A three-level fuzzy satisficing method for large-scale multiobjective nonlinear programming problems
This paper considers the large‐scale multiobjective nonlinear programming problem with a block angular structure. For the case where the membership function that specifies the fuzzy goal of the decision‐maker for each object function is the general nonlinear function, a three‐level decomposition by...
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| Vydáno v: | Electronics & communications in Japan. Part 3, Fundamental electronic science Ročník 80; číslo 2; s. 105 - 120 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Wiley Subscription Services, Inc., A Wiley Company
01.02.1997
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| ISSN: | 1042-0967, 1520-6440 |
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| Abstract | This paper considers the large‐scale multiobjective nonlinear programming problem with a block angular structure. For the case where the membership function that specifies the fuzzy goal of the decision‐maker for each object function is the general nonlinear function, a three‐level decomposition by the right‐hand side allocation is proposed in order to derive the compromise solution for the decision‐maker.
In the proposed method, the add‐operator is defined as an operator that integrates the fuzzy goals. It is noted that the corresponding compromise solution of the decision‐maker is the optimal solution for the problem for certain weight coefficients in the membership function space. A three‐level optimization method is the proposed where the weight coefficient problem in the objective function space is solved by the decomposition by the right‐hand side allocation. By updating the weight coefficient vector iteratively, the compromise solution for the decision‐maker finally is derived following the add‐operator. A computer program is constructed based on the proposed method. By applying the method to a simple numerical example with a block angular structure, the validity of the algorithm is examined. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(2): 105–120, 1997 |
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| AbstractList | This paper considers the large‐scale multiobjective nonlinear programming problem with a block angular structure. For the case where the membership function that specifies the fuzzy goal of the decision‐maker for each object function is the general nonlinear function, a three‐level decomposition by the right‐hand side allocation is proposed in order to derive the compromise solution for the decision‐maker.
In the proposed method, the add‐operator is defined as an operator that integrates the fuzzy goals. It is noted that the corresponding compromise solution of the decision‐maker is the optimal solution for the problem for certain weight coefficients in the membership function space. A three‐level optimization method is the proposed where the weight coefficient problem in the objective function space is solved by the decomposition by the right‐hand side allocation. By updating the weight coefficient vector iteratively, the compromise solution for the decision‐maker finally is derived following the add‐operator. A computer program is constructed based on the proposed method. By applying the method to a simple numerical example with a block angular structure, the validity of the algorithm is examined. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(2): 105–120, 1997 |
| Author | Sawada, Kazuya Sakawa, Masatoshi Yano, Hitoshi |
| Author_xml | – sequence: 1 givenname: Hitoshi surname: Yano fullname: Yano, Hitoshi organization: Nagoya Municipal Women's College, Nagoya, Japan 464 – sequence: 2 givenname: Masatoshi surname: Sakawa fullname: Sakawa, Masatoshi organization: Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan 739 – sequence: 3 givenname: Kazuya surname: Sawada fullname: Sawada, Kazuya organization: Information System Center, Matsushita Electric Works, Ltd., Osaka, Japan 571 |
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| References | R. Slowinski. A multicriteria fuzzy linear programming method for water supply system development planning. Fuzzy Sets and Systems, 19, pp. 217-237 (1986). M. Sakawa, H. Yano, and K. Sawada. Primal decomposition method for multiobjective structured nonlinear programs with fuzzy goals. Cybernetics and Systems: An International Journal, 26, pp. 413-426 (1995). M. Sakawa, H. Yano, and K. Sawada. Fuzzy dual decomposition method for large-scale multiobjective nonlinear programming problem with block angular structure. Trans. I.E.I.C.E., Japan, J77-A, pp. 1250-1257 (Sept. 1994). M. Sakawa. Fuzzy Sets and Interactive Multi-objective Optimization. Plenum Press, New York (1993). Y. Y. Haimes, K. Tarvainen, T. Shima, and J. Thadathil. Hierarchical Multiobjective Analysis of Large-Scale Systems. Hemisphere Publishing Corporation (1989). T. Fukao and J. Toyoda. Application of Computer to Power System. Sangyo Tosho Co. (1972). K. Shimizu. Theory of Multiobject and Competition. Kyoritsu Publ. Co. (1982). A. K. Bit, M. P. Biswal, and S. S. Alam. Fuzzy programming approach to multicriteria decision making transportation problem. Fuzzy Sets and Systems, 50, pp. 135-141 (1992). H. Odate. Programming problems in water resource system. System & Contr., 22, 3, pp. 138-145 (1978). R. E. Bellmann and L. A. Zadeh. Decision making in a fuzzy environment. Management Sci., 17, pp. 141-164 (1970). A. K. Bit, M. P. Biswal, and S. S. Alam. Fuzzy programming approach to multiobjective solid transportation problem. Fuzzy Sets and Systems, 57, pp. 183-194 (1993). L. S. Lasdon, A. D. Waren, and M. W. Ratner. GRG2 User's Guide. Technical Memorandum, University of Texas (1980). M. Tamura. Large-scale system-Modeling, control, and decision-making. Shokodo Publ. (1986). L. S. Lasdon (K. Shimizu, Tr.). Theory of Optimization for Large-Scale System. Nikkan Kogyo Press (1973). 1993; 57 1994; J77‐A 1978; 22 1995; 26 1986 1973 1986; 19 1972 1993 1982 1980 1970; 17 1992; 50 1989 1978 |
| References_xml | – reference: K. Shimizu. Theory of Multiobject and Competition. Kyoritsu Publ. Co. (1982). – reference: Y. Y. Haimes, K. Tarvainen, T. Shima, and J. Thadathil. Hierarchical Multiobjective Analysis of Large-Scale Systems. Hemisphere Publishing Corporation (1989). – reference: L. S. Lasdon, A. D. Waren, and M. W. Ratner. GRG2 User's Guide. Technical Memorandum, University of Texas (1980). – reference: M. Sakawa. Fuzzy Sets and Interactive Multi-objective Optimization. Plenum Press, New York (1993). – reference: M. Sakawa, H. Yano, and K. Sawada. Fuzzy dual decomposition method for large-scale multiobjective nonlinear programming problem with block angular structure. Trans. I.E.I.C.E., Japan, J77-A, pp. 1250-1257 (Sept. 1994). – reference: R. Slowinski. A multicriteria fuzzy linear programming method for water supply system development planning. Fuzzy Sets and Systems, 19, pp. 217-237 (1986). – reference: M. Tamura. Large-scale system-Modeling, control, and decision-making. Shokodo Publ. (1986). – reference: L. S. Lasdon (K. Shimizu, Tr.). Theory of Optimization for Large-Scale System. Nikkan Kogyo Press (1973). – reference: T. Fukao and J. Toyoda. Application of Computer to Power System. Sangyo Tosho Co. (1972). – reference: R. E. Bellmann and L. A. Zadeh. Decision making in a fuzzy environment. Management Sci., 17, pp. 141-164 (1970). – reference: A. K. Bit, M. P. Biswal, and S. S. Alam. Fuzzy programming approach to multiobjective solid transportation problem. Fuzzy Sets and Systems, 57, pp. 183-194 (1993). – reference: M. Sakawa, H. Yano, and K. Sawada. Primal decomposition method for multiobjective structured nonlinear programs with fuzzy goals. Cybernetics and Systems: An International Journal, 26, pp. 413-426 (1995). – reference: H. Odate. Programming problems in water resource system. System & Contr., 22, 3, pp. 138-145 (1978). – reference: A. K. Bit, M. P. Biswal, and S. S. Alam. Fuzzy programming approach to multicriteria decision making transportation problem. Fuzzy Sets and Systems, 50, pp. 135-141 (1992). – start-page: 303 year: 1978 end-page: 323 – year: 1986 – volume: 17 start-page: 141 year: 1970 end-page: 164 article-title: Decision making in a fuzzy environment publication-title: Management Sci. – year: 1982 – volume: 19 start-page: 217 year: 1986 end-page: 237 article-title: A multicriteria fuzzy linear programming method for water supply system development planning publication-title: Fuzzy Sets and Systems – volume: 57 start-page: 183 year: 1993 end-page: 194 article-title: Fuzzy programming approach to multiobjective solid transportation problem publication-title: Fuzzy Sets and Systems – year: 1980 – volume: 26 start-page: 413 year: 1995 end-page: 426 article-title: Primal decomposition method for multiobjective structured nonlinear programs with fuzzy goals publication-title: Cybernetics and Systems: An International Journal – year: 1989 – volume: 22 start-page: 138 issue: 3 year: 1978 end-page: 145 article-title: Programming problems in water resource system publication-title: System & Contr. – year: 1973 – year: 1972 – volume: 50 start-page: 135 year: 1992 end-page: 141 article-title: Fuzzy programming approach to multicriteria decision making transportation problem publication-title: Fuzzy Sets and Systems – volume: J77‐A start-page: 1250 year: 1994 end-page: 1257 article-title: Fuzzy dual decomposition method for large‐scale multiobjective nonlinear programming problem with block angular structure publication-title: Trans. I.E.I.C.E., Japan – year: 1993 |
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| SubjectTerms | add-operator block angular structure decomposition by right-hand side allocation fuzzy goal large-scale multiobjective nonlinear programming three-level optimization |
| Title | A three-level fuzzy satisficing method for large-scale multiobjective nonlinear programming problems |
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