An interactive fuzzy criteria method for multiobjective 0–1 programming problems with block angular structure using genetic algorithms

✍ Scribed by Kosuke Kato; Masatoshi Sakawa; Toshinori Ikegame

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 233 KB
• Volume: 81
• Category: Article
• ISSN: 1042-0967
• DOI: 10.1002/(sici)1520-6440(199808)81:8<10::aid-ecjc2>3.0.co;2-3

✦ Synopsis

This paper deals with multiobjective 0-1 programming problems having block angular structure. We propose an interactive fuzzy rule-satisfying method in order to obtain satisfactory solutions that take into account objective functions expressed by the decision maker in fuzzy form. In the proposed method, a membership function corresponding to each fuzzy object of the decision maker is specified by interaction with the decision maker. Subsequently, the Parato optimum solution, closest in the minimax sense to a reference point set by the decision maker in the membership function space, is derived by using a genetic algorithm. If satisfaction is not reached, the reference point is updated interactively so that the solution eventually derived is satisfactory to the solution maker. Since the minimax problem solved in this interactive process is a single-object 0-1 programming problem with block angular structure, a genetic algorithm is employed that contains a decomposition process for solving the problem by means of a special configuration. By means of simple numerical experiments, the effectiveness of the proposed method is demonstrated.