research-article

Open access

Taming the State-space Explosion in the Makespan Optimization of Flexible Manufacturing Systems

Authors:

Ramon Schiffelers,

Henk CorporaalAuthors Info & Claims

ACM Transactions on Cyber-Physical Systems, Volume 5, Issue 2

Article No.: 15, Pages 1 - 26

https://doi.org/10.1145/3426194

Published: 04 January 2021 Publication History

All formats PDF

Abstract

This article presents a modular automaton-based framework to specify flexible manufacturing systems and to optimize the makespan of product batches. The Batch Makespan Optimization (BMO) problem is NP-Hard and optimization can therefore take prohibitively long, depending on the size of the state-space induced by the specification. To tame the state-space explosion problem, we develop an algebra based on automata equivalence and inclusion relations that consider both behavior and structure. The algebra allows us to systematically relate the languages induced by the automata, their state-space sizes, and their solutions to the BMO problem. Further, we introduce a novel constraint-based approach to systematically prune the state-space based on the the notions of nonpermutation-repulsiveness and permutation-attractiveness. We prove that constraining a nonpermutation-repulsing automaton with a permutation-attracting constraint always reduces the state-space. This approach allows us to (i) compute optimal solutions of the BMO problem when the (additional) constraints are taken into account and (ii) compute bounds for the (original) BMO problem (without using the constraints). We demonstrate the effectiveness of our approach by optimizing an industrial wafer handling controller.

Supplementary Material

a15-bastos-apndx.pdf (bastos.zip)

Supplemental movie, appendix, image and software files for, Taming the State-space Explosion in the Makespan Optimization of Flexible Manufacturing Systems

Download
155.85 KB

References

[1]

Marianne Akian, Ravindra Bapat, and Stephane Gaubert. 2006. Max-plus algebra. Disc. Math. Applic. 39 (11 2006).

[2]

Chaudhry Imran Ali and Khan Abid Ali. 2016. A research survey: Review of flexible job shop scheduling techniques. Int. Trans. Op. Res. 23, 3 (2016), 551--591.

[3]

Ali Allahverdi. 2016. A survey of scheduling problems with no-wait in process. Eur. J. Op. Res. 255, 3 (2016), 665--686.

[4]

Ali Allahverdi, C. T. Ng, T. C. E. Cheng, and Mikhail Y. Kovalyov. 2008. A survey of scheduling problems with setup times or costs. Eur. J. Op. Res. 187, 3 (2008), 985--1032.

[5]

Francois Baccelli, Guy Cohen, Geert Jan Olsder, and Jean-Pierre Quadrat. 2001. Synchronization and linearity: An algebra for discrete event systems.

[6]

J. Bastos, J. P. M. Voeten, S. Stuijk, H. Corporaal, and R. R. H. Schiffelers. 2018. Exploiting specification modularity to prune the optimization-space of manufacturing systems. In Proceedings of the Software and Compilers for Embedded Systems Conference (SCOPES’18).

Digital Library

[7]

Kris Braekers, Katrien Ramaekers, and Inneke Van Nieuwenhuyse. 2016. The vehicle routing problem: State of the art classification and review. Comput. Industr. Eng. 99 (2016), 300--313.

Digital Library

[8]

Ed Brinksma. 1990. Constraint-oriented specification in a constructive formal description technique. In Stepwise Refinement of Distributed Systems Models, Formalisms, Correctness, J. W. de Bakker, W.-P. de Roever, and G. Rozenberg (Eds.). Springer Berlin Heidelberg, 130--152. https://link.springer.com/chapter/10.1007%2F3-540-52559-9_63.

[9]

R. de Groote, J. Kuper, H. Broersma, and G. J. M. Smit. 2012. Max-plus algebraic throughput analysis of synchronous dataflow graphs. In Proceedings of the 38th Euromicro Conference on Software Engineering and Advanced Applications. 29--38.

Digital Library

[10]

Robert Doering and Yoshio Nishi. 2007. Handbook of Semiconductor Manufacturing Technology. Vol. 32. CRC Press.

[11]

Twan Basten et al. 2020. Scenarios in the Design of Flexible Manufacturing Systems. Springer International Publishing, Cham, 181--224.

[12]

S. T. J. Forschelen, J. M. van de Mortel-Fronczak, Rong Su, and J. E. Rooda. 2012. Application of supervisory control theory to theme park vehicles. Disc. Event Dynam. Syst. 22, 4 (2012), 511--540.

Digital Library

[13]

Bernd Heidergott, Geert Jan Olsder, and Jacob van der Woude. 2006. Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications. Princeton University Press.

[14]

Robin Milner. 1983. Calculi for synchrony and asynchrony. Theoret. Comput. Sci. 25, 3 (1983), 267--310.

[15]

J. P. Nogueira Bastos. 2018. Modular Specification and Design Exploration for Flexible Manufacturing Systems. Ph.D. Dissertation. Technical University of Eindhoven, The Netherlands.

[16]

Peter J. Ramadge and W. Murray Wonham. 1987. Supervisory control of a class of discrete event processes. SIAM J. Contr. Optim. 25, 1 (1987), 206--230.

Digital Library

[17]

Ofira Shmueli, Nava Pliskin, and Lior Fink. 2015. Explaining over-requirement in software development projects: An experimental investigation of behavioral effects. Int. J. Project Manag. 33, 2 (2015), 380--394.

[18]

Dirk A. van Beek, Wan Fokkink, D. Hendriks, A. Hofkamp, Jasen Markovski, J. M. van de Mortel-Fronczak, and Michel A. Reniers. 2014. CIF 3: Model-based engineering of supervisory controllers. In Proceedings of the International Conference on Tools and Algorithms for the Construction and Analysis of Systems.

[19]

B. van der Sanden, J. Bastos, J. Voeten, M. Geilen, M. Reniers, T. Basten, J. Jacobs, and R. Schiffelers. 2016. Compositional specification of functionality and timing of manufacturing systems. In Proceedings of the Forum on Specification and Design Languages.

[20]

Bram van der Sanden, Marc Geilen, Michel A. Reniers, and Twan Basten. 2018. Partial-order reduction for performance analysis of max-plus timed systems. In Proceedings of the 18th International Conference on Application of Concurrency to System Design.

[21]

J. van Pinxten, M. Geilen, T. Basten, U. Waqas, and L. Somers. 2016. Online heuristic for the multi-objective generalized traveling salesman problem. In Proceedings of the Design, Automation Test in Europe Conference Exhibition (DATE’16). 822--825.

[22]

Joost van Pinxten, Umar Waqas, Marc Geilen, Twan Basten, and Lou Somers. 2017. Online scheduling of 2-re-entrant flexible manufacturing systems. ACM Trans. Embed. Comput. Syst. 16, 5s (Sept. 2017).

[23]

U. Waqas. 2017. Scheduling and Variation-aware Design of Self-re-entrant Flowshops. Ph.D. Dissertation. Technische Universiteit Eindhoven.

Cited By

van der Sanden BBlankenstein YSchiffelers RVoeten J(2021)LSAT: Specification and Analysis of Product Logistics in Flexible Manufacturing Systems2021 IEEE 17th International Conference on Automation Science and Engineering (CASE)10.1109/CASE49439.2021.9551412(1-8)Online publication date: 23-Aug-2021
https://doi.org/10.1109/CASE49439.2021.9551412

Index Terms

Taming the State-space Explosion in the Makespan Optimization of Flexible Manufacturing Systems

Recommendations

Exploiting Specification Modularity to Prune the Optimization-Space of Manufacturing Systems
SCOPES '18: Proceedings of the 21st International Workshop on Software and Compilers for Embedded Systems

In this paper we address the makespan optimization of industrial-sized manufacturing systems. We introduce a framework which specifies functional system requirements in a compositional way and automatically computes makespan optimal solutions respecting ...
An Efficient State Space Generation for the Analysis of Real-Time Systems

State explosion is a well-known problem that impedes analysis and testing based on state-space exploration. This problem is particularly serious in real-time systems because unbounded time values cause the state space to be infinite even for simple ...
A Relational Notation for State Transition Systems

A relational notation for specifying state transition systems is presented. Several refinement relations between specifications are defined. To illustrate the concepts and methods, three specifications of the alternating-bit protocol are given. The ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Cyber-Physical Systems

ACM Transactions on Cyber-Physical Systems Volume 5, Issue 2

Special Issue on Time for CPS and Regular Papers

April 2021

238 pages

ISSN:2378-962X

EISSN:2378-9638

DOI:10.1145/3446669

Editor:
Tei-Wei Kuo
City University of Hong Kong and National Taiwan University, Taiwan

Issue’s Table of Contents

Copyright © 2021 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Journal Family

ACM Journals for the Design of Smart and Connected Systems

Publication History

Published: 04 January 2021

Accepted: 01 September 2020

Revised: 01 June 2020

Received: 01 May 2019

Published in TCPS Volume 5, Issue 2

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed

Funding Sources

Nederlandse Organisatie voor Wetenschappelijk Onderzoek
ASML
Technische Universiteit Eindhoven

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

1
Total Citations
View Citations
297
Total Downloads

Downloads (Last 12 months)127
Downloads (Last 6 weeks)27

Reflects downloads up to 28 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

van der Sanden BBlankenstein YSchiffelers RVoeten J(2021)LSAT: Specification and Analysis of Product Logistics in Flexible Manufacturing Systems2021 IEEE 17th International Conference on Automation Science and Engineering (CASE)10.1109/CASE49439.2021.9551412(1-8)Online publication date: 23-Aug-2021
https://doi.org/10.1109/CASE49439.2021.9551412

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

HTML Format

View this article in HTML Format.

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Media

Figures

Other

Tables

View Issue’s Table of Contents