Skip to main content
SpringerLink
Log in

Minimizing Makespan on Identical Parallel Machines Using Neural Networks

  • Conference paper
Neural Information Processing (ICONIP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4234))

Included in the following conference series:

Abstract

This paper deals with the problem of minimizing the maximum completion time (makespan) of jobs on identical parallel machines. A Hopfield type dynamical neural network is proposed for solving the problem which is known to be NP-hard even for the case of two machines. A penalty function approach is employed to construct the energy function of the network and time evolving penalty coefficients are proposed to be used during simulation experiments to overcome the tradeoff problem. The results of proposed approach tested on a scheduling problem across 3 different datasets for 5 different initial conditions show that the proposed network converges to feasible solutions for all initialization schemes and outperforms the LPT (longest processing time) rule.

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 139.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aiyer, S.V.B., Niranjan, M., Fallside, F.: A theoretical investigation into the performance of the Hopfield model. IEEE Transactions on Neural Networks 1, 204–215 (1990)

    Article  Google Scholar 

  2. Akiyama, Y., Yamashita, A., Kajiura, M., Aiso, H.: Combinatorial Optimization with Gaussian Machines. In: Proceedings IEEE International Joint Conference on Neural Networks, vol. 1, pp. 533–540 (1989)

    Google Scholar 

  3. Brandt, R.D., Wang, Y., Laub, A.J., Mitra, S.K.: Alternative Networks for Solving the Travelling Salesman Problem and the List-Matching Problem. In: Proceedings of the International Conference on Neural Networks, vol. 2, pp. 333–340 (1988)

    Google Scholar 

  4. Cheng, T., Sin, C.: A State-of-the-Art Review of Parallel-Machine Scheduling Research. European Journal of Operation Research 47, 271–292 (1990)

    Article  MATH  Google Scholar 

  5. Coffman, E.G., Garey, M.R., Johnson, D.S.: An application of bin-packing to multi-processor scheduling. SIAM Journal of Computing 7, 1–17 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dogan, H., Guzelis, C.: A new approach based on a time varying penalty parameter providing robustness and fuzziness in spherical clustering. IEEE Transactions on Circuits and Systems-II (accepted paper)

    Google Scholar 

  7. Graham, R.L.: Bounds on multiprocessor timing anomalies. SIAM Journal of Applied Mathematics 17, 416–429 (1969)

    Article  MATH  Google Scholar 

  8. Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics 5, 287–326 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hedge, S., Sweet, J., Levy, W.: Determination of parameters in a Hopfield/Tank computational network. In: Proceedings IEEE International Conference on Neural Networks, vol. 2, pp. 291–298 (1988)

    Google Scholar 

  10. Hinton, G.E., Sejnowski, T.J.: Learning and relearning in Boltzmann machines. In: Rumelhart, D.E., McClelland, J.L. (eds.) Parallel Distributed Processing: Explorations in Microstructure of Cognition, MIT Press, Cambridge (1986)

    Google Scholar 

  11. Hopfield, J.: Neurons with graded response have collective computational properties like of two-state neurons. Proceedings of the National Academy of Sciences of the USA 81, 3088–3092 (1984)

    Article  Google Scholar 

  12. Hopfield, J., Tank, T.W.: Neural computation of decisions in optimization problems. Biological Cybernetics 52, 141–152 (1985)

    MATH  MathSciNet  Google Scholar 

  13. Kamgar-Parsi, B., Kamgar-Parsi, B.: Dynamical Stability and Parameter Selection in Neural Optimization. In: Proceedings of International Joint Conference on Neural Networks, vol. 4, pp. 566–571 (1992)

    Google Scholar 

  14. Lai, W.K., Coghill, G.G.: Genetic Breeding of Control Parameters for the Hopfield/Tank Neural Net. In: Proceedings of the International Joint Conference on Neural Networks, vol. 4, pp. 618–623 (1992)

    Google Scholar 

  15. Mokotoff, E.: Paralel Machine Scheduling Problems: A Survey. Asia-Pacific Journal of Operational Research 18, 193–242 (2001)

    MATH  MathSciNet  Google Scholar 

  16. Peterson, C., Anderson, J.R.: A mean-field theory learning algorithm for neural networks. Complex Systems 1, 995–1019 (1987)

    MATH  Google Scholar 

  17. Smith, K.A.: Neural Networks for Combinatorial Optimization: A Review of More Than a Decade of Research. INFORMS Journal on Computing 11, 15–34 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  18. Van Den Bout, D.E., Miller, T.K.: A Traveling Salesman Objective Function that Works. In: Proceedings of IEEE International Conference on Neural Networks, vol. 2, pp. 299–303 (1988)

    Google Scholar 

  19. Wang, J.: A Time-Varying Recurrent Neural System for Convex Programming. In: Proceedings of IJCNN-91-Seattle International Joint Conference on Neural Networks, pp. 147–152 (1991)

    Google Scholar 

  20. Watta, P.B., Hassoun, M.H.: A Coupled Gradient Network Approach for Static and Temporal Mixed-Integer Optimization. IEEE Transactions on Neural Networks 7, 578–593 (1996)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Dokuz Eylul University, 35100, Bornova-Izmir, Turkey

    Derya Eren Akyol & G. Mirac Bayhan

Authors
  1. Derya Eren Akyol
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Mirac Bayhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Computer Science and Engineering, The Chinese Univ. of Hong Kong, Shatin, N.T., Hong Kong

    Irwin King

  2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong, New Territories,, China

    Jun Wang

  3. The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Lai-Wan Chan

  4. Department of Computer Science and Engineering & Center for Cognitive Science, The Ohio State University, OH 43210, Columbus

    DeLiang Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Akyol, D.E., Bayhan, G.M. (2006). Minimizing Makespan on Identical Parallel Machines Using Neural Networks. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893295_61

Download citation

  • DOI: https://doi.org/10.1007/11893295_61

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46484-6

  • Online ISBN: 978-3-540-46485-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation