Decentralized Two-Level 0-1 Programming through Distributed Genetic Algorithms

In this paper, we consider decentralized two-level 0-1 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 each decision maker 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. We propose a modified computational method that solves problems related to computational methods for obtaining the Stackelberg solution. Specifically, in order to shorten the computational time of a computational method implementing a genetic algorithm (GA) proposed by us, a distributed genetic algorithm is introduced with respect to the upper level GA, which handles decision variables for the leader. Parallelization of the lower level GA is also performed along with parallelization of the upper level GA. In order to verify the effectiveness of the proposed method, we propose a comparison with the existing method by performing numerical experiments to verify both the accuracy of the solution and the time required for the computation.