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.

Abstract

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.