Network dual steepest-edge methods for solving capacitated multicommodity network problems

This paper presents a two-phased network dual steepest-edge method for solving capacitated multicommodity network problems. In the first phase, an advanced starting solution in concert with a dual steepest-edge method is applied to solve each capacitated single-commodity network problem. At each iteration, either the primal infeasibility is improved or the dual objective value is inceased. In the second phase, the steepest-edge selection criterion is used to determine the leaving infeasible coupling constraint. By maintaining dual feasibility while improving the dual objective value, the number of infeasible coupling constraints is monotonically reduced to zero. The finite convergency property of this algorithm is shown. Finally, this algorithm is coded using Pascal language and tested in several problems. Results show this algorithm is promising.