Fuzzy programming for multiobjective 0–1 programming problems through revised genetic algorithms

✍ Scribed by Masatoshi Sakawa; Kosuke Kato; Hideaki Sunada; Toshihiro Shibano

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 953 KB
• Volume: 97
• Category: Article
• ISSN: 0377-2217
• DOI: 10.1016/s0377-2217(96)00023-9

✦ Synopsis

Recently, genetic algorithms (GAS), a new leaming paradigm that models a natura1 evolution mechanism, have received a great deal of attention regarding their potential as optimization techniques for solving combinatorial optimization problems. In this paper, we focus on multiobjective 0-1 programming problems as a generalization of the traditional single objective ones. By considering the imprecise nature of human judgements, we assume that the decision maker may have a fuzzy goal for each of the objective functions. After eliciting the linear membership functions through the interaction with the decision maker, we adopt the fuzzy decision of Bellman and Zadeh or minimum-operator for combining them. In order to investigate the applicability of the conventional GAS for the solution of the formulated problems, a lot of numerical simulations are performed by assuming several genetic operators. Then, instead of using the penalty function for treating the constraints, we propose three types of revised GAS which generate only feasible solutions. Illustrative numerical examples demonstrate both feasibility and efficiency of the proposed methods.