Skip to main content
SpringerLink
Log in

BRKGA-VNS for Parallel-Batching Scheduling on a Single Machine with Step-Deteriorating Jobs and Release Times

  • Conference paper
  • First Online:
Machine Learning, Optimization, and Big Data (MOD 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10710))

Included in the following conference series:

Abstract

This paper investigates the problem of scheduling step-deteriorating jobs with release times on a single parallel-batching machine. The processing time of each job can be represented as a simple non-linear step function of its starting time. The machine can process up to \( c \) jobs simultaneously as a batch. The objective is to minimize the makespan, and we show that the problem is strongly NP-hard. Then, a hybrid meta-heuristic algorithm BRKGA-VNS combining biased random-key genetic algorithm (BRKGA) and variable neighborhood search (VNS) is proposed to solve this problem. A heuristic algorithm H is developed based on the structural properties of the problem, and it is applied in the decoding procedure of the proposed algorithm. A series of computational experiments are conducted and the results show that the proposed hybrid algorithm can yield better solutions compared with BRKGA, PSO (Particle Swarm Optismization), and VNS.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Li, S., Ng, C.T., Cheng, T.C.E., et al.: Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan. Eur. J. Oper. Res. 210(3), 482–488 (2011)

    Article  MathSciNet  Google Scholar 

  2. Ng, C.T., Barketau, M.S., Cheng, T.C.E., et al.: “Product Partition” and related problems of scheduling and systems reliability: computational complexity and approximation. Eur. J. Oper. Res. 207(2), 601–604 (2010)

    Article  MathSciNet  Google Scholar 

  3. Barketau, M.S., Cheng, T.C.E., Kovalyov, M.Y.: Batch scheduling of deteriorating reworkables. Eur. J. Oper. Res. 189(3), 1317–1326 (2008)

    Article  Google Scholar 

  4. Ji, M., Cheng, T.C.E.: Batch scheduling of simple linear deteriorating jobs on a single machine to minimize makespan. Eur. J. Oper. Res. 202(1), 90–98 (2010)

    Article  MathSciNet  Google Scholar 

  5. Mor, B., Mosheiov, G.: Batch scheduling with step-deteriorating processing times to minimize flowtime. Naval Res. Logist. (NRL) 59(8), 587–600 (2012)

    Article  MathSciNet  Google Scholar 

  6. Graham, R.L., Lawler, E.L., Lenstra, J.K., et al.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discret. Math. 5, 287–326 (1979)

    Article  MathSciNet  Google Scholar 

  7. Damodaran, P., Velez-Gallego, M.C.: Heuristics for makespan minimization on parallel batch processing machines with unequal job ready times. Int. J. Adv. Manuf. Technol. 49(9), 1119–1128 (2010)

    Article  Google Scholar 

  8. Brucker, P., Gladky, A., Hoogeveen, H., et al.: Scheduling a batching machine. J. Sched. 1(1), 31–54 (1998)

    Article  MathSciNet  Google Scholar 

  9. Lee, C.Y.: Minimizing makespan on a single batch processing machine with dynamic job arrivals. Int. J. Prod. Res. 37(1), 219–236 (1999)

    Article  Google Scholar 

  10. Gonçalves, J.F., Resende, M.G.C.: Biased random-key genetic algorithms for combinatorial optimization. J. Heuristics 17(5), 487–525 (2011)

    Article  Google Scholar 

  11. Resende, M.G.C., Ribeiro, C.C.: Biased ranom-key genetic algorithms: an advanced tutorial. In: Proceedings of the 2016 on Genetic and Evolutionary Computation Conference Companion. Association for Computing Machinery, pp. 483–514 (2016)

    Google Scholar 

  12. Hansen, P., Mladenović, N.: Variable Neighborhood Search. Search Methodologies, pp. 313–337. Springer, Ner York (2014). https://doi.org/10.1007/978-1-4614-6940-7_12

    Book  Google Scholar 

  13. Hansen, P., Mladenović, N., Perez-Britos, D.: Variable neighborhood decomposition search. J. Heuristics 7(4), 335–350 (2001)

    Article  Google Scholar 

  14. Kennedy, J.: Particle Swarm Optimization. Encyclopedia of Machine Learning, pp. 760–766. Springer, New York (2011). https://doi.org/10.1007/978-0-387-30164-8_630

    Book  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 71231004, 71601065, 71690235, 71501058, 71690230, 71601060), and Innovative Research Groups of the National Natural Science Foundation of China (71521001), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), Anhui Province Natural Science Foundation (No. 1608085QG167). Panos M. Pardalos is partially supported by the project of Distinguished International Professor by the Chinese Ministry of Education (MS2014HFGY026).

Author information

Authors and Affiliations

  1. School of Management, Hefei University of Technology, Hefei, 230009, China

    Chunfeng Ma, Min Kong & Jun Pei

  2. Department of Industrial and Systems Engineering, Center for Applied Optimization, University of Florida, Gainesville, 32611, USA

    Jun Pei & Panos M. Pardalos

Authors
  1. Chunfeng Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Min Kong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jun Pei
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Panos M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun Pei .

Editor information

Editors and Affiliations

  1. University of Catania, Catania, Italy

    Giuseppe Nicosia

  2. University of Florida, Gainesville, FL, USA

    Panos Pardalos

  3. University of Catania, Catania, Italy

    Giovanni Giuffrida

  4. Harvard University, Cambridge, MA, USA

    Renato Umeton

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ma, C., Kong, M., Pei, J., Pardalos, P.M. (2018). BRKGA-VNS for Parallel-Batching Scheduling on a Single Machine with Step-Deteriorating Jobs and Release Times. In: Nicosia, G., Pardalos, P., Giuffrida, G., Umeton, R. (eds) Machine Learning, Optimization, and Big Data. MOD 2017. Lecture Notes in Computer Science(), vol 10710. Springer, Cham. https://doi.org/10.1007/978-3-319-72926-8_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-72926-8_34

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72925-1

  • Online ISBN: 978-3-319-72926-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation