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Applying quantum approximate optimization to the heterogeneous vehicle routing problem.

David Fitzek1,2, Toheed Ghandriz3,4, Leo Laine3,4

  • 1Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden. davidfi@chalmers.se.

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This study explores quantum computing for the heterogeneous vehicle routing problem (HVRP). Researchers used the quantum approximate optimization algorithm (QAOA) to find approximate solutions, showing potential for quantum approaches to complex logistics challenges.

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Area of Science:

  • Quantum Computing
  • Operations Research
  • Combinatorial Optimization

Background:

  • Quantum computing presents novel heuristics for solving complex combinatorial problems.
  • Small- and intermediate-scale quantum devices enable testing these heuristics on practical problem sizes.
  • The heterogeneous vehicle routing problem (HVRP) is a key combinatorial challenge in logistics.

Purpose of the Study:

  • Investigate the application of quantum computing to find approximate solutions for the HVRP.
  • Utilize the quantum approximate optimization algorithm (QAOA) for HVRP.
  • Analyze the scalability and performance of quantum algorithms for logistics optimization.

Main Methods:

  • Formulated a mapping of the HVRP to an Ising Hamiltonian.
  • Simulated the QAOA on problem instances using up to 21 qubits.
  • Compared the performance of various classical optimizers within the QAOA framework.

Main Results:

  • The number of qubits required for the HVRP mapping scales quadratically with the number of customers.
  • Demonstrated the feasibility of using QAOA for approximate HVRP solutions.
  • Identified a trade-off between classical optimizer performance and runtime in QAOA for HVRP.

Conclusions:

  • Quantum computing, specifically QAOA, shows promise for addressing the heterogeneous vehicle routing problem.
  • The qubit requirements for this quantum approach scale quadratically with problem size (number of customers).
  • Further research is needed to optimize classical optimizers for QAOA in logistics applications.