A Dantzig-Wolfe Decomposition-Based Heuristic for Off-line Capacity Calibration of Dynamic Traffic Assignment

Abstract

One of the critical elements in considering any real-time traffic management strategy requires assessing network traffic dynamics. Traffic is inherently dynamic, since it features congestion patterns that evolve over time and queues that form and dissipate over a planning horizon. Dynamic traffic assignment (DTA) is therefore gaining wider acceptance among agencies and practitioners as a more realistic representation of traffic phenomena than static traffic assignment. Though it is imperative to calibrate the DTA model such that it can accurately reproduce field observations and avoid erroneous flow predictions when evaluating traffic management strategies, DTA calibration is an onerous task due to the large number of variables that can be modified and the intensive computational resources required. To compliment other research on behavioral and trip table issues, this work focuses on DTA capacity calibration and presents an efficient Dantzig-Wolfe decompositionbased heuristic that decomposes the problem into a restricted master problem and a series of pricing prob- * lems. The restricted master problem is a capacity manipulation problem, which can be solved by a linear programming solver. The pricing problem is the user optimal DTA which can be optimally solved by an existing combinatorial algorithm. In addition, the proposed set of dual variable approximation techniques is one of a very limited number of approaches that can be used to estimate network-wide dual information in facilitating algorithmic designs while maintaining scalability. Two networks of various sizes are empirically tested to demonstrate the efficiency and efficacy of the proposed heuristic. Based on the results, the proposed heuristic can calibrate the network capacity and match the counts within a 1% optimality gap.

Cross‐comparison of convergence algorithms to solve trip‐based dynamic traffic assignment problems

“…It corresponds © 2020 Computer-Aided Civil and Infrastructure Engineering to Wardrop's first principle (Wardrop, 1952), where users are assumed to be perfectly rational and have perfect information on the network's status (Miaou, Summers, & Lieu, 1999), that is, the predicted travel time on all the relevant alternatives is known at the beginning of all the users' trips (Ng & Waller, 2012). Implementing this simple behavioral rule for Dynamic Network Loading (DNL) is far from trivial (Lin, Valsaraj, & Waller, 2011). DNL is the combination of DTA with a traffic simulator that calculates network states and travel times (Yu, Ma, & Zhang, 2008).…”

A dual approximation-based quantum-inspired genetic algorithm for the dynamic network design problem

“…Therefore, we consider an alternative paradigm of approximating the dual variables from the upper-level objective function (1) in the single level form. It is worth noting that similar solution techniques have been used in the Dantzig-Wolfe decomposition solution scheme (Lin, Karoonsoontawong et al 2011) and in the calibration of capacities in a UODTA model (Lin, Valsaraj et al 2011), with various problem-specific modifications. Following the strategy discussed above, when the lower level user equilibrium objective function is removed, the BLPNDP collapses to a single level system optimum network design problem (SONDP) whose (primal) formulation is shown below.…”

Column Generation‐Based Approach for Solving Large‐Scale Ready Mixed Concrete Delivery Dispatching Problems

“…The dual variables thus obtained are feasible and optimal to the linear relaxation of compact formulation as well. Dantzig-Wolfe reformulation also has been used in transportation particularly for dynamic assessment of traffic such as in Lin et al (2011a), Lin et al (2011b), and Chang et al (2001), but in this article we only focus on VRP-based problems.…”