Quantum Annealing to Solve the Unrelated Parallel Machine Scheduling Problem

Abstract

Quantum computing has emerged in recent years as an alternative to classical computing, which could improve the latter in solving some types of problems. One of the quantum programming models, Adiabatic Quantum Computing, has been successfully used to solve problems such as graph partitioning, traffic routing and task scheduling. Specifically, in this paper we focus on the scheduling on unrelated parallel machines problem. It is a workload-balancing problem where the processing time of any procedure executed on any of the available processing elements is known. Here, the problem is expressed as Quadratic Unconstrained Binary Optimisation, which can be subsequently solved using quantum annealers. The quantum nonlinear programming framework discussed in this work consists of three steps: quadratic approximation of cost function, binary representation of parameter space, and solving the resulting Quadratic Unconstrained Binary Optimisation. One of the novelties in tackling this problem has been to compact the model bearing in mind the repetitions of each task, to make it possible to solve larger scheduling problems.