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An Improved Version of Tabu Search for Irregular Cutting Problems

  • J Błażewicz
  • R Walkowiak
Conference paper

Abstract

The two-dimensional cutting problem consists of cutting a set of pieces from a sheet of material in order to minimize a waste. The general problem is NP-hard in strong sense. Thus only approximate polynomial algorithms are useful for standard instances of the problem. For one of the most complex problems in this area - the two-dimensional irregular cutting problem a few algorithms of this type have been proposed [2,1,6]. The problem issue considered in the algorithms is constrained to the sub-class in which the elements of arbitrary shapes are to be placed in or cut from the rectangular area, whose one dimension is fixed and the other is to be minimized. The algorithms contain some idea from the artificial intelligence area, make use of the graph theory and are based on the observation of the manual layout generation process as well. Their scheme is rather rigid and hard to adapt for use with different sets of element’s shapes. Also the issue of rectangularity of allocation area is very hard to overcome in those algorithms. Tests made for some algorithms [3] and the results obtained led us through new methods investigation to tabu search approach [5]. The first application of the tabu search for the problem [4] though based on rather simple idea gave very interesting results. Some new elements of the method will be described it this paper.

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References

  1. [1]
    A. Albano, G. Sapuppo (1980) Optimal allocation of two-dimensional shapes using heuristic search methods. IEEE Trans. on Systems, Man and Cybernetics, Vol. SMC-10, No.5Google Scholar
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    R. C. Jr. Art (1966) An approach to the two-dimensional irregular cutting stock problem. IBM Report 320-2006, Cambridge.Google Scholar
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    J. Blaż, M. Drozdowski, B. Soniewicki, R. Walkowiak (1990) Decision support system for cutting irregular shapes — implementation and experimental comparison. Foundations of Computing and Decision Sciences, vol. 15, No. 3–4.Google Scholar
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    J. Blaż, P. Hawryluk, R. Walkowiak (1992): Using tabu search approach for solving two-dimensional irregular cutting problem. Annals of Operations Research on Tabu Search, to appear.Google Scholar
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    F. Glover (1989) Tabu search — Part I. ORSA Journal on Computing 1/3.Google Scholar
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    O. Gurel (1969) Circular graph of marker layout. IBM Data Processing Division, New York Scientific Center Report No. 320-2965.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • J Błażewicz
    • 1
  • R Walkowiak
    • 1
  1. 1.Institute of Computing ScienceTechnical University of PoznańPoznańPoland

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