An efficient improvement of the optimal routing search on the network routing problem by removing redundant paths

Abstract

The network routing problem is an important problem to consider behaviors of multiple transportations on a traffic network. This study focuses on the optimal routing problem whose objective is the cooperative and optimal assignment of flows to paths on the network routing. In the optimal routing problem, the amount of flow passing through each path is designated as the decision variable. Therefore, it is difficult to obtain the optimal solution of the optimal routing problem in large-scale networks with a vast number of paths in a realistic time. In many cases, flows pass through a few part of the paths only and no flow passes through other paths in the optimal solution of the optimal routing problem in large-scale networks. If some of paths which are zero-flow paths in the optimal solution can be removed from the decision variables in advance, the efficiency of the optimal routing search is expected to be improved. This study proposes a new solution search method to improve the efficiency of the optimal routing search by removing redundant paths which can be detected in advance by considering a condition with respect to the optimal solution. The effectiveness of the proposed method is confirmed through numerical experiments.