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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Published in:Electronics & communications in Japan. Part 3, Fundamental electronic science Vol. 80; no. 2; pp. 105 - 120
Main Authors: Yano, Hitoshi, Sakawa, Masatoshi, Sawada, Kazuya
Format: Journal Article
Language:English
Published: New York 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
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
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  surname: Sawada
  fullname: Sawada, Kazuya
  organization: Information System Center, Matsushita Electric Works, Ltd., Osaka, Japan 571
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Snippet This paper considers the large‐scale multiobjective nonlinear programming problem with a block angular structure. For the case where the membership function...
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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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