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A Feasibility-Preserved Quantum Approximate Solver for the Capacitated Vehicle Routing Problem (2308.08785v3)

Published 17 Aug 2023 in quant-ph and cs.DS

Abstract: The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that arises in various fields including transportation and logistics. The CVRP extends from the Vehicle Routing Problem (VRP), aiming to determine the most efficient plan for a fleet of vehicles to deliver goods to a set of customers, subject to the limited carrying capacity of each vehicle. As the number of possible solutions skyrockets when the number of customers increases, finding the optimal solution remains a significant challenge. Recently, the Quantum Approximate Optimization Algorithm (QAOA), a quantum-classical hybrid algorithm, has exhibited enhanced performance in certain combinatorial optimization problems compared to classical heuristics. However, its ability diminishes notably in solving constrained optimization problems including the CVRP. This limitation primarily arises from the typical approach of encoding the given problems as penalty-inclusive binary optimization problems. In this case, the QAOA faces challenges in sampling solutions satisfying all constraints. Addressing this, our work presents a new binary encoding for the CVRP, with an alternative objective function of minimizing the shortest path that bypasses the vehicle capacity constraint of the CVRP. The search space is further restricted by the constraint-preserving mixing operation. We examine and discuss the effectiveness of the proposed encoding under the framework of the variant of the QAOA, Quantum Alternating Operator Ansatz (AOA), through its application to several illustrative examples. Compared to the typical QAOA approach, the proposed method not only preserves the feasibility but also achieves a significant enhancement in the probability of measuring optimal solutions.

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References (30)
  1. G. B. Dantzig and J. H. Ramser, “The truck dispatching problem,” Management science, vol. 6, no. 1, pp. 80–91, 1959.
  2. L. K. Grover, “A fast quantum mechanical algorithm for database search,” in Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, 1996, pp. 212–219.
  3. P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM review, vol. 41, no. 2, pp. 303–332, 1999.
  4. A. Montanaro, “Quantum algorithms: an overview,” npj Quantum Information, vol. 2, no. 1, pp. 1–8, 2016.
  5. E. Farhi, J. Goldstone, and S. Gutmann, “A quantum approximate optimization algorithm,” arXiv preprint arXiv:1411.4028, 2014.
  6. S. Hadfield, Z. Wang, B. O’gorman, E. G. Rieffel, D. Venturelli, and R. Biswas, “From the quantum approximate optimization algorithm to a quantum alternating operator ansatz,” Algorithms, vol. 12, no. 2, p. 34, 2019.
  7. G. E. Crooks, “Performance of the quantum approximate optimization algorithm on the maximum cut problem,” arXiv preprint arXiv:1811.08419, 2018.
  8. C. Moussa, H. Calandra, and V. Dunjko, “To quantum or not to quantum: towards algorithm selection in near-term quantum optimization,” Quantum Science and Technology, vol. 5, no. 4, p. 044009, 2020.
  9. U. Azad, B. K. Behera, E. A. Ahmed, P. K. Panigrahi, and A. Farouk, “Solving vehicle routing problem using quantum approximate optimization algorithm,” IEEE Transactions on Intelligent Transportation Systems, 2022.
  10. A. Glos, A. Krawiec, and Z. Zimborás, “Space-efficient binary optimization for variational quantum computing,” npj Quantum Information, vol. 8, no. 1, p. 39, 2022.
  11. A. Awasthi, F. Bär, J. Doetsch, H. Ehm, M. Erdmann, M. Hess, J. Klepsch, P. A. Limacher, A. Luckow, C. Niedermeier et al., “Quantum computing techniques for multi-knapsack problems,” arXiv preprint arXiv:2301.05750, 2023.
  12. L. Palackal, B. Poggel, M. Wulff, H. Ehm, J. M. Lorenz, and C. B. Mendl, “Quantum-assisted solution paths for the capacitated vehicle routing problem,” arXiv preprint arXiv:2304.09629, 2023.
  13. Z. Wang, N. C. Rubin, J. M. Dominy, and E. G. Rieffel, “Xy mixers: Analytical and numerical results for the quantum alternating operator ansatz,” Physical Review A, vol. 101, no. 1, p. 012320, 2020.
  14. J. Cook, S. Eidenbenz, and A. Bärtschi, “The quantum alternating operator ansatz on max-k vertex cover,” Bulletin of the American Physical Society, vol. 65, 2020.
  15. A. Bärtschi and S. Eidenbenz, “Grover mixers for qaoa: Shifting complexity from mixer design to state preparation,” in 2020 IEEE International Conference on Quantum Computing and Engineering (QCE).   IEEE, 2020, pp. 72–82.
  16. S. Feld, C. Roch, T. Gabor, C. Seidel, F. Neukart, I. Galter, W. Mauerer, and C. Linnhoff-Popien, “A hybrid solution method for the capacitated vehicle routing problem using a quantum annealer,” Frontiers in ICT, vol. 6, p. 13, 2019.
  17. E. Boros, P. L. Hammer, and G. Tavares, “Local search heuristics for quadratic unconstrained binary optimization (qubo),” Journal of Heuristics, vol. 13, pp. 99–132, 2007.
  18. A. Mandal, A. Roy, S. Upadhyay, and H. Ushijima-Mwesigwa, “Compressed quadratization of higher order binary optimization problems,” in Proceedings of the 17th ACM International Conference on Computing Frontiers, 2020, pp. 126–131.
  19. E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, “Quantum computation by adiabatic evolution,” arXiv preprint quant-ph/0001106, 2000.
  20. H. Irie, G. Wongpaisarnsin, M. Terabe, A. Miki, and S. Taguchi, “Quantum annealing of vehicle routing problem with time, state and capacity,” 2019.
  21. R. Harikrishnakumar, S. Nannapaneni, N. H. Nguyen, J. E. Steck, and E. C. Behrman, “A quantum annealing approach for dynamic multi-depot capacitated vehicle routing problem,” arXiv preprint arXiv:2005.12478, 2020.
  22. G. Laporte and F. Semet, “Classical heuristics for the capacitated vrp,” in The vehicle routing problem.   SIAM, 2002, pp. 109–128.
  23. K. Shin and S. Han, “A centroid-based heuristic algorithm for the capacitated vehicle routing problem,” Computing and Informatics, vol. 30, no. 4, pp. 721–732, 2011.
  24. D. de Falco and D. Tamascelli, “An introduction to quantum annealing,” RAIRO-Theoretical Informatics and Applications, vol. 45, no. 1, pp. 99–116, 2011.
  25. A. Lucas, “Ising formulations of many np problems,” Frontiers in physics, vol. 2, p. 5, 2014.
  26. Y. Ruan, S. Marsh, X. Xue, Z. Liu, J. Wang et al., “The quantum approximate algorithm for solving traveling salesman problem,” Computers, Materials and Continua, vol. 63, no. 3, pp. 1237–1247, 2020.
  27. J. T. Seeley, M. J. Richard, and P. J. Love, “The bravyi-kitaev transformation for quantum computation of electronic structure,” The Journal of chemical physics, vol. 137, no. 22, 2012.
  28. C. Gidney, “Constructing large increment gates,” 2015. [Online]. Available: https://algassert.com/circuits/2015/06/12/Constructing-Large-Increment-Gates.html
  29. Qiskit contributors, “Qiskit: An open-source framework for quantum computing,” 2023.
  30. J. Preskill, “Quantum computing in the nisq era and beyond,” Quantum, vol. 2, p. 79, 2018.
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