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Computational Methods for Two-Level 0-1 Programming Problems through Distributed Genetic Algorithms

In this paper, we consider a two-level 0-1 programming problem in which there is not coordination between the decision maker (DM) at the upper level and the decision maker at the lower level. We propose a revised computational method that solves problems related to computational methods for obtaining the Stackelberg solution. Specifically, in order to improve the computational accuracy of approximate Stakelberg solutions and shorten the computational time of a computational method implementing a genetic algorithm (GA) proposed by the authors, a distributed genetic algorithm is introduced with respect to the upper level GA, which handles decision variables for the upper level DM. Parallelization of the lower level GA is also performed along with parallelization of the upper level GA. The proposed algorithm is also improved in order to eliminate unnecessary computation during operation of the lower level GA, which handles decision variables for the lower level DM. In order to verify the effectiveness of the proposed method, we propose comparisons with existing methods by performing numerical experiments to verify both the accuracy of the solution and the time required for the computation. Keywords—distributed genetic algorithm, Stackelberg solution, two-level 0-1 programming problem.