Genetic algorithms with decomposition procedures for multidimensional 0-1 knapsack problems with block angular structures

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 33, Issue 3, 2003, Pages 410-419

  Kato, Kosuke ^a   Sakawa, Masatoshi ^a  

^a HIROSHIMA UNIVERSITY   (Japan)

Author keywords

Block angular structures; Decomposition procedures; Genetic algorithms; Multidimensional 0 1 knapsack problems; Triple strings

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; GENETIC ALGORITHMS; PROBLEM SOLVING;

ANGULAR STRUCTURE;

LARGE SCALE SYSTEMS;

EID: 0038321354     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2003.811126     Document Type: Article

References (41)

1. T. Bäck, D. B. Fogel, and Z. Michalewicz, Hand Book of Evolutionary Computation. London, U.K.: Oxford Univ. Press, 1997.
2. R. E. Bellman and L. A. Zadeh, "Decision making in a fuzzy environment," Manage. Sci., vol. 17, pp. 141-164, 1970.
3. M. Berkelaar. lp_solve 2.0. [Online]. Available: ftp://ftp.es.ele.tue.nl/ pub/lp_solve
4. I. T. Christou, W. Martin, and R. R. Meyer, "Genetic algorithms as multi-coodinators in large-scale optimization," Dept of Computer Sciences, University of Wisconsin, Madison, WI, Tech. Rep. MP-TR-96-14, 1996.
5. R. J. Dakin, "A tree search algorithm for mixed integer programming problems," J. Comput., vol. 8, pp. 250-255, 1965.
6. G. B. Dantzig and P. Wolfe, "Decomposition principle for linear programs," Oper. Res., vol. 8, pp. 101-111, 1960.
7. -, "The decomposition algorithm for linear programming," Econometrica, vol. 29, pp. 767-778, 1961.
8. L. Davis, Ed., Genetic Algorithms and Simulated Annealing. San Mateo, CA: Morgan Kaufmann, 1987.
9. M. Gen and R. Cheng, Genetic Algorithms & Engineering Design. New York: Wiley, 1996.
10. A. M. Geoffrion, "Elements of large-scale mathematical programming," Manage. Sci., vol. 16, pp. 652-675, 1970.
11. -, "Elements of large-scale mathematical programming," Manage. Sci., vol. 16, pp. 676-691, 1970.
12. -, "Primal resource-directive approaches for optimizing nonlinear decomposable systems," Oper. Res., vol. 18, pp. 375-403, 1970.
13. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, MA: Addison-Wesley, 1989.
14. D. E. Goldberg and R. Lingle, "Alleles, loci, and the traveling salesman problem," in Proc. 1st Int. Conf. Genetic Algorithms Their Applications. Pittsburgh, PA: Lawrence Erlbaum, 1985, pp. 154-159.
15. J. J. Grefenstette, R. Gopal, B. Rosmaita, and D. Van Gucht, "Genetic algorithms for the traveling salesman problem," in Proc. 1st Int. Conf. Genetic Algorithms Their Applications. Pittsburgh, PA: Lawrence Erlbaum, 1985, pp. 160-168.
16. Y. Y. Haimes, K. Tarvainen, T. Shima, and J. Thadathil, Hierarchical Multiobjective Analysis of Large-Scale Systems. New York: Hemisphere, 1989.
17. D. M. Himmelblau, Ed., Decomposition of Large-Scale Problems. Amsterdam, The Netherlands: North-Holland, 1973.
18. J. K. Ho and E. Loute, "Computational experience with advanced implementation of decomposition algorithms for linear programming," Math. Programming, vol. 27, pp. 283-290, 1983.
19. J. K. Ho and R. P. Sundarraj, "An advanced implementation of the Dantzig-Wolfe decomposition algorithm for linear programming," Math. Programming, vol. 20, pp. 303-326, 1981.
20. -, "Computational experience with advanced implementation of decomposition algorithms for linear programming," Math. Programming, vol. 27, pp. 283-290, 1983.
21. -, DECOMP: An Implementation of Dantzig-Wolfe Decomposition for Linear Programming. New York: Springer-Verlag, 1989.
22. J. H. Holland, Adaptation in Natural and Artificial Systems. Ann Arbor, MI: Univ. Michigan Press, 1992.
23. S. Khuri, T. Back, and J. Heitkötter, "The zero/one multiple knapsack problem and genetic algorithms," in Proc. 1994 ACM Symp. Applied Computing, 1994, pp. 188-193.
24. L. S. Lasdon, "Duality and decomposition in mathematical programming," IEEE Trans. Syst. Sci. Cybern., vol. SSC-4, pp. 86-100, 1968.
25. -, Optimization Theory for Large Scale Systems. New York: Macmillan, 1970.
26. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs. Berlin, Germany: Springer-Verlag, 1992.
27. W. Orchard-Hays, Advanced Linear Programming: Computing Techniques. New York: MCGraw-Hill, 1968.
28. M. Sakawa, Fuzzy Sets and Interactive Multiobjective Optimization. New York: Plenum, 1993.
29. M. Sakawa, M. Inuignchi, H. Sunada, and K. Sawada, "Fuzzy multiobjective combinatorial optimization through revised genetic algorithms" (in Japanese), J. Jpn. Soc. Fuzzy Theory Syst., vol. 6, no. 1, pp. 177-186, 1994.
30. M. Sakawa, K. Kato, and T. Shibano, "'An interactive fuzzy satisficing method for multiobjective multidimensional 0-1 knapsack problems through genetic algorithms," in Proc. IEEE Int. Conf. Evolutionary Computation, 1996, pp. 243-246.
31. M. Sakawa, K. Kato, H. Sunada, and Y. Enda, "An interactive fuzzy satisficing method for multiobjective 0-1 programming problems through revised genetic algorithms" (in Japanese), J. Jpn. Soc. Fuzzy Theory Syst., vol. 7, no. 2, pp. 361-370, 1995.
32. M. Sakawa, K. Kato, H. Sunada, and T. Shibano, "Fuzzy programming for multiobjective 0-1 programming problems through revised genetic algorithms," Eur. J. Oper. Res., vol. 97, pp. 149-158, 1997.
33. M. Sakawa and F. Seo, "Interactive multiobjective decisionmaking for large-scale systems and its application to environmental systems," IEEE Trans. Syst., Man, Cybern., vol. SMC-10, pp. 796-806, 1980.
34. M. Sakawa and T. Shibano, "Interactive fuzzy programming for multiobjective 0-1 programming problems through genetic algorithms with double strings," in Fuzzy Logic Foundations and Industrial Applications, D. Ruan, Ed. Norwell, MA: Kluwer, 1996, pp. 111-128.
35. -. "Multiobjective fuzzy satisficing methods for 0-1 knapsack problems through genetic algorithms," in Fuzzy Evolutionary Computation, W. Pedrycz, Ed. Norwll, MA: Kluwer, 1997, pp. 155-177.
36. -, "An interactive fuzzy satisficing method for multiobjective 0-1 programming problems with fuzzy numbers through genetic algorithms with double strings," Eur. J. Oper. Res., vol. 107, pp. 564-574, 1998.
37. -, "An interactive approach to fuzzy multiobjective 0-1 programming problems using genetic algorithms," in Evolutionary Computations and Intelligent Systems, M. Gen and Y. Tsujimura, Eds: Gordon & Breach, Inc., 1999.
38. M. Sakawa and M. Tanaka, Genetic Algorithms (in Japanese). Tokyo, Japan: Asakura, 1995.
39. M. Sakawa and H. Yano, "An interactive fuzzy satisficing method using augmented minimax problems and its application to environmental systems," IEEE Trans. Syst., Man, Cybern., vol. SMC-15, pp. 720-729, 1985.
40. M. Sakawa, H. Yano, and T. Yumine, "An interactive fuzzy satisficing method for multiobjective linear-programming problems and its application," IEEE Trans. Syst., Man, Cybern., vol. SMC-17, pp. 654-661, 1987.
41. D. A. Wismer, Ed., Optimization Methods for Large-Scale Systems ... With Applications. New York: MCGraw-Hill, 1971.