Quantum Shift Scheduling - A Comparison to Classical Approaches

Abstract

Solving discrete optimization problems with constraints is a very common task in industry and research as it is fundamental in solving many planning tasks. In this paper we will look at an instance of a time table problem for generating shift schedules at the German Space Operation Center (GSOC). We describe the implementation of a quantum approach and compare the differences to classical optimization strategies, knowing that the problem sizes given to the quantum systems are not competitive yet. By doing so we are establishing a software chain that is able to map our problem to different physical systems which paves the way to problem solving as a hybrid solution where sub-problems are distributed among classical and quantum hardware. In this study we included three approaches to tackle the described problem. For the quantum part, we included a programmatically generated quantum circuit that yields a solution to a (sub) problem using Grovers algorithm, able to be run on any general quantum computer with sufficiently many qubits of sufficiently high quality. On the classical side, as a validation and benchmark reference, we use a heuristic search method, implemented by GSOCs own planning tool set Plato and PINTA (Lenzen et al. 2012; Nibler et al. 2021) as well as a constraint integer programming formulation solved by an external software framework, such as e. g. GLPK or SCIP (Gamrath et al. 2020). This paper builds on and extends results from (Scherer et al. 2021).