Computational Methods for DecentralizedTwo-Level 0-1 Programming Problems throughDistributed Genetic Algorithms

摘要

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 the followers are introduced so as to take fuzziness of their judgments into consideration. The leader maximizes the degree of satisfaction (the value of the membership function) and the followers choose in concert in order to maximize a minimum among their degrees of satisfaction. We propose a modified computational method that solves problems related to the computational method based on the genetic algorithm (the existing method) for obtaining the Stackelberg solution. Specifically, the distributed genetic algorithm is introduced with respect to the upper level genetic algorithm, which handles decision variables for the leader in order to shorten the computational time of the existing method. Parallelization of the lower level genetic algorithm is also performed along with parallelization of the upper level genetic algorithm. In order to demonstrate the effectiveness of the proposed computational method, numerical experiments are carried out.