Free Job-Shop Scheduling With Hardcoded Constraints

• URL: http://arxiv.org/abs/2211.05822v1
• Date: Thu, 10 Nov 2022 19:25:20 GMT
• Title: Free Job-Shop Scheduling With Hardcoded Constraints
• Authors: Gereon Ko{\ss}mann and Lennart Binkowski and Ren\'e Schwonnek
• Abstract summary: We show that desired properties of similarly constructed mixers can be directly linked to a purely classical object. We propose a new variational quantum algorithm that incorporates the underlying group structure more naturally.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hardcoding constrained optimization problems into a variational quantum algorithm often turns out to be a challenging task. In this work we provide a solution for the class of free job-shop problems (FJSP), which we achieve by rigorously employing the symmetries of the classical problem. An established approach for hardcoding the constraints of the closely related traveling salesman problem (TSP) into mixer Hamiltonians was recently given by Hadfield et al.'s Quantum Alternating Operator Ansatz (QAOA). For FJSP, which contains TSP as a subclass, we show that desired properties of similarly constructed mixers can be directly linked to a purely classical object: the group of feasibility-preserving bit value permutations. We also outline a generic way to construct QAOA-like-mixers for these problems. We further propose a new variational quantum algorithm that incorporates the underlying group structure more naturally, and provide a concrete numerical example. Unlike the QAOA, our algorithm allows bounding the amount of parameters necessary to reach every feasible solution from above: If $J$ jobs are to be distributed, we need at most $J {(J - 1)}^{2} / {2}$ parameters.

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