Quantum Annealing Implementation of Job-Shop Scheduling

TL;DR

This paper demonstrates how quantum annealing can be applied to solve small-scale job-shop scheduling problems by formulating them as quadratic unconstrained binary optimization problems and employing various embedding and preprocessing strategies.

Contribution

It introduces a detailed formulation of JSP for quantum annealing and explores embedding, preprocessing, and partitioning techniques to optimize solutions on D-Wave hardware.

Findings

Successful implementation of JSP on D-Wave Vesuvius processor

Comparison shows quantum approach competitive with classical solvers for small instances

Methodology enables future scaling and optimization of quantum scheduling algorithms

Abstract

A quantum annealing solver for the renowned job-shop scheduling problem (JSP) is presented in detail. After formulating the problem as a time-indexed quadratic unconstrained binary optimization problem, several pre-processing and graph embedding strategies are employed to compile optimally parametrized families of the JSP for scheduling instances of up to six jobs and six machines on the D-Wave Systems Vesuvius processor. Problem simplifications and partitioning algorithms, including variable pruning and running strategies that consider tailored binary searches, are discussed and the results from the processor are compared against state-of-the-art global-optimum solvers.