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Luis Fernando Perez Armas1, Samuel Deleplanque2, Riad Aggoune3

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This study introduces a hybrid quantum-classical algorithm for the parallel machine scheduling problem. It achieves competitive, high-quality solutions and computational advantages over classical methods.

Keywords:
column generationhybrid algorithmsquantum annealingscheduling

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Area of Science:

  • Operations Research
  • Quantum Computing
  • Computational Optimization

Background:

  • The parallel machine scheduling problem (PMSP) with sequence-dependent set-up times is critical for industrial efficiency.
  • Classical algorithms face challenges in optimizing complex scheduling decisions.

Purpose of the Study:

  • To develop and evaluate a novel hybrid quantum-classical algorithm for PMSP.
  • To leverage quantum annealing for solving subproblems within a column generation framework.

Main Methods:

  • A hybrid heuristic combining classical linear relaxation with quantum annealing (QA) for the pricing subproblem (PSP).
  • Formulating the PSP as a Quadratic Unconstrained Binary Optimization (QUBO) problem to solve the Traveling Salesman Problem (TSP).
  • Utilizing quantum annealers to generate high-quality scheduling columns efficiently.

Main Results:

  • The hybrid approach demonstrates synergy between quantum and classical methods.
  • Achieved competitive high-quality solutions for the PMSP.
  • Showcased computational advantages compared to traditional solution methods.

Conclusions:

  • Hybrid quantum-classical algorithms offer a powerful approach for complex scheduling problems.
  • Quantum annealing can significantly enhance the efficiency of combinatorial optimization tasks.
  • This method provides a viable alternative for industrial scheduling optimization.