Skip to main content
SpringerLink
Log in

Multi-objective Rectangular Packing Problem and Its Applications

  • Conference paper
  • First Online:
Book cover Evolutionary Multi-Criterion Optimization (EMO 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2632))

Included in the following conference series:

Abstract

In this paper, Neighborhood Cultivation GA (NCGA) is applied to the rectangular packing problem. NCGA is one of the multi-objective Genetic Algorithms that includes not only the mechanisms of effective algorithms such as NSGA-II and SPEA2, but also the mechanism of the neighborhood crossover. This model can derive good nondominated solutions in typical multi-objective optimization test problems. The rectangular packing problem (RP) is a well-known discrete combinatorial optimization problem in many applications such as LSI layout problems, setting of plant facility problems, and so on. The RP is a difficult and time-consuming problem since the number of possible placements of rectangles increase exponentially as the number of rectangles increases. In this paper, the sequent-pair is used for representing the solution of the rectangular packing and PPEX is used as the crossover. The results were compared to the other methods: SPEA2, NSGA-II and non-NCGA (NCGA without neighborhood crossover). Through numerical examples, the effectiveness of NCGA for the RP is demonstrated and it is found that the neighborhood crossover is very effective both when the number of modules is small and large.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. Deb. Multi-Objective Optimization using Evolutionary Algorithms. Chichester, UK: Wiley, 2001.

    MATH  Google Scholar 

  2. T. Hiroyasu, M. Miki, and S. Watanabe. The New Model of Parallel Genetic Algorithm in Multi-Objective Optimization Problems-Divided Range Multi-Objective Genetic Algorithms. In IEEE Proceedings of the 2000 Congress on Evolutionary Computation, pages 333–340, 2000.

    Google Scholar 

  3. J. D. Knowles and D. W. Corne. Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy. volume 8, pages 149–172, 2000.

    Google Scholar 

  4. H. Murata, K. Fujiyoshi, S. Nakatake, and Y. Kajitani. VLSI Module Placement Based on Rectangle-Packing by the Sequence-Pair. In IEEE Transactions on Computer Aided Design, volume 15, pages 1518–1524, 1996.

    Article  Google Scholar 

  5. S. Nakatake, H. Murata, K. Fujiyoshi, and Y. Kajitani. Module Placement on BSG-Structure and IC Layout Applications. In Proc. of International Conference on Computer Aided Design’ 96, pages 484–491, 1996.

    Google Scholar 

  6. S. Nakaya, S. Wakabayashi, and T. Koide. An adaptive genetic algorithm for vlsi floorplanning based on sequence-pair. In 2000 IEEE International Symposium on Circuits and Systems, (ISCAS2000), volume 3, pages 65–68, 2000.

    Google Scholar 

  7. Y. Shirai and N. Matsumoto. Performance Evaluation of ES Type Genetic Algorithms for Solving Block Layout Problems with Floor Constraints. In PTransaction of JSME (C)65-634, pages 296–304, 1999.

    Google Scholar 

  8. Shinya Watanabe, Tomoyuki Hiroyasu, and Mitsunori Miki. NCGA: Neighborhood Cultivation Genetic Algorithm for Multi-Objective Optimization Problems. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’2002) LATE-BREAKING PAPERS, pages 458–465, 2002.

    Google Scholar 

  9. E. Zitzler, M. Laumanns, and L. Thiele. SPEA2: Improving the Performance of the Strength Pareto Evolutionary Algorithm. In Technical Report 103, Computer Engineering and Communication Networks Lab (TIK), Swiss Federal Institute of Technology (ETH) Zurich, 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Knowledge Engineering and Computer Sciences, Doshisha University, 1-3 Tatara Miyakodani, Kyo-tanabe, Kyoto, 610-0321, JAPAN

    Shinya Watanabe (Graduate Student), Tomoyuki Hiroyasu & Mitsunori Miki

Authors
  1. Shinya Watanabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tomoyuki Hiroyasu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mitsunori Miki
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Sciences and Technology, Centre for Intelligent Systems, University of the Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    Carlos M. Fonseca

  2. Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK

    Peter J. Fleming

  3. Department of Electrical Engineering, Computer Engineering and Networks Laboratory, Swiss Federal Institute of Technology, Gloriastraße 35, 8092, Zürich, Switzerland

    Eckart Zitzler  & Lothar Thiele  & 

  4. Department of Mechanical Engineering, Kanpur Genetic Algorithms Laboratory, Indian Institute of Technology, Kanpur, UP, 208 016, India

    Kalyanmoy Deb

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Watanabe, S., Hiroyasu, T., Miki, M. (2003). Multi-objective Rectangular Packing Problem and Its Applications. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds) Evolutionary Multi-Criterion Optimization. EMO 2003. Lecture Notes in Computer Science, vol 2632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36970-8_40

Download citation

  • DOI: https://doi.org/10.1007/3-540-36970-8_40

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-01869-8

  • Online ISBN: 978-3-540-36970-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation