Quantum computer-aided job scheduling for storage and retrieval systems
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Stefan Windmann
Abstract
In this paper, a quantum computer-aided approach to job scheduling for automated storage and retrieval systems is introduced. The approach covers application cases, where various objects need to be transported between storage positions and the order of transport operations can be freely chosen. The objective of job scheduling is to arrange the transport operations in a sequence, where the cumulative costs of the transport operations and empty runs between subsequent transport operations are minimized. The scheduling problem is formulated as an asymmetric quadratic unconstrained binary optimization (QUBO) problem, in which the transport operations are modeled as nodes and empty runs are modeled as edges, with costs assigned to each node and each edge. An Quantum Approximate Optimization Algorithm (QAOA) is used to solve the QUBO. Evaluations of the quantum computer-aided job scheduling approach have been conducted on the IBM Q System One quantum computer in Ehningen. In particular, the running time for the solution of the QUBO has been investigated, as well as the scalability of the approach with respect to the required number of qubits.
Zusammenfassung
In diesem Beitrag wird ein Quantencomputer-gestützter Ansatz zur Auftragsplanung für automatisierte Regalbediengeräte vorgestellt. Der Ansatz adressiert Anwendungsfälle, in denen verschiedene Objekte zwischen Lagerpositionen transportiert werden, wobei die Reihenfolge der Transportvorgänge frei gewählt werden kann. Das Ziel der Auftragsplanung ist es, die Reihenfolge so zu optimieren, dass die kumulierten Kosten für die eigentlichen Transportvorgänge sowie zusätzlich erforderliche Leerfahrten minimiert werden. Das Scheduling-Problem wird als asymmetrisches quadratisches, binäres Optimierungsproblem (QUBO) formuliert, in dem die eigentlichen Transportvorgänge als Knoten und die Leerfahrten als Kanten modelliert werden, denen jeweils Kosten zugeordnet werden. Zur Lösung des QUBO-Problems wird ein Quantum Approximate Optimization Algorithm (QAOA) verwendet. Die Evaluierung des vorgeschlagenen Ansatzes wurde auf dem IBM Q System One Quantencomputer in Ehningen durchgeführt, wobei insbesondere die Laufzeit für die Lösung des QUBOs sowie die Skalierbarkeit des Ansatzes in Bezug auf die benötigte Anzahl von Qubits untersucht wurde.
About the author
Stefan Windmann received the Dipl.-Ing. and Dipl.-Inf. degrees in electrical engineering and technical computer sciences from University of Paderborn, Germany, in 2004, where he received the Ph.D. degree in electrical engineering in 2008. He is currently employed as senior scientist at Fraunhofer IOSB-INA in Lemgo, Germany. His current research interests include machine learning algorithms and methods for diagnosis and optimization of automated production systems.
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Author contributions: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The author declares no conflicts of interest regarding this article.
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Editorial
- Vorwort 2024
- Survey
- Unmanned vehicles on the rise: a review on projects of cooperating robot teams
- Methods
- Quantum computer-aided job scheduling for storage and retrieval systems
- On computation of Floquet-transformations and their applicability to controller synthesis for electrical machines
- Adaptive tracking control of a nonholonomic wheeled mobile robot with multiple disturbances and input constraints
- Fault detection in automated production systems based on a long short-term memory autoencoder
- Applications
- SysML’ – incorporating component properties in early design phases of automated production systems
- Persönliches
- Prof. Dr.-Ing. habil. Hartmut Janocha zum 80. Geburtstag
Articles in the same Issue
- Frontmatter
- Editorial
- Vorwort 2024
- Survey
- Unmanned vehicles on the rise: a review on projects of cooperating robot teams
- Methods
- Quantum computer-aided job scheduling for storage and retrieval systems
- On computation of Floquet-transformations and their applicability to controller synthesis for electrical machines
- Adaptive tracking control of a nonholonomic wheeled mobile robot with multiple disturbances and input constraints
- Fault detection in automated production systems based on a long short-term memory autoencoder
- Applications
- SysML’ – incorporating component properties in early design phases of automated production systems
- Persönliches
- Prof. Dr.-Ing. habil. Hartmut Janocha zum 80. Geburtstag
