Network Partitioning Algorithms for Solving the Traffic Assignment Problem using a Decomposition Approach

Abstract

Recent methods in the literature to parallelize the traffic assignment problem consider partitioning a network into subnetworks to reduce the computation time. In this article, a partitioning method is sought that generates subnetworks minimizing the computation time of a decomposition approach for solving the traffic assignment (DSTAP). The aim is to minimize the number of boundary nodes, the interflow between subnetworks, and the computation time when the traffic assignment problem is solved in parallel on the subnetworks. Two different methods for partitioning are tested. The first is an agglomerative clustering heuristic that reduces the subnetwork boundary nodes. The second is a flow weighted spectral partitioning algorithm that uses the normalized graph Laplacian to partition the network. The performance of both algorithms is assessed on different test networks. The results indicate that the agglomerative heuristic generates subnetworks with a lower number of boundary nodes, which reduces the per iteration computation time of DSTAP. However, the partitions generated may be heavily imbalanced leading to a higher computation time when the subnetworks are solved in parallel separately at a particular DSTAP iteration. For the Austin network partitioned into four subnetworks, the agglomerative heuristic requires 3.5 times more computation time to solve the subnetworks in parallel. The results also show that the spectral partitioning method is superior for minimizing the interflow between subnetworks. This leads to a faster convergence rate of the DSTAP algorithm.