Efficient Algorithm for the Traffic Assignment Problem with Side Constraints

Feng, Liyang; Xie, Jianli; Nie, Yu; Liu, Xiaobo

doi:10.1177/0361198120912234

Cited by 13 publications

(7 citation statements)

References 22 publications

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“…Another possibility is to predetermine K, once and for all before the bilevel program is solved. This may be achieved by solving the routing game multiple times, using algorithms designed to find all UE path flows (Xie et al, 2018;Feng et al, 2020). A different set of upper-level design variables is fed into the routing game each time, and the union of the UE paths obtained from all scenarios then provides an estimate for K.…”

Section: Algorithms For Stackelberg Congestion Gamesmentioning

confidence: 99%

Differentiable Bilevel Programming for Stackelberg Congestion Games

Li¹,

Yu²,

Wang³

et al. 2022

Preprint

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A Stackelberg congestion game (SCG) is a bilevel program in which a leader aims to maximize their own gain by anticipating and manipulating the equilibrium state at which followers settle by playing a congestion game. Large-scale SCGs are well known for their intractability and complexity. This study approaches SCGs through differentiable programming, which marries the latest developments in machine learning with conventional methodologies. The core idea centers on representing the lower-level equilibrium problem using an evolution path formed by the imitative logit dynamics. It enables the use of automatic differentiation over the evolution path towards equilibrium, leading to a double-loop gradient descent algorithm. We further show the fixation on the lower-level equilibrium may be a self-imposed computational obstacle. Instead, the leader may only look ahead along the followers' evolution path for a few steps, while updating their decisions in sync with the followers through a co-evolution process. The revelation gives rise to a single-loop algorithm that is more efficient in terms of both memory consumption and computation time. Through numerical experiments that cover a wide range of benchmark problems, we find the single-loop algorithm consistently strikes a good balance between solution quality and efficiency, outperforming not only the standard double-loop implementation but also other methods from the literature. Importantly, our results highlight both the wastefulness of "full anticipation" and the peril of "zero anticipation". If a quick-and-dirty heuristic is needed for solving a really large SCG, the proposed single-loop algorithm with a one-step look-ahead makes an ideal candidate.

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Section: Algorithms For Stackelberg Congestion Gamesmentioning

confidence: 99%

Differentiable Bilevel Programming for Stackelberg Congestion Games

Li¹,

Yu²,

Wang³

et al. 2022

Preprint

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“…Although there are some existing algorithms that aim to resolve solution accuracy of subproblems, e.g., origin-based algorithm (Shi et al 2015 ) and path-based greedy algorithm (Feng et al 2020 ), we use a soft constraint technique to handle the three additional constraints of the proposed model for two reasons. Firstly, the soft constraint technique always guarantees the feasible solution because the penalization of violating side constraints is imposed in the objective function instead of destroying the Cartesian product structure of the feasible set.…”

Section: Solution Algorithmmentioning

confidence: 99%

Modeling the α-max capacity of transportation networks: a single-level mathematical programming formulation

Zang

Chen

et al. 2021

Transportation

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Network capacity, defined as the largest sum of origin–destination (O–D) flows that can be accommodated by the network based on link performance function and traffic equilibrium assignment, is a critical indicator of network-wide performance assessment in transportation planning and management. The typical modeling rationale of estimating network capacity is to formulate it as a mathematical programming (MP), and there are two main approaches: single-level MP formulation and bi-level programming (BLP) formulation. Although single-level MP is readily solvable, it treats the transportation network as a physical network without considering level of service (LOS). Albeit BLP explicitly models the capacity and link LOS, solving BLP in large-scale networks is challenging due to its non-convexity. Moreover, the inconsideration of trip LOS makes the existing models difficult to differentiate network capacity under various traffic states and to capture the impact of emerging trip-oriented technologies. Therefore, this paper proposes the α-max capacity model to estimate the maximum network capacity under trip or O–D LOS requirement α. The proposed model improves the existing models on three aspects: (a) it considers trip LOS, which can flexibly estimate the network capacity ranging from zero to the physical capacity including reserve, practical and ultimate capacities; (b) trip LOS can intuitively reflect users’ maximum acceptable O–D travel time or planners’ requirement of O–D travel time; and (c) it is a convex and tractable single-level MP. For practical use, we develop a modified gradient projection solution algorithm with soft constraint technique, and provide methods to obtain discrete trip LOS and network capacity under representative traffic states. Numerical examples are presented to demonstrate the features of the proposed model as well as the solution algorithm.

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“…Attempts have been made to improve the augmented Lagrange multiplier (ALM) method and the inner penalty function (IPF) method [32]. Readers could refer to [32,33] for more information about the CTAP.…”

Section: The Link-capacitated Traffic Assignment (Ctap) Problemmentioning

confidence: 99%