Mathematical model and solution method of optimization problem of placement of rectangles and circles taking into account special constraints

International Transactions in Operational Research

Volumn 5, Issue 1, 1998, Pages 45-57

  Stoyan, Y G ^a   Yaskov, G N ^a  

^a INSTITUTE OF HYDROBIOLOGY   (Ukraine)

Author keywords

Geometric design; Modelling; Optimization; Packing

Indexed keywords

EID: 0442297986     PISSN: 09696016     EISSN: 14753995     Source Type: Journal    
DOI: 10.1111/j.1475-3995.1998.tb00101.x     Document Type: Article

References (25)

1. Bailleul, I., Tiaibia, K. and Soenen, R. (1983) Nesting two dimensional irregular shapes in anisotropic material. Advances in CAD/CAM: Proc. PROLAMAT 82, Leningrad, USSR, 16-18 May 1982, Amsterdam, etc.
2. Beasley, J. E. (1985) An exact two-dimensional non-guillotine cutting tree search procedure: Operational Research 33, 49-65.
3. Chen, C. S., Ram, B. and Sarin, S. (1989) An integer programming model for a class of assortment problems. Report Dept: Of Ind. North Carolina, A&T State University, Greensboro.
4. Dowsland, K. A. and Dowsland, W. B. (1992) Packing problems. European Journal of Operational Research 56, 2-14.
5. Dowsland, K. A. and Dowsland, W. B. (1993) Heuristic approaches to irregular cutting problems. Working Paper, pp. 1-15.
6. Dyckhoff, H. (1990) A topology of cutting and packing problems. European Journal of Operational Research 44, 145-160.
7. George, J. A., George, J. M. and Lamar, B. W. (1995) Packing different-sized circles into a rectangular container. European Journal of Operational Research 84, 693-712.
8. Gill, P. E., Murray, W. and Wright, M. H. (1981) Practical Optimization. Academic Press, London, New York.
9. Kurosh, A. G. (1976) Lectures on General Algebra. Nauka, Moscow (in Russian).
10. Li, Zh. and Milenkovic, V. (1993) A compaction algorithm for non-convex polygons and its application. 9th Annual ACM Symposium on Computational Geometry. May 19-21.
11. Magas, S. L. (1984) Methods of solving extremal problems in allocation of polygonal geometric objects on a strip. Author’s Abstract Cand. Phys.-Math. Sci. Dissertation. Moscow, (in Russian).
12. Marques, V. M. M., Bispo, C. F. G. and Sentieiro, J. J. S. (1991) A system for the compaction of two dimensional irregular shapes based on simulated annealing. IECON′91 (IEEE)1911-1916.
13. Milenkovic, V., Daniels, K. and Li, Zh. (1992) Placement and compaction of nonconvex polygons for clothing manufacture. Paper for Forth Canadian Conference on Computational Geometry, St. John’s, Newfoundland, Canada.
14. Oliveira, J. F. S. and Ferreira, J. A. S. (1992) Algorithms for nesting problems. In Applied Simulated Annealing, ed. R. V. Vidal, pp. 255-275. Springer Verlag.
15. Rvachev, V. L. (1967) Geometric applications of Boolean algebra. Tehnika, Kiev, pp. 212 Ukraine (Russian).
16. Rvachev, V. L. and Stoyan, Yu. G. (1965) On the problem of optimal cutting of materials. In Problems in Theoretical Cybernetics, pp. 189-199. Naukova dumka, Kiev, Ukraine (in Russian).
17. Rvachev, V. L. and Stoyan, Yu. G. (1965a) Solution algorithms of optimal cutting problem by circles when distances between a pair of circles are given. In Cybernetics, Vol. 3, pp. 77-83. Kiev, Ukraine, (in Russian).
18. Rvachev, V. L. and Stoyan, Yu. G. (1965b) At the problem on optimal placement of circles. Cybernetics, Vol. 4, pp. 70-75. Kiev, Ukraine (in Russian).
19. Stoyan, Yu. G. and Gil’, N. I. (1976) Methods and Algorithms of Allocation of Planar Geometric Objects. Naukova Dumka, Kiev, Ukraine (in Russian).
20. Stoyan, Yu. G. and Ponomarenko, L. D. (1978) Rational placement of geometric bodies in automatic design problems. In Izvestiya AN SSSR, Technical Cybernetics, pp. 37-42. Moscow (in Russian).
21. Stoyan, Yu. G. et al (1996) Mathematical model and method of searching for a local extremum for the non-convex oriented polygons allocation problem. European Journal of Operational Research 92, 192-210.
22. Sweeney, P. E. and Ridenour, E. L. (1989) Cutting and packing problems: A categorized, application orientated research bibliography. Working Paper 610, School of Business Administration, University of Michigan.
23. Taha, H. A. (1975) Integer Programming. Theory, Applications, and Computations. Academic Press, New York, San Francisco, London, pp. 139-176.
24. Yanasse, H. H., Zinober, A. S. I. and Harris, R. G. (1991) Two-dimensional cutting stock with multiple stock sizes. Journal of Operational Research Society 42, 8.
25. Zahn, S. T. (1962) Black box maximization of circular coverage, Journal of Research of the National Bureau Standards 66B.