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

Abstract

Word count: 28 4448 words text+ 29 188 words abstract+ 30 580 words references+ 31 5 tables/figures ×250 words (each) = 6466 words 32 ABSTRACT 1Recent methods in the literature to parallelize the traffic assignment problem consider partitioning 2 a network into subnetworks to reduce the computation time for large-scale networks. In this arti-3 cle, we seek a partitioning method that generates subnetworks minimizing the computation time 4 of a decomposition approach for solving the traffic assignment (DSTAP). We aim to minimize the 5 number of boundary nodes, the inter-flow between subnetworks, and the computation time when 6 the traffic assignment problem is solved in parallel on the subnetworks. We test two different meth-7 ods for partitioning. The first is an agglomerative clustering algorithm heuristic that decomposes 8 a network with the objectives of minimizing subnetwork boundary nodes. The second is a flow 9 weighted spectral clustering algorithm that uses the normalized graph Laplacian to partition the 10 network. 11We assess the performance of both algorithms on different test networks. The results indi-12 cate that the agglomerative heuristic generates subnetworks with a low number of boundary nodes, 13 which reduces the per iteration computation time of DSTAP. However, the partitions generated may 14 be heavily imbalanced leading to significantly higher computation time when the subnetworks are 15 solved in parallel separately at a certain DSTAP iteration. For the Austin network partitioned into 16 4 subnetworks, the agglomerative heuristic requires 3.5 times more computational time to solve 17 the subnetworks in parallel. We also show that the spectral partitioning method is superior in terms 18 of minimizing the inter-flow between subnetworks. This leads to a faster convergence rate of the 19 DSTAP algorithm. 20

A Topological Approach to Partitioning Flow Networks for Parallel Simulation

“…To address concerns of disproportionately long links and limited connectivity, transportation researchers have used both spectral analysis and domain decomposition techniques. These have been compared to METIS's multi-level partitioning algorithms, with mixed results (Yahia et al 2018;Jianbo Shi and Malik 2000;Ji and Geroliminis 2012;Johnson et al 2016). As yet, the literature is not dispositive on the best approach; nor is their clear agreement on the conditions where one approach might outperform another.…”

“…Spectral analysis and domain decomposition each have an underlying assumption of undirected graphs, meaning that the edge from node V i to node V j has the same weight as the edge from V j to V i (Ji and Geroliminis 2012;Yahia et al 2018). Domain decomposition, additionally, leverages clustered loops that have a high level of "group connectivity" to sidestep the individual node connectivity limit (Yahia et al 2018). However, water drainage Tiernan, March 21, 2022 networks are directed graphs that do not fit the undirected transportation paradigm.…”

“…A formal NP-Complete partitioning solution requires proving C(X) is minimized. However, many algorithms simply reduce the objective function iteratively, approaching the minimum until no improvement can be achieved (Yahia et al 2018;Gupta 1997;Meyerhenke et al 2014), which is taken as an acceptable solution even if it cannot be proven to be the minimum. Other algorithms (Li et al 2017;Schlag et al 2018) and BIPquick herein, focus on efficiency of the algorithm rather than minimization of the solution.…”

Dynamic Routing of Heterogeneous Users After Traffic Disruptions Under a Mixed Information Framework

“…The number of calculations required to estimate the path marginal cost would be reduced in this case, since the path marginal cost can be inferred from the spatiotemporal correlation between various routes. Including spatiotemporal correlation in a region based model which includes between-region marginal costs could further improve performance by reducing the number of calculations needed to determine the marginal cost within each region and providing additional methods of parallelization such as network partitioning (Yahia et al, 2018).…”

Research on Road Network Partitioning Considering the Coupling of Network Connectivity and Traffic Attributes

“…While simple, this method is restrictive and fails to consider segment attributes. The heuristic algorithm suffers from slow convergence and difficulty in reducing the connection between sub-areas [10]. Other clustering algorithms, such as k-means [11], spectral clustering [12], and related graph partitioning methods such as N-cut [13,14], α-cut [15], and k-way [16] are commonly used in road network partitioning.…”