Origin-destination matrix estimation with SPSA and STAQ

Gellenbeck, T.L. (2016) Origin-destination matrix estimation with SPSA and STAQ.

Abstract:Origin-destination matrices describe the trafic demand between different zones of a net- work. Their entries, the number of trips for every origin-destination pair, can be assigned to a network to give corresponding link ows and speeds. The OD matrix calibration problem is the problem of finding an OD-matrix which after the assignment step corresponds as good as possible with some given criteria. During this thesis, the only criteria considered are measured values for ow and speed on specific links of the network. This problem can be formulated as a bi-level optimization problem. In the upper level, a minimization of the difference between the estimated ow and the measured ow is done while in the lower level the relation between the OD matrices and the link ows is derived by means of a trafic assignment model. Although there are good methods to solve the problem when using static trafic assignment models, when it comes to (semi-) dynamic assignment models (such as STAQ), the problem becomes more complex and computationally intense. (Semi-) dynamic assignment models accurately model the primary effects of congestion ( ow metering and spillback), which, in the context of matrix calibration, can cause a misinterpretation of the traffic ow measurements. In the situation of (semi-) dynamic models, the sensitivity of the assignment model plays a crucial role in the minimization part in the upper level. This dependence makes the matrix approximation more difficult. To hold the amount of required calculations low, the stochastic approximation method SPSA is used in this thesis. This method requires less measures of the objective function per iteration than other methods (like e.g. FDSA), hence less computations of the assignment model. Since the calculation times are still large for most networks and there are a lot of parameters that need to be tuned, the further exploration of SPSA might be sensible. There also exist modifications for SPSA that might help to reduce the computational time until convergence. The aim of this master thesis is to implement and test the basic version of SPSA and its modifications to minimize the differences in the upper level. This is done in combination with the semi-dynamic assignment model STAQ for the traffic assignment part in the lower level. Also some tests of the different parameters of the SPSA algorithm are performed to improve the convergence of the method further.
Item Type:Essay (Master)
dat.Mobility B.V.
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics, 55 traffic technology, transport technology, 56 civil engineering
Programme:Applied Mathematics MSc (60348)
Link to this item:http://purl.utwente.nl/essays/71077
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