Table 1 - uploaded by John Gibb
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Successive averaging algorithms are commonly used to solve equilibrium for model systems combining travel demand and traffic assignment. Each iteration updates the solution estimate as a weighted average of the previous estimate and a new iterate from the feedback cycle. The chosen weights are crucial to whether iteration converges toward the solut...
Contexts in source publication
Context 1
... MSA gives equal weight to all iterates from the beginning, the alternatives give more weight to the most recent iterates, which are presumably closer to the solution. After George and Powell's work in dynamic programming (14), plus contributions to dynamic and stochastic traffic assignment by Hiele (15), Liu et al (16), and others cited, Table 1 compiles several step size schedules. (20) , , , , 1 1 ...
Context 2
... step size schedules in Table 1 satisfy Blum's theorem, except Reset MSA with unending resets, and McClain's; McClain's is designed to approach constant asymptotically. All can reduce the rate at which the step size decreases, compared to MSA. ...
Context 3
... or tuning a step size schedule from Table 1 is by trial-and-error, with controls for both the early step sizes and the rate of reduction. If a particular model is known to converge efficiently with a certain constant step size, then one can start with a schedule providing roughly similar step sizes among the number of iterations normally needed. ...
Context 4
... alternative convergence safeguard is proposed here, which avoids the risk of wasted linesearch iterations altogether: impose upper and lower bounds on the step size, such that both satisfy the criteria of Blum's theorem. Many of the step size formulas in Table 1 Figure 2 shows the application algorithm, generically for any choice of feedback variable (trips, skims, etc.) and either of the two step size formulas. Note that the second iteration uses an assumed step size rather than one computed from the initial point , because in many experimental runs, this iteration's computed step size was almost always very close to 1, due to independence and vastly different magnitudes between and . ...
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Citations
... The authors attributed this improvement to the system's ability to leverage shared information to optimize route planning [38]. There have been many studies that considered the impact of route guidance systems on travel time [39], travel cost [40,41], driver behavior [17,19,[42][43][44][45], cell occupancy and travel demand [42], and vehicle performance [46]. Another way to classify routing systems is based on the techniques used to make routing decisions. ...
... Other studies have investigated SO-DTA using path-based assignment. For instance, different studies have examined the topic using optimal control formulation methodology [17,19,[43][44][45]. The studies used trial and error, non-linear convex programming, sensitivity analysis, non-convex non-linear programming, and optimal control methods. ...
Highlights
What are the main findings?
Both transportation and communication networks should be considered simultaneously for a successful implementation of communication network for dynamic route guidance systems.
There is a need for in-depth investigation to address the scalability and robustness of comprehensive communication architecture for dynamic route guidance systems.
An integrated framework that considers the transportation and communication networks is presented.
What is the implication of the main finding?
The proposed framework shows promise for real-life implementation of comprehensive communication network for dynamic route guidance systems.
Combining the transportation and communication networks may lead to a robust and efficient communication architecture for dynamic route guidance systems.
Abstract
Due to its anticipated impacts on the performance of transportation systems, intelligent transport systems (ITS) have emerged as one of the most extensively investigated topics. The U.S. Department of Transportation has defined route guidance systems (RGSs) as one of the main categories within ITS. Systems like these are essential components when managing travel and transportation. While RGSs play a pivotal role in both present and future transportation, there has been limited research on evaluating the effectiveness and dependability of integrating them with vehicular communication frameworks. Therefore, this paper aims to evaluate the RGS architectures proposed to date in the literature, providing comparisons and classifications based on their structures and requirements for communication systems. Moreover, it explores existing, next generation, as well as prospective choices for V2X communication technologies, evaluating how well they contribute to the development of RGS applications by integrating them with potential communication systems. Specifically, this study assesses the suitability of communication technologies in meeting the requirements of RGS applications. In conclusion, it suggests a framework for integrating RGS and V2X systems and offers directions for future research in this area.
... It can be seen that the BB step size requires milder computational efforts than the steepest descent method and runs substantially faster (Yuan, 2008). The BB method has recently been extended and promisingly reported to solve various transportation problems, such as the travel demand forecasting model (Gibb, 2016) and stochastic user equilibrium models (Du et al., 2021). Interested readers please refer to Du et al. (2021) for a detailed review of the BB step size. ...
The non-additive traffic equilibrium problem (NaTEP) overcomes the inadequacies of the additivity assumption in traditional traffic equilibrium models by relaxing the cost incurred on each path that is not a simple sum of the link costs on that path. The computation of the NaTEP heavily depends on the efficiency of the step size determination. This paper aims to accelerate the path-based gradient projection (GP) algorithm for solving the NaTEP using the Barzilai-Borwein (BB) step size scheme. The GP algorithm with the BB step size scheme uses the solution information of the last two iterations to determine a suitable step size and avoids extra evaluations of the mapping value. The proposed algorithm only needs to perform one-time projection onto the nonnegative orthant at each iteration. Two approaches with and without column generation are considered in the GP algorithm implementation. A non-additive shortest path algorithm is adopted for the column generation approach. Numerical results on four transportation networks demonstrate the superior efficiency and robustness of the GP algorithm with the BB step size scheme over the self-adaptive GP method.
... However, the existing solution algorithms often need to either frequently evaluate the objective function (and/or its derivative) or use inflexible step size determination rules (e.g., monotonically decreasing the step size sequence), which impede the efficiency on both speed and precision of the algorithmic convergence. Recently, a novel step size determination scheme, called the BB step size ( Barzilai & Borwein, 1988 ), has been reported to show great potential for solving the travel demand forecasting models ( Gibb, 2016 ). The BB step size originates from the Newton-type method (secondorder approach), but it involves nearly no extra cost over the standard gradient method (first-order approach) for solving various optimization problems. ...
... The BB step size has been extended to solve other mathematical problems, e.g., unconstrained/constrained system of equations ( Cruz & Raydan, 2003 ;Liu & Feng, 2019 ) and variational inequality with convex constraints ( He, Han & Li, 2012 ). Also, the BB step size has been employed in practice to solve the travel demand forecasting problem ( Gibb, 2016 ). Besides, the convergence of the BB step size has been extensively discussed by Barzilai and Borwein (1988 ), Raydan (1993 ) and Yuan (2008 ). ...
Step size determination (also known as line search) is an important component in effective algorithmic development for solving the traffic assignment problem. In this paper, we explore a novel step size determination scheme, the Barzilai-Borwein (BB) step size, and adapt it for solving the stochastic user equilibrium (SUE) problem. The BB step size is a special step size determination scheme incorporated into the gradient method to enhance its computational efficiency. It is motivated by the Newton-type methods, but it does not need to explicitly compute the second-order derivative. We apply the BB step size in a path-based traffic assignment algorithm to solve two well-known SUE models: the multinomial logit (MNL) and cross-nested logit (CNL) SUE models. Numerical experiments are conducted on two real transportation networks to demonstrate the computational efficiency and robustness of the BB step size. The results show that the BB step size outperforms the current step size strategies, i.e., the Armijo rule and the self-regulated averaging scheme.
