The Hierarchical Algorithm For Large-scale Linear Programming Problems And Its Application
HE Jian-min, DA Qing-li · 2005
In this paper a new hierarchical algorithm is proposed for solving linear programming problems of high dimensionality. Its coordination level exposes the form of direct iteration, and the first level just requires solving the lower dimensional linear programming problems, both can sufficiently use the results of last iteration, so the calculation efficiency is raised greatly. The convergence of the algorithm is then studied in detail and the conclusions obtained have distinct meaning to the decomposition of the problems. Finally, the algorithm is used to solve the linear programming problems in a port management and the results show that the algorithm has fast convergence and is better than the revised simplex method when the dimensionality of the problems is higher.