Interactive fuzzy stochastic two-level integer programming through fractile criterion optimization

Operational Research

Volumn 12, Issue 2, 2012, Pages 209-227

  Sakawa, Masatoshi ^a   Katagiri, Hideki ^a   Matsui, Takeshi ^a  

^a HIROSHIMA UNIVERSITY   (Japan)

Author keywords

Chance constraints; Double strings; Fractile criterion optimization; Genetic algorithms; Interactive fuzzy programming; Stochastic programming; Two level integer programming

Indexed keywords

EID: 84862262631     PISSN: 11092858     EISSN: 18661505     Source Type: Journal    
DOI: 10.1007/s12351-010-0085-z     Document Type: Article

References (49)

1. Abo-Sinna MA, Baky IA (2007) Interactive balance space approach for solving multi-level multi-objective programming problems. Inf Sci 177: 3397-3410.
2. Back T (1996) Evolutionary algorithms in theory and practice. Oxford University Press, New York.
3. Back T, Fogel DB, Michalewicz Z (1997) Handbook of evolutionary computation. Institute of Physics Publishers, Bristol.
4. Bellman RE, Zadeh LA (1970) Decision making in a fuzzy environment. Manag Sci 17: 141-164.
5. Charnes A, Cooper WW (1959) Chance constrained programming. Manag Sci 6: 73-79.
6. Coello CAC, van Veldhuizen DA, Lamont GB (2002) Evolutionary algorithms for solving multi-objective problems. Kluwer, New York.
7. Dantzig GB (1955) Linear programming under uncertainty. Manag Sci 1: 197-206.
8. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chichester.
9. Eiben AE, Smith JE (2003) Introduction to evolutionary computing. Springer, Berlin.
10. Gen M, Cheng R (1996) Genetic algorithms and engineering design. Wiley, New York.
11. Goldberg DE, Lingle R (1985) Alleles, loci, and the traveling salesman problem. In: Proceedings of 1st international conference on genetic algorithms and their applications, pp 154-159.
12. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison Wesley, Massachusetts.
13. Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor.
14. Kataoka S (1963) A stochastic programming model. Econometrica 31: 181-196.
15. Kozieł S, Michalewicz Z (1999) Evolutionary algorithms, homomorphous mapping, and constrained parameter optimization. Evol Comput 7: 19-44.
16. Lai YJ (1996) Hierarchical optimization: a satisfactory solution. Fuzzy Sets Syst 77: 321-335.
17. Lai YJ, Hwang CL (1992) Fuzzy mathematical programming. Springer, Berlin.
18. Lee ES (2001) Fuzzy multiple level programming. Appl Math Comput 120: 79-90.
19. Luhandjula MK (1987) Multiple objective programming problems with possibilistic coefficients. Fuzzy Sets Syst 21: 135-145.
20. Michalewicz Z (1992) Genetic algorithms + data structures = evolution programs. Springer, Berlin (1992). Second extended edition (1994). Third revised and extended edition (1996).
21. Pramanik S, Roy TK (2007) Fuzzy goal programming approach to multilevel programming problems. Eur J Oper Res 176: 1151-1166.
22. Roghanian E, Sadjadi SJ, Aryanezhad MB (2007) A probabilistic bi-level linear multi-objective programming problem to supply chain planning. Appl Math Comput 188: 786-800.
23. Rommelfanger H (1996) Fuzzy linear programming and applications. Eur J Oper Res 92: 512-527.
24. Sakawa M (1993) Fuzzy sets and interactive multiobjective optimization. Plenum Press, New York.
25. Sakawa M (2000) Large scale interactive fuzzy multiobjective programming. Physica-Verlag, Heidelberg.
26. Sakawa M (2001) Genetic algorithms and fuzzy multiobjective optimization. Kluwer, Boston.
27. Sakawa M, Kato K (2008) Interactive fuzzy multi-objective stochastic linear programming. In: Kahraman C (ed) Fuzzy multi-criteria decision making-theory and applications with recent developments. Springer, New York, pp 375-408.
28. Sakawa M, Nishizaki I (2002a) Interactive fuzzy programming for decentralized two-level linear programming problems. Fuzzy Sets Syst 125: 301-315.
29. Sakawa M, Nishizaki I (2002b) Interactive fuzzy programming for two-level nonconvex programming problems with fuzzy parameters through genetic algorithms. Fuzzy Sets Syst 127: 185-197.
30. Sakawa M, Nishizaki I (2009) Cooperative and noncooperative multi-level programming. Springer, New York.
31. Sakawa M, Yano, H (1985) Interactive fuzzy satisficing method using augumented minimax problems and its application to environmental systems. IEEE Trans Syst Man Cybern SMC 15: 720-729.
32. Sakawa M, Yano H (1989) Interactive decision making for multiobjective nonlinear programming problems with fuzzy parameters. Fuzzy Sets Syst 29: 315-326.
33. Sakawa M, Yano H (1990) An interactive fuzzy satisficing method for generalized multiobjective linear programming problems with fuzzy parameters. Fuzzy Sets Syst 35: 125-142.
34. Sakawa M, Yano H, Yumine T (1987) An interactive fuzzy satisficing method for multiobjective linear-programming problems and its application. IEEE Trans Syst Man Cybern SMC 17: 654-661.
35. Sakawa M, Nishizaki I, Uemura Y (1998) Interactive fuzzy programming for multi-level linear programming problems. Comput Math Appl 36: 71-86.
36. Sakawa M, Nishizaki I, Uemura Y (2000) Interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters. Fuzzy Sets Syst 109: 3-19.
37. Sakawa M, Nishizaki I, Uemura Y (2001) Interactive fuzzy programming for two-level linear and linear fractional production and assignment problems: a case study. Eur J Oper Res 135: 142-157.
38. Sakawa M, Nishizaki I, Uemura Y (2002) A decentralized two-level transportation problem in a housing material manufacturer-interactive fuzzy programming approach. Eur J Oper Res 141: 167-185.
39. Sakawa M, Kato K, Nishizaki I (2003) An interactive fuzzy satisficing method for multiobjective stochastic linear programming problems through an expectation model. Eur J Oper Res 145: 665-672.
40. Sakawa M, Kato K, Katagiri H (2004) An interactive fuzzy satisficing method for multiobjective linear programming problems with random variable coefficients through a probability maximization model. Fuzzy Sets Syst 146: 205-220.
41. Sakawa M, Kato K, Azad MAK, Watanabe R (2005) A genetic algorithm with double string for nonlinear integer programming problems. In: IEEE SMC 2005 conference proceedings. pp 3281-3286.
42. Shih HS, Lai YJ, Lee ES (1996) Fuzzy approach for multi-level programming problems. Comput Oper Res 23: 73-91.
43. Shimizu K, Ishizuka Y, Bard JF (1997) Nondifferentiable and two-level mathematical programming. Kluwer, Boston.
44. Sinha S (2003) Fuzzy programming approach to multi-level programming problems. Fuzzy Sets Syst 136: 189-202.
45. Slowinski R (ed) (1998) Fuzzy sets in decision analysis, operations research and statistics. Kluwer, Dordrecht/Boston/London.
46. Slowinski R, Teghem J (eds) (1990) Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty. Kulwer, Dordrecht/Boston/London.
47. Stancu-Minasian IM (1990) Overview of different approaches for solving stochastic programming problems with multiple objective functions. In: Slowinski R, Teghem J (eds) Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, Kluwer, Dordrecht/Boston/London, pp 71-101.
48. Zimmermann H-J (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1: 45-55.
49. Zimmermann H-J (1987) Fuzzy sets, decision-making and expert systems. Kluwer, Boston.