Advances in Operations Research
Volume 2009 (2009), Article ID 372548, 17 pages
Research Article

An Interactive Fuzzy Satisficing Method for Multiobjective Nonlinear Integer Programming Problems with Block-Angular Structures through Genetic Algorithms with Decomposition Procedures

Department of Artificial Complex Systems Engineering, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan

Received 19 August 2008; Revised 27 March 2009; Accepted 29 May 2009

Academic Editor: Walter J. Gutjahr

Copyright © 2009 Masatoshi Sakawa and Kosuke Kato. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We focus on multiobjective nonlinear integer programming problems with block-angular structures which are often seen as a mathematical model of large-scale discrete systems optimization. By considering the vague nature of the decision maker's judgments, fuzzy goals of the decision maker are introduced, and the problem is interpreted as maximizing an overall degree of satisfaction with the multiple fuzzy goals. For deriving a satisficing solution for the decision maker, we develop an interactive fuzzy satisficing method. Realizing the block-angular structures that can be exploited in solving problems, we also propose genetic algorithms with decomposition procedures. Illustrative numerical examples are provided to demonstrate the feasibility and efficiency of the proposed method.