Decentralized two-level 0-1 programming through genetic algorithms with double strings

We consider two-level programming problems in which there are one decision maker (the leader) at the upper level and two or more decision makers (the followers) at the lower level and decision variables of the leader and the followers are 0-1 variables. We assume that there is coordination among the followers while between the leader and the group of all the followers, there is no motivation to cooperate each other, and fuzzy goals for objective functions of the leader and followers are introduced in order to take fuzziness of their judgments into consideration. The leader maximizes the degree of satisfaction and the followers choose in concert so as to maximize a minimum among their degrees of satisfaction. A computational method, which is based on the genetic algorithms, for obtaining a solution to the above mentioned problem is developed. To demonstrate the feasibility and efficiency of the proposed algorithm, numerical experiments are carried out.