Fuzzy multiobjective 0-1 programming through revised genetic algorithms

In this paper, we consider multiobjective 0-1 programming problems and propose the fuzzy decision making method based on revised genetic algorithms. In the proposed method, by considering the imprecise nature of human judgements, it is assumed that the decision maker (DM) has a fuzzy goal for each of the objective functions and adopt the minimum-operator for combining the membership functions for fuzzy goals of the DM. Then the formulated problem can be reduced to the usual 0-1 programming problems. Considering the difficulty to solve 0-1 programming problems, we propose the revised genetic algorithm in which the `random 0-1 reverse method' is introduced to deal with the linear constraints whose parameters may be positive or negative. In order to show the efficiency of the proposed method, we apply the proposed method to two types of problems; one is the real-world decision making problem, i.e., the media selection planning problem, and the others are numerical examples, which involves 3 objectives, 30 variables and 5, 10 or 15 constraints, and whose parameters are generated at random.