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Asian Conference on Intelligent Information and Database Systems

ACIIDS 2012: Intelligent Information and Database Systems pp 321–330Cite as

DC Programming and DCA for Large-Scale Two-Dimensional Packing Problems

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7197))

Abstract

In this paper, we propose a global optimization method based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) involving cutting plane techniques for solving two-dimensional Bin packing and Strip packing problems. Given a set of rectangular items, we consider problems of allocating each item to larger rectangular standardized units. In two-dimensional bin packing problem, these units are finite rectangles, and the objective is to pack all the items into the minimum number of units. In two-dimensional strip packing problem, there is a single standardized unit of given width, and the objective is to pack all the items within the minimum height. These problems are characterized as BLP (Binary Linear Programming) problems. Thanks to exact penalty technique in DC Programming, the BLP can be reformulated as polyhedral DC program which can be efficiently solved via the proposed DC programming approach. Computational experiments on large-scale dataset involving up to 200 items show the good performance of our algorithm.

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Author information

Authors and Affiliations

  1. Laboratory of Mathematics of Decision and Numerical Analysis, Cheikh Anta Diop University - Dakar, BP 45087, Dakar-Fann, Senegal

    Babacar Mbaye Ndiaye

  2. Laboratory of Theoretical and Applied Computer Science, UFR MIM, University of Paul Verlaine, Metz, Ile du Saulcy, 57045, Metz, France

    Le Thi Hoai An

  3. Laboratory of Mathematics, National Institute for Applied Sciences - Rouen, University Avenue, BP 08, 76801, Saint-Etienne-du-Rouvray, France

    Pham Dinh Tao & Yi Shuai Niu

Authors
  1. Babacar Mbaye Ndiaye
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  2. Le Thi Hoai An
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  3. Pham Dinh Tao
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  4. Yi Shuai Niu
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Editor information

Editors and Affiliations

  1. Department of Electronic Engineering, National Kaohsiung University of Applied Sciences, No. 415, Chien-Kung Road, 80778, Kaohsiung, Taiwan

    Jeng-Shyang Pan

  2. Graduate Institute of Educational Measurement and Statistics, National Taichung University of Education, No. 140, Min-Shen Road, 40306, Taichung, Taiwan

    Shyi-Ming Chen

  3. Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland

    Ngoc Thanh Nguyen

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© 2012 Springer-Verlag Berlin Heidelberg

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Ndiaye, B.M., An, L.T.H., Tao, P.D., Niu, Y.S. (2012). DC Programming and DCA for Large-Scale Two-Dimensional Packing Problems. In: Pan, JS., Chen, SM., Nguyen, N.T. (eds) Intelligent Information and Database Systems. ACIIDS 2012. Lecture Notes in Computer Science(), vol 7197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28490-8_34

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  • DOI: https://doi.org/10.1007/978-3-642-28490-8_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28489-2

  • Online ISBN: 978-3-642-28490-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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