systems with Applications, 37(10), 6809-6817.
Chen, P. K., Li, L., and Ye, Y. (2017). Development of a supply chain integration process in China. Paper presented at the 2017 International Conference on Applied System Innovation (ICASI).
Christopher, M. (1985). Logistics and Supply Chain Management: Strategies for Reducing Cost and Improving Customer Service, Pitman Publishing, Singapore.
Çimen, M., and Soysal, M. (2017). Time-dependent green vehicle routing problem with stochastic vehicle speeds: an approximate dynamic programming algorithm. Transportation Research Part D: Transport and Environment, 54, 82-98.
Cordasco, G., Malewicz, G., and Rosenberg, A. L. (2010). Extending IC-scheduling via the sweep algorithm. Journal of Parallel and Distributed Computing, 70(3), 201-211.
de Oliveira da Costa, P. R., Mauceri, S., Carroll, P., and Pallonetto, F. (2018). A genetic algorithm for a green vehicle routing problem. Electronic Notes in Discrete Mathematics, 64, 65-74.
Dimitrakos, T. D., and Kyriakidis, E. G. (2015). A single vehicle routing problem with pickups and deliveries, continuous random demands and predefined customer order. European Journal of Operational Research, 244(3), 990-993.
Du, T. C., Li, E. Y., and Chou, D. (2005). Dynamic vehicle routing for online B2C delivery. Omega, 33(1), 33-45.
Ekström, M., Esseen, P. A., Westerlund, B., Grafström, A., Jonsson, B. G., and Ståhl, G. (2018). Logistic regression for clustered data from environmental monitoring programs. Ecological Informatics, 43, 165-173.
Euchi, J., Yassine, A., and Chabchoub, H. (2015). The dynamic vehicle routing problem: solution with hybrid metaheuristic approach. Swarm and Evolutionary Computation, 21, 41-53.
Fanti, M., Iacobellis, G., and Ukovich, W. (2015). A decision support system for multimodal logistic management. Paper presented at the 2015 IEEE International Conference on Automation Science and Engineering (CASE).
Fernandez-Viagas, V., Leisten, R., and Framinan, J. M. (2016). A computational evaluation of constructive and improvement heuristics for the blocking flow shop to minimise total flowtime. Expert Systems with Applications, 61, 290-301.
Gajpal, Y., and Abad, P. L. (2009). Multi-ant colony system (MACS) for a vehicle routing problem with backhauls. European Journal of Operational Research, 196(1), 102-117.
Ghannadpour, S. F., Noori, S., Tavakkoli-Moghaddam, R., and Ghoseiri, K. (2014). A multi-objective dynamic vehicle routing problem with fuzzy time windows: model, solution and application. Applied Soft Computing, 14, 504-527.
Ghorbani, A., and Akbari Jokar, M. R. (2016). A hybrid imperialist competitive-simulated annealing algorithm for a multisource multi-product location-routing-inventory problem. Computers & Industrial Engineering, 101, 116-127.
Haghani, A., and Jung, S. (2005). A dynamic vehicle routing problem with time–dependent travel times. Computers and Operations Research, 32(11), 2959–2986.
Hart, M., Tomaštík, M., and Heinzová, R. (2015). The methodology of demand forecasting system creation in an industrial company the foundation to logistics management. Paper presented at the 2015 4th International Conference on Advanced Logistics and Transport (ICALT).
Haugland, D., Ho, S. C., and Laporte, G. (2007). Designing delivery districts for the vehicle routing problem with stochastic demands. European Journal of Operational Research, 180(3), 997-1010.
Hoff, A., Gribkovskaia, I., Laporte, G., and Løkketangen, A. (2009). Lasso solution strategies for the vehicle routing problem with pickups and deliveries. European Journal of Operational Research, 192(3), 755-766.
Hojabri, H., Gendreau, M., Potvin, J.-Y., and Rousseau, L.-M. (2018). Large neighborhood search with constraint programming for a vehicle routing problem with synchronization constraints. Computers & Operations Research, 92, 87-97.
Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor, MI.
Homberger, J., and Gehring, H. (2005). A two-phase hybrid metaheuristic for the vehicle routing problem with time windows. European Journal of Operational Research, 162(1), 220-238.
Horn, M. E. T. (2002). Fleet scheduling and dispatching for demand-responsive passenger services. Transportation Research Part C: Emerging Technologies, 10(1), 35-63.
Hosseini, S. M., Khaled, A. A., and Jin, M. (2012). Solving Euclidean minimal spanning tree problem using a new meta-heuristic approach: imperialist competitive algorithm (ICA). Paper presented at the 2012 IEEE International Conference on Industrial Engineering and Engineering Management.
Hsieh, P.F. (2003). Basic information of warehousing and logistics industries. Taiwan Institute of Economic Research.
Hsu, C.-I., Hung, S.-F., and Li, H.-C. (2007). Vehicle routing problem with time-windows for perishable food delivery. Journal of Food Engineering, 80(2), 465-475.
Imai, A., Nishimura, E., and Current, J. (2007). A Lagrangian relaxation-based heuristic for the vehicle routing with full container load. European Journal of Operational Research, 176(1), 87-105.
Jie-sheng, W., Chang, L., and Ying, Z. (2011). Solving capacitated vehicle routing problem based on improved genetic algorithm. Paper presented at the 2011 Chinese Control and Decision Conference (CCDC).
Juan, A., Faulin, J., Grasman, S., Riera, D., Marull, J., and Mendez, C. (2011). Using safety stocks and simulation to solve the vehicle routing problem with stochastic demands. Transportation Research Part C: Emerging Technologies, 19(5), 751-765.
Koç, Ç., Bektaş, T., Jabali, O., and Laporte, G. (2015). A hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows. Computers & Operations Research, 64, 11-27.
Koç, Ç., and Laporte, G. (2018). Vehicle routing with backhauls: review and research perspectives. Computers & Operations Research, 91, 79-91.
Köster, F., Ulmer, M. W., and Mattfeld, D. C. (2015). Cooperative traffic control management for city logistic routing. Transportation Research Procedia, 10, 673-682.
Lakshmi, K., and Vasantharathna, S. (2014). Gencos wind–thermal scheduling problem using artificial immune system algorithm. International Journal of Electrical Power & Energy Systems, 54, 112-122.
Laporte, G. (2009). Fifty years of vehicle routing. Transportation Science, 43(4), 408-416.
Laporte, G., and Nobert, Y. (1987). Exact algorithms for the vehicle routing problem. Annals of Discrete Mathematics, 31, 147-184.
Laporte, G., and Osman, I. H. (1995). Routing problems: a bibliography. Annals of Operations Research, 61(1), 227-262.
Leggieri, V., and Haouari, M. (2018). A matheuristic for the asymmetric capacitated vehicle routing problem. Discrete Applied Mathematics, 234, 139-150.
Letchford, A. N., and Salazar-González, J.-J. (2015). Stronger multi-commodity flow formulations of the capacitated vehicle routing problem. European Journal of Operational Research, 244(3), 730-738.
Li, H., Chang, X., Zhao, W., and Lu, Y. (2017). The vehicle flow formulation and savings-based algorithm for the rollon-rolloff vehicle routing problem. European Journal of Operational Research, 257(3), 859-869.
Liao, T.-Y., and Hu, T.-Y. (2011). An object-oriented evaluation framework for dynamic vehicle routing problems under real-time information. Expert Systems with Applications, 38(10), 12548-12558.
Lin, J. L., Chuan, H. C., Tsai, Y. H., and Cho, C. W. (2013). Improving imperialist competitive algorithm with local search for global optimization. Paper presented at the 2013 7th Asia Modelling Symposium.
Liu, F.-H. F., and Shen, S.-Y. (1999). A route-neighborhood-based metaheuristic for vehicle routing problem with time windows. European Journal of Operational Research, 118(3), 485-504.
Loo Hay, L., Kay Chen, T., Ke, O., and Yoong Han, C. (2003). Vehicle capacity planning system: a case study on vehicle routing problem with time windows. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 33(2), 169-178.
Luo, J., Wang, J., and Yu, H. (2010). A dynamic vehicle routing problem for responding to large-scale emergencies. Paper presented at the 2010 International Conference on E-Business and E-Government.
Makarova, I., Shubenkova, K., and Pashkevich, A. (2017). Logistical costs minimization for delivery of shot lots by using logistical information systems. Procedia Engineering, 178, 330-339.
Mancini, S. (2017). A combined multistart random constructive heuristic and set partitioning based formulation for the vehicle routing problem with time dependent travel times. Computers & Operations Research, 88, 290-296.
Mańdziuk, J., and Żychowski, A. (2016). A memetic approach to vehicle routing problem with dynamic requests. Applied Soft Computing, 48, 522-534.
Mazzeo, S., and Loiseau, I. (2004). An ant colony algorithm for the capacitated vehicle routing. Electronic Notes in Discrete Mathematics, 18, 181–186.
Mo, D., Ho, D. C. K., and Chan, N. (2017). Excess inventories redeployment strategy for spare parts service logistics management. Paper presented at the 2017 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM).
Mohammed, M. A., Ahmad, M. S., and Mostafa, S. A. (2012). Using genetic algorithm in implementing capacitated vehicle routing problem. Paper presented at the 2012 International Conference on Computer & Information Science (ICCIS).
Mollinetti, M. A. F., Almeida, J. N. M., Pereira, R. L., and Teixeira, O. N. (2013). Performance analysis of the imperialist competitive algorithm using benchmark functions. Paper presented at the 2013 International Conference on Soft Computing and Pattern Recognition (SoCPaR).
Moon, I., Lee, J.-H., and Seong, J. (2012). Vehicle routing problem with time windows considering overtime and outsourcing vehicles. Expert Systems with Applications, 39(18), 13202-13213.
Moretti Branchini, R., Amaral Armentano, V., and Løkketangen, A. (2009). Adaptive granular local search heuristic for a dynamic vehicle routing problem. Computers & Operations Research, 36(11), 2955-2968.
Müller, J. (2010). Approximative solutions to the bicriterion vehicle routing problem with time windows. European Journal of Operational Research, 202(1), 223-231.
Nazif, H., and Lee, L. S. (2012). Optimised crossover genetic algorithm for capacitated vehicle routing problem. Applied Mathematical Modelling, 36(5), 2110-2117.
Ng, K. K. H., Lee, C. K. M., Zhang, S. Z., Wu, K., and Ho, W. (2017). A multiple colonies artificial bee colony algorithm for a capacitated vehicle routing problem and re-routing strategies under time-dependent traffic congestion. Computers & Industrial Engineering, 109, 151-168.
Niu, Y., Yang, Z., Chen, P., and Xiao, J. (2018). Optimizing the green open vehicle routing problem with time windows by minimizing comprehensive routing cost. Journal of Cleaner Production, 171, 962-971.
Norouzi, N., Sadegh-Amalnick, M., and Alinaghiyan, M. (2015). Evaluating of the particle swarm optimization in a periodic vehicle routing problem. Measurement, 62, 162-169.
Novoa, C., and Storer, R. (2009). An approximate dynamic programming approach for the vehicle routing problem with stochastic demands. European Journal of Operational Research, 196(2), 509-515.
Ochi, L. S., Vianna, D. S., Drummond L. M. A., and Victor, A. O. (1998). An evolutionary hybrid metaheuristic for solving the vehicle routing problem with heterogeneous fleet. Lecture Notes in Computer Science, 1391, 187-195.
Okike, E. U., and Morogosi, M. (2017). Measuring the usability probability of learning management software using logistic regression model. Paper presented at the 2017 Computing Conference.
Okulewicz, M., and Mańdziuk, J. (2017). The impact of particular components of the PSO-based algorithm solving the dynamic vehicle routing problem. Applied Soft Computing, 58, 586-604.
Oliveira, J. B., Lima, R. S., Kobza, J. E., and Jin, M. (2016). An analysis on logistics risk management: Tools, techniques and review. Paper presented at the 2016 6th International Conference on Information Communication and Management (ICICM).
Ozbaygin, G., Ekin Karasan, O., Savelsbergh, M., and Yaman, H. (2017). A branch-and-price algorithm for the vehicle routing problem with roaming delivery locations. Transportation Research Part B: Methodological, 100, 115-137.
Paessens, H. (1988). The savings algorithm for the vehicle routing problem. European Journal of Operational Research, 34(3), 336-344.
Palhazi Cuervo, D., Goos, P., Sörensen, K., and Arráiz, E. (2014). An iterated local search algorithm for the vehicle routing problem with backhauls. European Journal of Operational Research, 237(2), 454-464.
Pillac, V., Gendreau, M., Guéret, C., and Medaglia, A. L. (2013). A review of dynamic vehicle routing problems. European Journal of Operational Research, 225(1), 1-11.
Pillac, V., Guéret, C., and Medaglia, A. L. (2012). An event-driven optimization framework for dynamic vehicle routing. Decision Support Systems, 54(1), 414-423.
Pisinger, D., and Ropke, S. (2007). A general heuristic for vehicle routing problems. Computers & Operations Research, 34(8), 2403-2435.
Psaraftis, H. (1980). A dynamic programming solution to the single vehicle many-tomany immediate request dial-a-ride problem. Transportation Science, 14, 130–154.
Purnomo, H. D., Wee, H. M., and Praharsi, Y. (2012). Two inventory review policies on supply chain configuration problem. Computers & Industrial Engineering, 63(2), 448-455.
Razali, N. M. (2015). An efficient genetic algorithm for large scale vehicle routing problem subject to precedence constraints. Procedia - Social and Behavioral Sciences, 195, 1922-1931.
Reed, M., Yiannakou, A., and Evering, R. (2014). An ant colony algorithm for the multi-compartment vehicle routing problem. Applied Soft Computing, 15, 169-176.
Reimann, M., and Laumanns, M. (2006). Savings based ant colony optimization for the capacitated minimum spanning tree problem. Computers & Operations Research, 33(6), 1794-1822.
Saebi, J., Ghasemi, H., Afsharnia, S., and Mashhadi, H. R. (2012). Imperialist competitive algorithm for reactive power dispatch problem in electricity markets. Paper presented at the 20th Iranian Conference on Electrical Engineering (ICEE2012).
Salhi, S., Wassan, N., and Hajarat, M. (2013). The fleet size and mix vehicle routing problem with backhauls: formulation and set partitioning-based heuristics. Transportation Research Part E: Logistics and Transportation Review, 56, 22-35.
Saxena, G. (2018). Multidimensional competency construct for social entrepreneurs: a logistic regression approach. Kasetsart Journal of Social Sciences.
Secomandi, N. (2000). Comparing neuro-dynamic programming algorithms for the vehicle routing problem with stochastic demands. Computers & Operations Research, 27(11), 1201-1225.
Sharma, N., Chauhan, N., and Chand, N. (2016). Smart logistics vehicle management system based on internet of vehicles. Paper presented at the 2016 Fourth International Conference on Parallel, Distributed and Grid Computing (PDGC).
Shijin, W., and Yulun, W. (2017). A genetic algorithm for energy minimization Vehicle Routing Problem. Paper presented at the 2017 International Conference on Service Systems and Service Management.
Silvestrin, P. V., and Ritt, M. (2017). An iterated Tabu search for the multi-compartment vehicle routing problem. Computers & Operations Research, 81, 192-202.
Soleimani, H., Chaharlang, Y., and Ghaderi, H. (2018). Collection and distribution of returned-remanufactured products in a vehicle routing problem with pickup and delivery considering sustainable and green criteria. Journal of Cleaner Production, 172, 960-970.
Sörensen, K., and Schittekat, P. (2013). Statistical analysis of distance-based path relinking for the capacitated vehicle routing problem. Computers & Operations Research, 40(12), 3197-3205.
Tan, K. C., Lee, L. H., Zhu, Q. L., and Ou, K. (2001). Heuristic methods for vehicle routing problem with time windows. Artificial Intelligence in Engineering, 15(3), 281-295.
Tan, L., Tan, Y., Yun, G., and Wu, Y. (2016). Genetic algorithms based on clustering for traveling salesman problems. Paper presented at the 2016 12th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD).
Tarantilis, C. D., Kiranoudis, C. T., and Markatos, N. C. (2002). Use of the BATA algorithm and MIS to solve the mail carrier problem. Applied Mathematical Modelling, 26(4), 481-500.
Tavakkoli-Moghaddam, R., Saremi, A. R., and Ziaee, M. S. (2006). A memetic algorithm for a vehicle routing problem with backhauls. Applied Mathematics and Computation, 181(2), 1049-1060.
Toth, P., and Vigo, D. (2001). The Vehicle Routing Problem (Monographs on Discrete Mathematics and Applications). Philadelphia, PA: SIAM.
Trappey, A. J. C., Trappey, C. V., Dai, D. W. T., Chang, S. W. C., and Lee, W. T. (2014). The implementation of global logistic services using one-stop logistics management. Paper presented at the Proceedings of the 2014 IEEE 18th International Conference on Computer Supported Cooperative Work in Design (CSCWD).
Wade, A. C., and Salhi, S. (2002). An investigation into a new class of vehicle routing problem with backhauls. Omega, 30(6), 479-487.
Wang, G. J., Zhang, Y. B., and Chen, J. W. (2011). A novel algorithm to solve the vehicle routing problem with time windows: imperialist competitive algorithm. Advances in Information Sciences and Service Sciences, 3(5), 108-116
Wassan, N., Wassan, N., Nagy, G., and Salhi, S. (2017). The multiple trip vehicle routing problem with backhauls: formulation and a two-level variable neighbourhood search. Computers & Operations Research, 78, 454-467.
Wei, L., Zhang, Z., Zhang, D., and Leung, S. C. H. (2018). A simulated annealing algorithm for the capacitated vehicle routing problem with two-dimensional loading constraints. European Journal of Operational Research, 265(3), 843-859.
Wen, M., Cordeau, J.-F., Laporte, G., and Larsen, J. (2010). The dynamic multi-period vehicle routing problem. Computers & Operations Research, 37(9), 1615-1623.
Wilson N. H. M. and Colvin N. J. (1977) Computer control of the rochester dial-a-ride system. Dept of Civil Engineering, M.I.T. Report R77-31.
Wu, G.-H., Cheng, C.-Y., Yang, H.-I., and Chena, C.-T. (2017). An improved water flow-like algorithm for order acceptance and scheduling with identical parallel machines. Applied Soft Computing. (https://doi.org/10.1016/j.asoc.2017.10.015)
Wu, W., Tian, Y., and Jin, T. (2016). A label based ant colony algorithm for heterogeneous vehicle routing with mixed backhaul. Applied Soft Computing, 47, 224-234.
Yanik, S., Bozkaya, B., and deKervenoael, R. (2014). A new VRPPD model and a hybrid heuristic solution approach for e-tailing. European Journal of Operational Research, 236(3), 879-890.
Yassen, E. T., Ayob, M., Nazri, M. Z. A., and Sabar, N. R. (2017). An adaptive hybrid algorithm for vehicle routing problems with time windows. Computers & Industrial Engineering, 113, 382-391.
Ye, F., Li, Y., and Yang, Q. (2018). Designing coordination contract for biofuel supply chain in China. Procedia, 128, 306-314.
Yurtkuran, A., and Emel, E. (2010). A new hybrid electromagnetism-like algorithm for capacitated vehicle routing problems. Expert Systems with Applications, 37(4), 3427-3433.
Zachariadis, E. E., and Kiranoudis, C. T. (2012). An effective local search approach for the vehicle routing problem with backhauls. Expert Systems with Applications, 39(3), 3174-3184.
Zhang, Z., Qin, H., Zhu, W., and Lim, A. (2012). The single vehicle routing problem with toll-by-weight scheme: A branch-and-bound approach. European Journal of Operational Research, 220(2), 295-304.
Zhu, L., Rousseau, L.-M., Rei, W., and Li, B. (2014). Paired cooperative reoptimization strategy for the vehicle routing problem with stochastic demands. Computers & Operations Research, 50, 1-13.

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