Capacitated vehicle routing problem with column generation and reinforcement learning techniques

Capacitated vehicle routing problem is one of the variants of the vehicle routing problem which was studied in this research. In this research we applied a reinforcement learning algorithm to find set of routes from a depot to the set of customers while also considering the capacity of the vehicles, in order to reduce the cost of transportation of goods and services. Each vehicle originates from a depot, service the customers and return to the depot. We compare the reinforcement learning model with an exact method; column generation and Google’s OR-tool. Our objective is to solve a large-size of problem to near-optimality. We were able to use reinforcement learning to solve upto 101 nodes to near-optimality.

[1]  Marius M. Solomon,et al.  Recent Advances in the Vehicle Routing Problem with Time Windows , 2006 .

[2]  Christopher D. Manning,et al.  Effective Approaches to Attention-based Neural Machine Translation , 2015, EMNLP.

[3]  G.P.T. van Lent Using column generation for the Time Dependent Vehicle Routing Problem with Soft Time Windows and Stochastic Travel Times , 2018 .

[4]  Jorge Pinho de Sousa,et al.  Dynamic VRP in pharmaceutical distribution—a case study , 2006, Central Eur. J. Oper. Res..

[5]  Christopher Clingerman,et al.  Analysis and Counterexamples Regarding Yatsenko's Polynomial-Time Algorithm for Solving the Traveling Salesman Problem , 2008, ArXiv.

[6]  G. Nemhauser Column Generation for Linear and Integer Programming , 2012 .

[7]  L MarcoE.,et al.  Dual variable based fathoming in dynamic programs for column generation , 2004 .

[8]  Martin Desrochers,et al.  A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows , 1990, Oper. Res..

[9]  T. Bektaş The multiple traveling salesman problem: an overview of formulations and solution procedures , 2006 .

[10]  Stefan Ropke,et al.  Heuristic and exact algorithms for vehicle routing problems , 2006 .

[11]  Abdullahi A. Ibrahim,et al.  Vehicle Routing Problem with Exact Methods , 2019 .

[12]  Vandana A. Patil,et al.  Capacitated vehicle routing problem , 2017, 2017 2nd International Conference on Communication Systems, Computing and IT Applications (CSCITA).

[13]  Lawrence V. Snyder,et al.  Reinforcement Learning for Solving the Vehicle Routing Problem , 2018, NeurIPS.

[14]  Jacques Desrosiers,et al.  2-Path Cuts for the Vehicle Routing Problem with Time Windows , 1997, Transp. Sci..

[15]  Renato F. Werneck,et al.  Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem , 2004, Math. Program..

[16]  DAVID ÖDLING A metaheuristic for vehicle routing problems based on reinforcement learning , 2018 .

[17]  Kevin M. Curtin,et al.  A Comparative Analysis of Traveling Salesman Solutions from Geographic Information Systems , 2014, Trans. GIS.

[18]  Moshe Dror,et al.  Note on the Complexity of the Shortest Path Models for Column Generation in VRPTW , 1994, Oper. Res..

[19]  Thibaut Vidal,et al.  New benchmark instances for the Capacitated Vehicle Routing Problem , 2017, Eur. J. Oper. Res..

[20]  Lixin Tang,et al.  A multiple traveling salesman problem model for hot rolling scheduling in Shanghai Baoshan Iron & Steel Complex , 2000, Eur. J. Oper. Res..

[21]  Patrick Prosser,et al.  Dynamic VRPs: A Study of Scenarios , 1998 .

[22]  G. D. H. Claassen,et al.  An application of Special Ordered Sets to a periodic milk collection problem , 2007, Eur. J. Oper. Res..

[23]  Michel Gendreau,et al.  Neighborhood Search Heuristics for a Dynamic Vehicle Dispatching Problem with Pick-ups and Deliveries , 2006 .

[24]  Jacques Desrosiers,et al.  VRP with Pickup and Delivery , 2000, The Vehicle Routing Problem.

[25]  Carlos Alberto Ochoa Ortíz Zezzatti,et al.  Comparison between instances to solve the CVRP , 2018, Int. J. Comb. Optim. Probl. Informatics.

[26]  Hassan Basri,et al.  Backtracking search algorithm in CVRP models for efficient solid waste collection and route optimization. , 2017, Waste management.

[27]  Bjørn Nygreen,et al.  Nested column generation applied to the crude oil tanker routing and scheduling problem with split pickup and split delivery , 2012 .

[28]  Rabiat Abdulaziz,et al.  Solving some variants of vehicle routing problem with Branch-and-cut and Column generation algorithms , 2020 .

[29]  Abhiram Ranade,et al.  Improving Branch-And-Price Algorithms For Solving One Dimensional Cutting , 2007 .

[30]  Richard S. Sutton,et al.  Reinforcement Learning: An Introduction , 1998, IEEE Trans. Neural Networks.

[31]  Santiago-Omar Caballero-Morales,et al.  Capacitated vehicle routing problem model for carriers , 2018, Journal of Transport and Supply Chain Management.

[32]  A. Mingozzi,et al.  Lower Bounds and an Exact Method for the Capacitated Vehicle Routing Problem , 2006, 2006 International Conference on Service Systems and Service Management.

[33]  Jacques Desrosiers,et al.  Row-reduced column generation for degenerate master problems , 2014, Eur. J. Oper. Res..

[34]  Ángel Corberán,et al.  Separating capacity constraints in the CVRP using tabu search , 1998, Eur. J. Oper. Res..

[35]  Samy Bengio,et al.  Neural Combinatorial Optimization with Reinforcement Learning , 2016, ICLR.

[36]  Nassirou Lo,et al.  A comparative analysis of the travelling salesman problem: Exact and machine learning techniques , 2019, Open Journal of Discrete Applied Mathematics.

[37]  G. Clarke,et al.  Scheduling of Vehicles from a Central Depot to a Number of Delivery Points , 1964 .

[38]  Jacques Desrosiers,et al.  On Compact Formulations for Integer Programs Solved by Column Generation , 2005, Ann. Oper. Res..

[39]  Navdeep Jaitly,et al.  Pointer Networks , 2015, NIPS.

[40]  Quoc V. Le,et al.  Sequence to Sequence Learning with Neural Networks , 2014, NIPS.

[41]  Michel Gendreau,et al.  A path relinking algorithm for a multi-depot periodic vehicle routing problem , 2013, J. Heuristics.

[42]  Paolo Toth,et al.  Models, relaxations and exact approaches for the capacitated vehicle routing problem , 2002, Discret. Appl. Math..

[43]  J. F. Pierce,et al.  ON THE TRUCK DISPATCHING PROBLEM , 1971 .