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A unified solution framework for multi-attribute vehicle routing problems. (English) Zbl 1304.90004
Summary: Vehicle routing attributes are extra characteristics and decisions that complement the academic problem formulations and aim to properly account for real-life application needs. Hundreds of methods have been introduced in recent years for specific attributes, but the development of a single, general-purpose algorithm, which is both efficient and applicable to a wide family of variants remains a considerable challenge. Yet, such a development is critical for understanding the proper impact of attributes on resolution approaches, and to answer the needs of actual applications. This paper contributes towards addressing these challenges with a component-based design for heuristics, targeting multi-attribute vehicle routing problems, and an efficient general-purpose solver. The proposed Unified Hybrid Genetic Search metaheuristic relies on problem-independent unified local search, genetic operators, and advanced diversity management methods. Problem specifics are confined to a limited part of the method and are addressed by means of assignment, sequencing, and route-evaluation components, which are automatically selected and adapted and provide the fundamental operators to manage attribute specificities. Extensive computational experiments on 29 prominent vehicle routing variants, 42 benchmark instance sets and overall 1099 instances, demonstrate the remarkable performance of the method which matches or outperforms the current state-of-the-art problem-tailored algorithms. Thus, generality does not necessarily go against efficiency for these problem classes.

MSC:
90-04 Software, source code, etc. for problems pertaining to operations research and mathematical programming
90B06 Transportation, logistics and supply chain management
90B10 Deterministic network models in operations research
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[1] Anagnostopoulou, A. K., Repoussis, P. P., & Tarantilis, C. D. (2013). GRASP with path relinking for vehicle routing problems with clustered and mixed backhauls. Tech. rep., Athens University of Economics and Business.
[2] Andersson, H.; Hoff, A.; Christiansen, M.; Hasle, G.; Lokketangen, A., Industrial aspects and literature survey: combined inventory management and routing, Computers & Operations Research, 37, 9, 1515-1536, (2010) · Zbl 1190.90012
[3] Baldacci, R.; Bartolini, E.; Laporte, G., Some applications of the generalized vehicle routing problem, Journal of the Operational Research Society, 61, 7, 1072-1077, (2009) · Zbl 1193.90036
[4] Baldacci, R.; Bartolini, E.; Mingozzi, A.; Valletta, A., An exact algorithm for the period routing problem, Operations Research, 59, 1, 228-241, (2011) · Zbl 1218.90118
[5] Baldacci, R.; Mingozzi, A., A unified exact method for solving different classes of vehicle routing problems, Mathematical Programming, 120, 2, 347-380, (2009) · Zbl 1180.90260
[6] Baldacci, R.; Mingozzi, A.; Calvo, R. W., An exact method for the capacitated location-routing problem, Operations Research, 59, 5, 1284-1296, (2011) · Zbl 1233.90060
[7] Balseiro, S. R.; Loiseau, I.; Ramonet, J., An ant colony algorithm hybridized with insertion heuristics for the time dependent vehicle routing problem with time windows, Computers & Operations Research, 38, 6, 954-966, (2011) · Zbl 1205.90042
[8] Bektas, T.; Erdogan, G.; Ropke, S., Formulations and branch-and-cut algorithms for the generalized vehicle routing problem, Transportation Science, 45, 3, 299-316, (2011)
[9] Belhaiza, S. (2010). Hybrid variable neighborhood - Tabu search algorithm for the site dependent vehicle routing problem with time windows. Tech. rep., GERAD, Montreal, Canada.
[10] Bostel, N.; Dejax, P.; Guez, P.; Tricoire, F., Multiperiod planning and routing on a rolling horizon for field force optimization logistics, (Golden, Bruce; Raghavan, S.; Wasil, Edward, The vehicle routing problem: Latest advances and new challenges, 43, (2008), Springer New York), 503-525 · Zbl 1187.90040
[11] Bräysy, O.; Dullaert, W.; Hasle, G.; Mester, D.; Gendreau, M., An effective multirestart deterministic annealing metaheuristic for the fleet size and mix vehicle-routing problem with time windows, Transportation Science, 42, 3, 371-386, (2008)
[12] Bräysy, O.; Porkka, P. P.; Dullaert, W.; Repoussis, P. P.; Tarantilis, C. D., A well-scalable metaheuristic for the fleet size and mix vehicle routing problem with time windows, Expert Systems with Applications, 36, 4, 8460-8475, (2009)
[13] Burke, E. K.; Hyde, M.; Kendall, G.; Ochoa, G.; Özcan, E.; Woodward, J. R., A classification of hyper-heuristic approaches, (Gendreau, M.; Potvin, J.-Y., Handbook of metaheuristics, (2010), Springer US), 449-468
[14] Cahon, S.; Melab, N.; Talbi, E.-G., Paradiseo: A framework for the reusable design of parallel and distributed metaheuristics, Journal of Heuristics, 10, 3, 357-380, (2004) · Zbl 1098.68644
[15] Campbell, A. M.; Savelsbergh, M., Efficient insertion heuristics for vehicle routing and scheduling problems, Transportation Science, 38, 3, 369-378, (2004)
[16] Christofides, N.; Mingozzi, A.; Toth, P., The vehicle routing problem, (Christofides, N.; Mingozzi, A.; Toth, P.; Sandi, C., Combined Optimization, (1979), Wiley Chichester, UK), 315-338
[17] Cordeau, J.-F.; Gendreau, M.; Laporte, G., A tabu search heuristic for periodic and multi-depot vehicle routing problems, Networks, 30, 2, 105-119, (1997) · Zbl 0885.90037
[18] Cordeau, J.-F.; Laporte, G., A tabu search algorithm for the site dependent vehicle routing problem with time windows, INFOR, 39, 3, 292-298, (2001)
[19] Cordeau, J.-F.; Laporte, G., A tabu search heuristic for the static multi-vehicle dial-a-ride problem, Transportation Research Part B: Methodological, 37, 6, 579-594, (2003)
[20] Cordeau, J.-F.; Laporte, G.; Mercier, A., A unified tabu search heuristic for vehicle routing problems with time windows, Journal of the Operational Research Society, 52, 8, 928-936, (2001) · Zbl 1181.90034
[21] Cordeau, J.-F.; Laporte, G.; Mercier, A., Improved tabu search algorithm for the handling of route duration constraints in vehicle routing problems with time windows, Journal of the Operational Research Society, 55, 5, 542-546, (2004) · Zbl 1060.90019
[22] Cordeau, J.-F.; Maischberger, M., A parallel iterated tabu search heuristic for vehicle routing problems, Computers & Operations Research, 39, 9, 2033-2050, (2012)
[23] Cormen, T. H.; Stein, C.; Rivest, R. L.; Leiserson, C. E., Introduction to algorithms, (2001), McGraw-Hill Higher Education · Zbl 1047.68161
[24] Crainic, T. G.; Toulouse, M., Parallel meta-heuristics, (Gendreau, M.; Potvin, J.-Y., Handbook of metaheuristics, (2010), Springer US, Boston, MA), 497-541
[25] Desaulniers, G.; Desrosiers, J.; Ioachim, I.; Solomon, M. M.; Soumis, F.; Villeneuve, D., A unified framework for deterministic time constrained vehicle routing and crew scheduling problems, (Crainic, T. G.; Laporte, G., Fleet management and logistics, (1998), Kluwer Academic Publishers Boston, MA), 129-154
[26] (Desaulniers, G.; Desrosiers, J.; Solomon, M. M., Column generation, (2005), Springer) · Zbl 1084.90002
[27] Du, T. C.; Wu, J.-L., Using object-oriented paradigm to develop an evolutional vehicle routing system, Computers in Industry, 44, 3, 229-249, (2001)
[28] Eksioglu, B.; Vural, A. V.; Reisman, A., The vehicle routing problem: A taxonomic review, Computers & Industrial Engineering, 57, 4, 1472-1483, (2009)
[29] Figliozzi, M. A., An iterative route construction and improvement algorithm for the vehicle routing problem with soft time windows, Transportation Research Part C: Emerging Technologies, 18, 5, 668-679, (2010)
[30] Fink, A.; Voss, S., HOTFRAME: A heuristic optimization framework, (Voss, S.; Woodruff, D. L., Optimization software class libraries, Operations research/computer science interfaces series, Vol. 18, (2003), Springer), 81-154
[31] Fischetti, M.; Toth, P.; Vigo, D., A branch-and-bound algorithm for the capacitated vehicle routing problem on directed graphs, Operations Research, 42, 5, 846-859, (1994) · Zbl 0815.90065
[32] Fisher, M. L., Optimal solution of vehicle routing problems using minimum k-trees, Operations Research, 42, 4, 626-642, (1994) · Zbl 0815.90066
[33] Fu, Z.; Eglese, R.; Li, L. Y.O., A unified tabu search algorithm for vehicle routing problems with soft time windows, Journal of the Operational Research Society, 59, 5, 663-673, (2007) · Zbl 1153.90357
[34] Gajpal, Y.; Abad, P., Multi-ant colony system (MACS) for a vehicle routing problem with backhauls, European Journal of Operational Research, 196, 1, 102-117, (2009) · Zbl 1156.90318
[35] Garcia, B.-L. (1996). Une approche générique des méthodes par amélioration itérative. Application à la résolution de problèmes d’optimisation dans les réseaux. Ph.D. thesis, Laboratoire d’Informatique de l’Université Blaise Pascal, Clermont-Ferrand, France.
[36] Gehring, H.; Homberger, J., A parallel hybrid evolutionary metaheuristic for the vehicle routing problem with time windows, Proceedings of EURO-GEN’99, 57-64, (1999)
[37] Gélinas, S.; Desrochers, M.; Desrosiers, J.; Solomon, M. M., A new branching strategy for time constrained routing problems with application to backhauling, Annals of Operations Research, 61, 1, 91-109, (1995) · Zbl 0839.90029
[38] Gendreau, M.; Potvin, J. Y.; Bräysy, O.; Hasle, G.; Lokketangen, A., Metaheuristics for the vehicle routing problem and its extensions: A categorized bibliography, (Golden, B.; Raghavan, S.; Wasil, E., The vehicle routing problem: Latest advances and new challenges, (2008), Springer New York), 143-169 · Zbl 1187.90001
[39] Glover, F.; Hao, J.-K., The case for strategic oscillation, Annals of Operations Research, 183, 1, 163-173, (2011) · Zbl 1214.90097
[40] Goel, A., Vehicle scheduling and routing with drivers’ working hours, Transportation Science, 43, 1, 17-26, (2009)
[41] Goel, A.; Kok, L., Truck driver scheduling in the united states, Transportation Science, 46, 3, 317-326, (2012)
[42] Goel, A.; Vidal, T., Hours of service regulations in road freight transport: an optimization-based international assessment, Transportation Science, (2013), in press
[43] Goetschalckx, M.; Jacobs-Blecha, C., The vehicle routing problem with backhauls, European Journal of Operational Research, 42, 1, 39-51, (1989) · Zbl 0669.90074
[44] Golden, B., The fleet size and mix vehicle routing problem, Computers & Operations Research, 11, 1, 49-66, (1984) · Zbl 0607.90043
[45] (Golden, B.; Raghavan, S.; Wasil, E., The vehicle routing problem: Latest advances and new challenges, (2008), Springer New York) · Zbl 1142.90004
[46] Golden, B. L.; Wasil, E. A.; Kelly, J. P.; Chao, I. M., The impact of metaheuristics on solving the vehicle routing problem: algorithms, problem sets, and computational results, (Crainic, T. G.; Laporte, G., Fleet management and logistics, (1998), Kluwer Academic Publishers Boston, MA), 33-56 · Zbl 0997.90021
[47] Groër, C.; Golden, B.; Wasil, E., A library of local search heuristics for the vehicle routing problem, Mathematical Programming Computation, 2, 2, 79-101, (2010) · Zbl 1230.90033
[48] Groër, C.; Golden, B.; Wasil, E., A parallel algorithm for the vehicle routing problem, INFORMS Journal on Computing, 23, 2, 315-330, (2011) · Zbl 1243.90186
[49] Hashimoto, H.; Ibaraki, T.; Imahori, S.; Yagiura, M., The vehicle routing problem with flexible time windows and traveling times, Discrete Applied Mathematics, 154, 16, 2271-2290, (2006) · Zbl 1130.90053
[50] Hashimoto, H.; Yagiura, M.; Ibaraki, T., An iterated local search algorithm for the time-dependent vehicle routing problem with time windows, Discrete Optimization, 5, 2, 434-456, (2008) · Zbl 1169.90326
[51] Hemmelmayr, V. C.; Doerner, K. F.; Hartl, R. F., A variable neighborhood search heuristic for periodic routing problems, European Journal of Operational Research, 195, 3, 791-802, (2009) · Zbl 1156.90307
[52] Hendel, Y.; Sourd, F., Efficient neighborhood search for the one-machine earliness-tardiness scheduling problem, European Journal of Operational Research, 173, 1, 108-119, (2006) · Zbl 1125.90017
[53] Ibaraki, T.; Imahori, S.; Kubo, M.; Masuda, T.; Uno, T.; Yagiura, M., Effective local search algorithms for routing and scheduling problems with general time-window constraints, Transportation Science, 39, 2, 206-232, (2005)
[54] Ibaraki, T.; Imahori, S.; Nonobe, K.; Sobue, K.; Uno, T.; Yagiura, M., An iterated local search algorithm for the vehicle routing problem with convex time penalty functions, Discrete Applied Mathematics, 156, 11, 2050-2069, (2008) · Zbl 1153.90446
[55] Imran, A.; Salhi, S.; Wassan, N. A., A variable neighborhood-based heuristic for the heterogeneous fleet vehicle routing problem, European Journal of Operational Research, 197, 2, 509-518, (2009) · Zbl 1159.90525
[56] Irnich, S., A unified modeling and solution framework for vehicle routing and local search-based metaheuristics, INFORMS Journal on Computing, 20, 2, 270-287, (2008) · Zbl 1243.90225
[57] Irnich, S., Resource extension functions: properties, inversion, and generalization to segments, OR Spectrum, 30, 113-148, (2008) · Zbl 1133.90309
[58] Jin, J., Crainic, T. G., & Lokketangen, A. (2012). A cooperative parallel metaheuristic for the capacitated vehicle routing problem. Tech. rep., CIRRELT. · Zbl 1307.90024
[59] Kindervater, G. A.P.; Savelsbergh, M. W.P., Vehicle routing: handling edge exchanges, (Aarts, E. H.L.; Lenstra, J. K., Local search in combinatorial optimization, (1997), Princeton Univ Pr), 337-360 · Zbl 0887.90060
[60] Kritzinger, S., Tricoire, F., Doerner, K. F., Hartl, R. F., & Stützle, T. (2012). A unified framework for routing problems with fixed fleet size. Tech. rep., Johannes Kepler University, Linz, Austria.
[61] Labadi, N.; Prins, C.; Reghioui, M., A memetic algorithm for the vehicle routing problem with time windows, RAIRO Operations Research, 42, 3, 415-431, (2008) · Zbl 1152.90334
[62] Liu, F.-H.; Shen, S.-Y., The fleet size and mix vehicle routing problem with time windows, Journal of the Operational Research Society, 50, 7, 721-732, (1999) · Zbl 1054.90522
[63] Mester, D.; Bräysy, O., Active-guided evolution strategies for large-scale capacitated vehicle routing problems, Computers & Operations Research, 34, 10, 2964-2975, (2007) · Zbl 1185.90176
[64] Meyer, B., Object-oriented software construction, (1997), Prentice Hall Englewood Cliffs, USA · Zbl 0987.68516
[65] Moccia, L.; Cordeau, J.-F.; Laporte, G., An incremental tabu search heuristic for the generalized vehicle routing problem with time windows, Journal of the Operational Research Society, 63, 2, 232-244, (2012)
[66] Montané, F. A.T.; Galvão, R. D., A tabu search algorithm for the vehicle routing problem with simultaneous Pick-up and delivery service, Computers & Operations Research, 33, 3, 595-619, (2006) · Zbl 1077.90058
[67] Nagata, Y.; Bräysy, O., Edge assembly-based memetic algorithm for the capacitated vehicle routing problem, Networks, 54, 4, 205-215, (2009) · Zbl 1206.90025
[68] Nagata, Y.; Bräysy, O.; Dullaert, W., A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows, Computers & Operations Research, 37, 4, 724-737, (2010) · Zbl 1175.90046
[69] Ngueveu, S. U.; Prins, C.; Wolfler Calvo, R., An effective memetic algorithm for the cumulative capacitated vehicle routing problem, Computers & Operations Research, 37, 11, 1877-1885, (2010) · Zbl 1188.90037
[70] Pirkwieser S., & Raidl, G. R. (2008). A variable neighborhood search for the periodic vehicle routing problem with time windows. In Proceedings of the 9th EU meeting on metaheuristics for logistics and vehicle routing, Troyes, France.
[71] Pisinger, D.; Ropke, S., A general heuristic for vehicle routing problems, Computers & Operations Research, 34, 8, 2403-2435, (2007) · Zbl 1144.90318
[72] Polacek, M.; Benkner, S.; Doerner, K. F.; Hartl, R. F., A cooperative and adaptive variable neighborhood search for the multi depot vehicle routing problem with time windows, BuR-Business Research, 1, 2, 207-218, (2008)
[73] Prescott-Gagnon, E.; Desaulniers, G.; Drexl, M.; Rousseau, L.-M., European driver rules in vehicle routing with time windows, Transportation Science, 44, 4, 455-473, (2010)
[74] Prins, C., A simple and effective evolutionary algorithm for the vehicle routing problem, Computers & Operations Research, 31, 12, 1985-2002, (2004) · Zbl 1100.90504
[75] Prins, C., Two memetic algorithms for heterogeneous fleet vehicle routing problems, Engineering Applications of Artificial Intelligence, 22, 6, 916-928, (2009)
[76] Prins, C.; Bouchenoua, S., A memetic algorithm solving the VRP, the CARP, and more general routing problems with nodes, edges and arcs, (Hart, W.; Krasnogor, N.; Smith, J., Recent advances in memetic algorithms, Studies in fuzziness and soft computing, (2005), Springer), 65-85
[77] Puranen, T. (2011). Metaheuristics meet metamodels - A modeling language and a product line architecture for route optimization systems. Ph.D. thesis, University of Jyväskylä, Finland.
[78] Repoussis, P. P.; Tarantilis, C. D., Solving the fleet size and mix vehicle routing problem with time windows via adaptive memory programming, Transportation Research Part C: Emerging Technologies, 18, 5, 695-712, (2010)
[79] Repoussis, P. P.; Tarantilis, C. D.; Bräysy, O.; Ioannou, G., A hybrid evolution strategy for the open vehicle routing problem, Computers & Operations Research, 37, 3, 443-455, (2010) · Zbl 1173.90520
[80] Repoussis, P. P.; Tarantilis, C. D.; Ioannou, G., An evolutionary algorithm for the open vehicle routing problem with time windows, (Pereira, F. B.; Tavares, J., Bio-inspired algorithms for the vehicle routing problem, Studies in computational intelligence, (2009), Springer), 55-75
[81] Ribeiro, G. M.; Laporte, G., An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem, Computers & Operations Research, 39, 3, 728-735, (2012) · Zbl 1251.90057
[82] Ropke, S.; Pisinger, D., A unified heuristic for a large class of vehicle routing problems with backhauls, European Journal of Operational Research, 171, 3, 750-775, (2006) · Zbl 1116.90019
[83] Ropke, S.; Pisinger, D., An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows, Transportation Science, 40, 4, 455-472, (2006)
[84] Sahoo, S.; Kim, S.; Kim, B.-I.; Kraas, B.; Popov, A., Routing optimization for waste management, Interfaces, 35, 1, 24-36, (2005)
[85] Salhi, S.; Nagy, G., A cluster insertion heuristic for single and multiple depot vehicle routing problems with backhauling, Journal of the Operational Research Society, 50, 10, 1034-1042, (1999) · Zbl 1054.90523
[86] Savelsbergh, M. W.P., Local search in routing problems with time windows, Annals of Operations Research, 4, 1, 285-305, (1985)
[87] Savelsbergh, M. W.P., The vehicle routing problem with time windows: minimizing route duration, ORSA Journal on Computing, 4, 2, 146-154, (1992) · Zbl 0780.90105
[88] Silva, M. M.; Subramanian, A.; Vidal, T.; Ochi, L. S., A simple and effective metaheuristic for the minimum latency problem, European Journal of Operational Research, 221, 3, 513-520, (2012) · Zbl 1253.90012
[89] Solomon, M. M., Algorithms for the vehicle routing and scheduling problems with time window constraints, Operations Research, 35, 2, 254-265, (1987) · Zbl 0625.90047
[90] Subramanian, A.; Drummond, L. M.A.; Bentes, C.; Ochi, L. S.; Farias, R., A parallel heuristic for the vehicle routing problem with simultaneous pickup and delivery, Computers & Operations Research, 37, 11, 1899-1911, (2010) · Zbl 1188.90041
[91] Subramanian, A.; Penna, P. H.V.; Uchoa, E.; Ochi, L. S., A hybrid algorithm for the heterogeneous fleet vehicle routing problem, European Journal of Operational Research, 221, 2, 285-295, (2012) · Zbl 1253.90054
[92] Subramanian, A.; Uchoa, E.; Ochi, L. S., A hybrid algorithm for a class of vehicle routing problems, Computers & Operations Research, 40, 10, 2519-2531, (2013) · Zbl 1348.90132
[93] Tarantilis, C. D.; Anagnostopoulou, A. K.; Repoussis, P. P., Adaptive path relinking for vehicle routing and scheduling problems with product returns, Transportation Science, (2013), Articles in advance
[94] Toth, P., & Vigo D. (Eds.) (2002). The vehicle routing problem. Society for Industrial Mathematics, Philadelphia, PA, USA. · Zbl 0979.00026
[95] Toth, P.; Vigo, D., The granular tabu search and its application to the vehicle-routing problem, INFORMS Journal on Computing, 15, 4, 333-346, (2003) · Zbl 1238.90141
[96] Vidal, T.; Crainic, T. G.; Gendreau, M.; Lahrichi, N.; Rei, W., A hybrid genetic algorithm for multidepot and periodic vehicle routing problems, Operations Research, 60, 3, 611-624, (2012) · Zbl 1260.90058
[97] Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2011). A unifying view on timing problems and algorithms. Tech. rep., CIRRELT.
[98] Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2012). Implicit depot assignments and rotations in vehicle routing heuristics. Tech. rep., CIRRELT, Montréal. · Zbl 1304.90046
[99] Vidal, T.; Crainic, T. G.; Gendreau, M.; Prins, C., A hybrid genetic algorithm with adaptive diversity management for a large class of vehicle routing problems with time-windows, Computers & Operations Research, 40, 1, 475-489, (2013) · Zbl 1349.90137
[100] Vidal, T.; Crainic, T. G.; Gendreau, M.; Prins, C., Heuristics for multi-attribute vehicle routing problems: A survey and synthesis, European Journal of Operational Research, 231, 1, 1-21, (2013) · Zbl 1317.90006
[101] Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2013c). Time-window relaxations in vehicle routing heuristics. Tech. rep., CIRRELT, Montréal. · Zbl 1317.90006
[102] Wolpert, D. H., No free lunch theorems for optimization, IEEE Transactions on Evolutionary Computation, 1, 1, 67-82, (1997)
[103] Xiao, Y.; Zhao, Q.; Kaku, I.; Xu, Y., Development of a fuel consumption optimization model for the capacitated vehicle routing problem, Computers & Operations Research, 39, 7, 1419-1431, (2012) · Zbl 1251.90063
[104] Zachariadis, E. E.; Kiranoudis, C. T., An open vehicle routing problem metaheuristic for examining wide solution neighborhoods, Computers & Operations Research, 37, 4, 712-723, (2010) · Zbl 1175.90052
[105] Zachariadis, E. E.; Kiranoudis, C. T., A local search metaheuristic algorithm for the vehicle routing problem with simultaneous Pick-ups and deliveries, Expert Systems with Applications, 38, 3, 2717-2726, (2011) · Zbl 1210.90040
[106] Zachariadis, E. E.; Kiranoudis, C. T., An effective local search approach for the vehicle routing problem with backhauls, Expert Systems with Applications, 39, 3, 3174-3184, (2012)
[107] Zachariadis, E. E.; Tarantilis, C. D.; Kiranoudis, C. T., An adaptive memory methodology for the vehicle routing problem with simultaneous Pick-ups and deliveries, European Journal of Operational Research, 202, 2, 401-411, (2010) · Zbl 1175.90345
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.