Skip to main content
SpringerLink
Log in

A Neuro-Based Optimization Algorithm for Tiling Problems with Rotation

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper describes a neuro-based optimization algorithm for 2 dimensional (2-D) tiling problems which are to pack a checkerboard with polyominoes. First, we review the previous neuro-based parallel algorithms for tiling problems without rotation. Next, we expand the algorithm, which has been proposed for 2-D tiling problems without rotation, to the optimization one for 2-D tiling problems with rotation, where a novel nonlinear energy function is defined. Finally, we show the simulation results and the estimation.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hopfield, J. J. and Tank, D. W.: Neural computation of decisions in optimization problems, Bio. Cybern., 52 (1985), 141-152.

    Google Scholar 

  2. Joppe, A., Cardon, H. R. A. and Bioch, J. C.: A Neural Networks for Solving the Traveling Salesman Problem on the Basis of City Adjacency in the Tour, International Neural Network Conference, Paris, (1989).

  3. Ninomiya, H., Sato, K., Nakayama, T. and Asai, H.: Neural Network Approach to Traveling Salesman Problem Based on Hierarchical City Adjacency, Proc. IEEE/ICNN '95, 5 (1995), 2626-2631.

    Google Scholar 

  4. Golomb, S. W.: Tiling with sets of polyominoes. J. Combinat. Theory, 9 (1970), 60-71.

    Google Scholar 

  5. Akiyama, Y., Yamashita, A., Kajiura, M. and Aiso, H.: Combinatorial optimization with Gaussian machines, Proc. Int. Joint Conf. Neural Networks., (1989).

  6. Takefuji, Y. and Lee, K. C.: A Parallel Algorithm for Tiling Problems, IEEE Trans. Neural Networks, 1 (1990), 143-145.

    Google Scholar 

  7. Asai, H., Nakayama, T. and Ninomiya, H.: Tiling Algorithm with Fitting Violation Function for Analog Neural Array, Proc. IEEE/ICNN '96, 1 (1996), 565-570.

    Google Scholar 

  8. Ninomiya, H., Nakayama, T. and Asai, H.: Analog Neuro-Based Approach to Tiling Problem Using Fitting Function of Polyominoes, IEICE Trans. Fundamentals, J80-A(11) (1997), 1951-1959.

    Google Scholar 

  9. Yamamoto, H., Nakayama, T., Ninomiya, H. and Asai, H.: A Neuro-Based Optimization Algorithm for Three Dimensional Cylindric Puzzles, IEICE Trans. Fundamentals, E80-A(6) (1997), 1049-1054.

    Google Scholar 

  10. Yamamoto, H., Nakayama, T., Ninomiya, H. and Asai, H.: Application of Neuro-Based Optimization Algorithm to Three Dimensional Cylindric Puzzles, Proc. IEEE/ICNN '97, 2 (1997), 1246-1250.

    Google Scholar 

  11. Yamamoto, H., Ninomiya, T. and Asai, H.: Application of Neuro-Based Optimization to 3-D Rectangular Puzzles, Proc. IEEE/ICNN '98, May 1998, pp. 1652-1656.

  12. Yamamoto, H. Ninomiya, H. and Asai, H.: A Neuro-Based Optimization Algorithm for Rectangular Puzzles, IEICE Trans. Fundamentals, E81-A(6) (1998), 1113-1118.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Systems Engineering, Shizuoka University 3-5-1, Johoku, Hamamatsu, 432-8561, Japan

    Shinsuke Manabe & Hideki Asai

Authors
  1. Shinsuke Manabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hideki Asai
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Manabe, S., Asai, H. A Neuro-Based Optimization Algorithm for Tiling Problems with Rotation. Neural Processing Letters 13, 267–275 (2001). https://doi.org/10.1023/A:1011365314563

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011365314563

Search

Navigation