Abstract
The Capacitated Vehicle Routing Problem (CVRP) is an important combinatorial optimization problem in which a fleet of vehicles must be routed to a set of customers. Many exact and heuristic methods have been proposed to solve this problem. Recently, efficient machine learning algorithms have been developed for solving the VRP. A major component of these algorithms is the Attention Mechanism which enables the vehicle to make more informed decisions on which customer to serve next. This paper compares various topologies for implementing such attention mechanisms when solving VRPs. Using simulations, it is found that Single-Head Attention works better with larger node instances, whereas Multi-Head Attention is superior for smaller node instances.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adiwardana D, Luong MT, So DR, Hall J, Fiedel N, Thoppilan R, Yang Z, Kulshreshtha A, Nemade G, Lu Y et al (2020) Towards a human-like open-domain chatbot. arXiv:2001.09977
Ajayan S, Dileep A, Mohan A, Gutjahr G, Sreeni K, Nedungadi P (2019) Vehicle routing and facility-location for sustainable lemongrass cultivation. In: 2019 9th international symposium on embedded computing and system design (ISED). IEEE, pp 1–6
Anbuudayasankar S, Ganesh K, Lee TR (2011) Meta-heuristic approach to solve mixed vehicle routing problem with backhauls in enterprise information system of service industry. In: Enterprise information systems: concepts, methodologies, tools and applications. IGI Global, pp 1537–1552
Augerat P (1995) Approche polyèdrale du problème de tournées de véhicules. PhD thesis, Institut National Polytechnique de Grenoble-INPG
Christofides N, Eilon S (1969) An algorithm for the vehicle-dispatching problem. J Oper Res Soc 20(3):309–318
Christofides N, Mingozzi A, Toth P (1981) Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations. Math Program 20(1):255–282
Dantzig G, Fulkerson R, Johnson S (1954) Solution of a large-scale traveling-salesman problem. J Oper Res Soc Am 2(4):393–410
Gutjahr G, Krishna LC, Nedungadi P (2018) Optimal tour planning for measles and rubella vaccination in Kochi, South India. In: 2018 international conference on advances in computing, communications and informatics (ICACCI). IEEE, pp 1366–1370
Gutjahr G, Viswanath H (2020) A genetic algorithm for post-flood relief distribution in Kerala, South India. In: ICT systems and sustainability. Springer, Berlin, pp 125–132
Kool W, Van Hoof H, Welling M (2018) Attention, learn to solve routing problems! arXiv:1803.08475
Laporte G (2009) Fifty years of vehicle routing. Transp Sci 43(4):408–416
Letchford AN, Salazar-González JJ (2019) The capacitated vehicle routing problem: stronger bounds in pseudo-polynomial time. Eur J Oper Res 272(1):24–31
Libovickỳ J, Helcl J (2017) Attention strategies for multi-source sequence-to-sequence learning. arXiv:1704.06567
Malairajan R, Ganesh K, Punnniyamoorthy M, Anbuudayasankar S (2013) Decision support system for real time vehicle routing in Indian dairy industry: a case study. Int J Inf Syst Supply Chain Manag (IJISSCM) 6(4):77–101
Mohan A, Dileep A, Ajayan S, Gutjahr G, Nedungadi P (2019) Comparison of metaheuristics for a vehicle routing problem in a farming community. In: Symposium on machine learning and metaheuristics algorithms, and applications, Springer, Berlin, pp 49–63
Nazari M, Oroojlooy A, Snyder LV, Takáč M (2018) Reinforcement learning for solving the vehicle routing problem. arXiv:1802.04240
Peng B, Wang J, Zhang Z (2019) A deep reinforcement learning algorithm using dynamic attention model for vehicle routing problems. In: International symposium on intelligence computation and applications. Springer, Berlin, pp 636–650
Rao TS (2019) An ant colony and simulated annealing algorithm with excess load VRP in a FMCG company. In: IOP conference series: materials science and engineering, vol 577. IOP Publishing, p 012191
Sutskever I, Vinyals O, Le QV (2014) Sequence to sequence learning with neural networks. In: Advances in neural information processing systems, pp 3104–3112
Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Kaiser Ł, Polosukhin I (2017) Attention is all you need. In: Advances in neural information processing systems, pp 5998–6008
Vinyals O, Fortunato M, Jaitly N (2015) Pointer networks. arXiv:1506.03134
Yu Y, Si X, Hu C, Zhang J (2019) A review of recurrent neural networks: Lstm cells and network architectures. Neural Comput 31(7):1235–1270
Zheng S (2019) Solving vehicle routing problem: A big data analytic approach. IEEE Access 7:169565–169570
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Krishna Munjuluri Vamsi, V.S., Telukuntla, Y.R., Kumar, P.S., Gutjahr, G. (2023). Comparison of Attention Mechanisms in Machine Learning Models for Vehicle Routing Problems. In: Singh, P., Singh, D., Tiwari, V., Misra, S. (eds) Machine Learning and Computational Intelligence Techniques for Data Engineering. MISP 2022. Lecture Notes in Electrical Engineering, vol 998. Springer, Singapore. https://doi.org/10.1007/978-981-99-0047-3_53
Download citation
DOI: https://doi.org/10.1007/978-981-99-0047-3_53
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-99-0046-6
Online ISBN: 978-981-99-0047-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)