A Quantum Annealing Approach for Dynamic Multi-Depot Capacitated Vehicle Routing Problem

Quantum annealing (QA) is a quantum computing algorithm that works on the principle of Adiabatic Quantum Computation (AQC), and it has shown significant computational advantages in solving combinatorial optimization problems such as vehicle routing problems (VRP) when compared to classical algorithms. This paper presents a QA approach for solving a variant VRP known as multi-depot capacitated vehicle routing problem (MDCVRP). This is an NP-hard optimization problem with real-world applications in the fields of transportation, logistics, and supply chain management. We consider heterogeneous depots and vehicles with different capacities. Given a set of heterogeneous depots, the number of vehicles in each depot, heterogeneous depot/vehicle capacities, and a set of spatially distributed customer locations, the MDCVRP attempts to identify routes of various vehicles satisfying the capacity constraints such as that all the customers are served. We model MDCVRP as a quadratic unconstrained binary optimization (QUBO) problem, which minimizes the overall distance traveled by all the vehicles across all depots given the capacity constraints. Furthermore, we formulate a QUBO model for dynamic version of MDCVRP known as D-MDCVRP, which involves dynamic rerouting of vehicles to real-time customer requests. We discuss the problem complexity and a solution approach to solving MDCVRP and D-MDCVRP on quantum annealing hardware from D-Wave.

[1]  Ian D. Reid,et al.  Data-Driven Approximations to NP-Hard Problems , 2017, AAAI.

[2]  Travis S. Humble,et al.  Application of Quantum Annealing to Nurse Scheduling Problem , 2019, Scientific Reports.

[3]  D. Venturelli,et al.  Quantum Annealing Implementation of Job-Shop Scheduling , 2015, 1506.08479.

[4]  Daniel A. Lidar,et al.  Quantum annealing versus classical machine learning applied to a simplified computational biology problem , 2018, npj Quantum Information.

[5]  Shinichirou Taguchi,et al.  Quantum Annealing of Vehicle Routing Problem with Time, State and Capacity , 2019, QTOP@NetSys.

[6]  Henry C. W. Lau,et al.  Application of Genetic Algorithms to Solve the Multidepot Vehicle Routing Problem , 2010, IEEE Transactions on Automation Science and Engineering.

[7]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

[8]  E. Tosatti,et al.  Quantum annealing of the traveling-salesman problem. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Theodore Andronikos,et al.  A QUBO Model for the Traveling Salesman Problem with Time Windows , 2019, Algorithms.

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

[11]  R. Biswas,et al.  A quantum annealing approach for fault detection and diagnosis of graph-based systems , 2014, The European Physical Journal Special Topics.

[12]  Michael J. Dinneen,et al.  Solving the Hamiltonian Cycle Problem using a Quantum Computer , 2019, ACSW.

[13]  Daniel A. Lidar,et al.  Consistency of the Adiabatic Theorem , 2004, Quantum Inf. Process..

[14]  P. Shor,et al.  Performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs , 2012, 1208.3757.

[15]  Davide Venturelli,et al.  Quantum Annealing Implementation of Job-Shop Scheduling , 2015, 1506.08479.

[16]  Alán Aspuru-Guzik,et al.  Adiabatic Quantum Simulation of Quantum Chemistry , 2013, Scientific Reports.

[17]  Vicky Choi,et al.  Minor-embedding in adiabatic quantum computation: I. The parameter setting problem , 2008, Quantum Inf. Process..

[18]  G. Rose,et al.  Finding low-energy conformations of lattice protein models by quantum annealing , 2012, Scientific Reports.

[19]  Catherine D. Schuman,et al.  Adiabatic Quantum Computation Applied to Deep Learning Networks , 2018, Entropy.

[20]  S. Lloyd,et al.  Quantum gradient descent and Newton’s method for constrained polynomial optimization , 2016, New Journal of Physics.

[21]  E. Farhi,et al.  A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem , 2001, Science.

[22]  James Clark,et al.  Towards Real Time Multi-robot Routing using Quantum Computing Technologies , 2019, HPC Asia.

[23]  H. Nishimori,et al.  Quantum annealing in the transverse Ising model , 1998, cond-mat/9804280.

[24]  Lei He,et al.  A quantum annealing approach for Boolean Satisfiability problem , 2016, 2016 53nd ACM/EDAC/IEEE Design Automation Conference (DAC).

[25]  Endre Boros,et al.  Local search heuristics for Quadratic Unconstrained Binary Optimization (QUBO) , 2007, J. Heuristics.

[26]  Seth Lloyd,et al.  Adiabatic quantum computation is equivalent to standard quantum computation , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[27]  David Von Dollen,et al.  Traffic Flow Optimization Using a Quantum Annealer , 2017, Front. ICT.

[28]  Scott Pakin,et al.  Embedding Inequality Constraints for Quantum Annealing Optimization , 2019, QTOP@NetSys.

[29]  Nicholas Chancellor,et al.  Domain wall encoding of discrete variables for quantum annealing and QAOA , 2019, Quantum Science and Technology.

[30]  Florian Neukart,et al.  A Hybrid Solution Method for the Capacitated Vehicle Routing Problem Using a Quantum Annealer , 2018, Front. ICT.

[31]  Shinichi Takayanagi,et al.  Application of Ising Machines and a Software Development for Ising Machines , 2019, Journal of the Physical Society of Japan.