PC–SPSA: Employing Dimensionality Reduction to Limit SPSA Search Noise in DTA Model Calibration

Abstract

Calibration and validation have long been a significant topic in traffic model development. In fact, when moving to Dynamic Traffic Assignment (DTA) models, the need to dynamically update the demand and supply component creates a considerable burden on the existing calibration algorithms, often rendering them impractical. These calibration approaches are mostly restricted either due to non-linearity or increasing problem dimensionality. Simultaneous Perturbation Stochastic Approximation (SPSA) has been proposed for DTA model calibration, with encouraging results, for more than a decade. However, it often fails to converge reasonably with the increase in problem size and complexity. In this research, we combine SPSA with Principal Components Analysis (PCA), to form a new algorithm we call PC-SPSA. PCA limits the search area of SPSA within the structural relationships captured from historical estimates in lower dimensions, reducing the problem size and complexity. We formulate the algorithm, demonstrate its operation and explore its performance using an urban network of Vitoria, Spain. Practical issues that emerge from the scale of different variables and bounding their values are also analyzed through a sensitivity analysis using a non-linear synthetic function.

Improving the accuracy and efficiency of online calibration for simulation-based Dynamic Traffic Assignment

“…In contrast with the aforementioned approaches which focus on demand parameters, Balakrishna et al [2007] proposed a more generic solution method for the offline problem based on the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm that simultaneously incorporates demand and supply side parameters and is applicable to any type of measurement data. Several variants of the SPSA algorithm have since been proposed including weighted SPSA or W-SPSA [Lu et al, 2015a], cluster-wise SPSA or c-SPSA [Tympakianaki et al, 2015], discrete W-SPSA [Oh et al, 2019], PC-SPSA [Qurashi et al, 2019], and gradient approximation [Cipriani et al, 2011]. A more detailed review of the offline calibration problem can be found in Osorio [2019], Djukic [2014].…”

“…10: A gradient incidence matrix and its corresponding optimal graph with 3 colors At this point, we would like to briefly discuss similarities and differences of this approach compared to variants of the SPSA algorithm. Despite the overt similarity, the variants of the SPSA including c-SPSA [Tympakianaki et al, 2015], w-SPSA [Lu et al, 2015a] and PC-SPSA [Qurashi et al, 2019] do not in fact identify means of partitioning the parameters in the manner that we wish to do (i.e. ensuring that any two parameters in the same partition do not jointly affect a measurement).…”

Assignment Matrix Free Algorithms for On-line Estimation of Dynamic Origin-Destination Matrices

“…This is achieved by transforming the dataset into a new set of variables-the Principal Components (PCs)-which are uncorrelated and ordered so that the first few retain most of the variation present in all of the original variables (Jolliffe, 2002). PCA is an assumption-free procedure that already calculates how ODs are correlated (Prakash et al, 2018;Qurashi et al, 2019). As showed by Djukic et al (2012) and Prakash et al (2018), replacing the OD demand with its Principal Components reduces the problem complexity thus making the ODDE problem simpler.…”

Composite Surrogate for Likelihood-Free Bayesian Optimisation in High-Dimensional Settings of Activity-Based Transportation Models

“…Calibration of Preday ABM has been performed in several studies, whereby parameters are estimated by Simultaneous perturbation stochastic approximation (SPSA) method with its variants [28,29,31]. However, all studies considered reduction of the dimensionality of the parameter space either by sensitivity analysis (SA) [34] or principal component analysis (PCA) [19].…”

“…Application of the Preday ABM in simulating various environments requires systematic adjustments or calibration of a large set of parameters (further referred to as ABM parameters), in order to align the associated outputs more closely to the observed values or true output statistics. For that purpose, various optimisation methods are adopted, including primarily gradient-free metaheuristics [28,29,31]. However, Bayesian inference with the recent developments provides a valuable analytical approach for the calibration process [35,36], a great advantage of which is the elimination of necessity to simulate a large sample set in finding the global optima [14,18,20,36].…”