Journal of KIISE:Software and Applications (한국정보과학회논문지:소프트웨어및응용)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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Composite Stock Cutting using Distributed Simulated Annealing

분산 시뮬레이티드 어닐링을 이용한 복합 재료 재단

  • 홍철의 (상명대학교 정보통신학부)
  • Published : 2002.02.01
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Abstract

The composite stock cutting problem is to allocate rectangular and/or irregular patterns onto a large composite stock sheet of finite dimensions in such a way that the resulting scrap will be minimized. In this paper, the distributed simulated annealing with the new cost error tolerant spatial decomposition is applied to the composite stock cutting problem in MPI environments. The cost error tolerant scheme relaxes synchronization and chooses small perturbations on states asynchronously in a dynamically changed stream length to keep the convergence property of the sequential annealing. This paper proposes the efficient data structures for representation of patterns and their affinity relations and also shows how to determine move generations, annealing parameters, and a cost function. The spatial decomposition method is addressed in detail. This paper identifies that the final quality is not degraded with almost linear speedup. Composite stock shapes are not constrained to convex polygons or even regular shapes, but the rotations are only allowed to 2 or 4 due to its composite nature.

복합 재료로 구성된 원판으로부터 여러 가지 패턴을 버려지는 부분이 최소화되게 배치시킨 후 절단하는 문제를 복합 재료 재단 문제라 부른다. 본 논문은 목적 함수의 비용 오류를 감내하는 영역 분할 분산 시뮬레이티드 어닐링 알고리즘을 MPI 환경하에서 복합 재료 재단 문제에 적용한다. 비용 오류 감내기법은 최적해 접근 특성을 유지하기 위하여 스트림 길이를 동적으로 변화하며 상태변환을 비동기적으로 수행한다. 또한 복합 재료 재단 도구 개발을 위한 여러 가지 모양을 가진 패턴의 정보 및 친화도 생성, 목적함수, 상태변환 방법, 어닐링 스케줄 및 이를 위한 효율적인 자료 구조에 대하여 정의한다. 배치될 패턴은 정형이나 convex 다각형으로 제한되어 있지 않고 어떠한 모양도 가능하며 원판은 복합 재료의 성격상 2 또는 4 방향으로 고정되어 있다.

Keywords

References

  1. Kirkpatrick, S., Gellatt Jr. C. D., and Vecci, M. P., Optimization by simulated annealing, Science, Vol. 220, pp. 975-986, 1983 https://doi.org/10.1126/science.220.4598.671
  2. Lee, S and Lee, K, Synchronous and asynchronous parallel simulated annealing, with multiple Markov chains, IEEE Trans. on Parallel and Distributed Systems, Vol.7, No. 10, pp. 993-1008, 1996 https://doi.org/10.1109/71.539732
  3. Fowler, R.J., Paterson, M.S., and Tanimoto, S.L., Optimal Packing and covering in the plane are NP-complete. Information Processing Letters, Vol.12, No.3, pp. 133-137, 1981 https://doi.org/10.1016/0020-0190(81)90111-3
  4. Balas, E., Ceria, S., Cornuejols, G., and Natraj, N., Gomery cut revisited, Operations Research Letters 19, pp. 1-9, 1996 https://doi.org/10.1016/0167-6377(96)00007-7
  5. Degraeve, Z., and Vandebroek, M., A mixed integer programming model for solving a layout problem in the fashion industry, Management Science 44, pp. 301-310, 1998 https://doi.org/10.1287/mnsc.44.3.301
  6. Stoyan, Y.G., Novozhilova, M. V., and Kartashov, Mathematical model and method of searching for a local extremum for the non-convex oriented polygons allocation problem, European Journal of Operational Research 92, pp. 193-210, 1996 https://doi.org/10.1016/0377-2217(95)00038-0
  7. Beasley, J. E. An exact two-dimensional nonguillotine cutting tree search procedure, Operations Research, Vol.33, No. 1, pp. 49-64, 1985 https://doi.org/10.1287/opre.33.1.49
  8. Morabito, R., and Arenales, M. N., Staged and constrained two-dimensional guillotine cutting problcms: An AND/OR-graph approach, European Journal of Operational Research 94, pp. 548-560. 1996 https://doi.org/10.1016/0377-2217(95)00128-X
  9. Baker, B.S., Coffman, E.G., and Rivest, R.L., Orthogonal packings in two dimensions, SIAM Journal on Computing, Vol.9, No.4, pp. 846-855, 1980 https://doi.org/10.1137/0209064
  10. Bean, J. C., A multiple-choice genetic algorithm for a nonlinear cutting stock problem, Computing in Science and Engineering, Vol.2, No.2, pp. 80-83, 2000 https://doi.org/10.1109/5992.877404
  11. Dagli, C.H., Poshyanonda, P., New approaches to nesting rectangular patterns, Journal of Intelligent Manufacturing, Vol.8, pp. 177-190, 1997 https://doi.org/10.1023/A:1018517106992
  12. Petridis V., Kazarlis,S., and Bakirtzis, A., Varying fitness functions in genetic algorithm constrained optimization The cutting stock and unit commitment problems, IEEE Trans. on Systems, Man, and Cybernetics-Part B: Cybernetics, Vol.28, No.5, pp. 629-640, 1998 https://doi.org/10.1109/3477.718514
  13. Jakobs, S., On genetic algorithms for the apcking polygons, European Journal of Operational Research 88, pp. 165-181, 1996 https://doi.org/10.1016/0377-2217(94)00166-9
  14. Lutfiyya,II. B. McMillin, P. Poshyanonda, and C. Dagli, Composite stock cutting through simulated anncaling, Mathl. Comput. Modeling, Vol.16, No.1, pp. 57-74, 1992 https://doi.org/10.1016/0895-7177(92)90078-Y
  15. 홍철의, 김영준, 시뮬레이티드 어닐링에서의 비용오류 측정 및 분석, 한국정보처리학회 논문지, 제7권 제4호, pp. 1141-1149, 2000