Abstract
The two-dimensional irregular cutting problem consists of cutting figures of various shapes from a rectangular area to minimize the area required. We adapt the tabu search metaheuristic to the problem, defining a specific neighborhood and various types of moves and search strategies. A standard type of tabu search, with simple and combined evaluating functions as well as a probabilistic tabu search variants are considered. In the paper, the behavior of different probabilistic approaches and the advantage of a newly proposed random candidate list version over a simple ranking approach are demonstrated. An exact algorithm for finding a placement of the polygon has been used in order to enhance the quality of solutions. Preview of wide range of experiments performed gives an idea about the efficiency of different approaches proposed.
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References
A. Albano and G. Sapuppo. Optimal Allocation of Two-Dimensional Shapes using Heuristic Search Methods. IEEE Transactions on Systems, Man and Cybernetic, 10:242–248, 1980.
F. Avnaim and J.D. Boissonnat. Polygon Placement under Translation and Rotation. Lecture Notes in Computer Science, 294:322–333, 1988.
R.S. Barr, B.L. Golden, J.P. Kelly, M.G.C. Resende, and W.R. Stewart Jr. Designing and Reporting on Computational Experiments with Heuristic Methods. Journal of Heuristics, 1:9–32, 1995.
J. Błażewicz (editor). Computational Complexity Analysis of Algorithms for Automatic Cutting Layout Design (in Polish). Research report for OBR-PTK Tekoma, 1988.
J. Błażewicz, M. Drozdowski, B. Soniewicki, and R. Walkowiak. Two-Dimensional Cutting Problem: Basic Complexity Results and Algorithms for Irregular Shapes. Foundations of Control Engineering, 14:137–160, 1989.
J. Błażewicz, P. Hawryluk, and R. Walkowiak. Using a Tabu Search Approach for Solving the Two-Dimensional Irregular Cutting Problem. Annals of Operations Research, 41:313–325, 1993.
J. Błażewicz and R. Walkowiak. A Local Search Approach for Two-Dimensional Irregular Cutting. OR Spektrum, 17:93–98, 1995.
M.R. Garey, and D.S. Johnson. Strong NP-Completeness Results, Motivation, Examples and Implications. Journal of the ACM, 25:499–508, 1978.
F. Glover. Tabu Search — Part I. ORSA Journal on Computing, 1:190–206, 1989.
F. Glover. Tabu Search — Part II. ORSA Journal on Computing, 2:4–32, 1990.
F. Glover and M. Laguna. Tabu Search. Kluwer, 1997.
F. Glover, E. Taillard, and D. de Werra. A User’s Guide to Tabu Search. Annals of Operations Research, 41:3–28, 1993.
O. Gurel. Circular Graph of Marker Layout. Report No 320–2965, IBM Data Processing Division, New York Scientific Center, 1969.
P.E. Sweeny and E.R. Paternoster. Cutting and Packing Problems: A Categorized Application Orientated Research Bibliography. Journal of the Operational Research Society, 43:691–706, 1992.
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Btażewicz, J., Salvador, A.M., Walkowiak, R. (2002). Tabu Search for Two-Dimensional Irregular Cutting. In: Essays and Surveys in Metaheuristics. Operations Research/Computer Science Interfaces Series, vol 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1507-4_5
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DOI: https://doi.org/10.1007/978-1-4615-1507-4_5
Publisher Name: Springer, Boston, MA
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