A Cross Entropy Based Multi-Agent Approach to Traffic Assignment Problems

Ma, Tai-Yu; Lebacque, Jean-Patrick

doi:10.1007/978-3-540-77074-9_14

Cited by 9 publications

(19 citation statements)

References 6 publications

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“…To address such questions, it is common to use computer simulations of urban traffic flows (Axhausen & Gärling 1992;Biham et al 1992;Nagel & Schreckenberg 1992;Schadschneider & Schrenkenberg 1993;Daganzo 1994;Herrmann 1996;Klar & Wegener 1998;Charypar & Nagel 2005;Herty et al 2006;Bretti et al 2007;Lämmer et al 2007;Ma & Lebacque 2007;De Martino et al 2009;Padberg et al 2009). However, the frequency and evolution of flow breakdowns and congestion spreading processes are still poorly understood, probably because of the interplay between topology and dynamics (Zhao et al 2005).…”

Section: Introductionmentioning

confidence: 99%

The Spatial Variability of Vehicle Densities as Determinant of Urban Network Capacity

2009

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Section: Introductionmentioning

confidence: 99%

The Spatial Variability of Vehicle Densities as Determinant of Urban Network Capacity

2009

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“…The first order optimality condition states: , which makes the field converge to the fixed points. The reader is referred to (13,14,15) for more detailed description.…”

Section: Solution Algorithmmentioning

confidence: 99%

“…The computation of time-dependent path marginal cost on the multimodal transit system is discussed. In section 4, the solution algorithm based on the cross entropy (CE) method is presented (13,14,15). In Section 5, we validate the proposed solution method on a static small netwok and compare its soultion quality and convergence speed with the MSA method.…”

Section: Introductionmentioning

confidence: 99%

Dynamic System Optimal Routing in Multimodal Transit Network

Lebacque

2013

Transportation Research Record

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The system optimal routing problem has been widely studied for road networks, though less considered for public transit systems. Traditional shortest path–based multimodal itinerary guidance systems may deteriorate the system performance when the assigned lines become congested. The dynamic system optimal routing model for multimodal transit system is formulated for that issue. The transit system is represented by a multilevel graph to explicitly simulate passenger flow and transit system operations. A solution algorithm based on the cross entropy method is proposed, and its performance is compared with the method of successive averages in static and dynamic cases. A numerical study of a simple multimodal transit network provides the basis for comparing system optimal routing and user optimal routing under different congestion levels.

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“…The resulting probability updates shift the users to cheaper choice alternatives towards the UE. The reader is referred to [7][8] for more detailed description. In current application, the user's decision choice concerns only the departure time choice and path choice in the dynamic capacitated transit network.…”

Section: Cross Entropy Learning Algorithmmentioning

confidence: 99%

“…The simulation-based VI problem is generally difficult to solve in the dynamic transit system. For this issue, Ma and Lebacque [7][8] proposed a cross entropy (CE) based solution algorithm to iteratively derive optimal travel choice probabilities towards user equilibrium based on minimizing the Kullback-Liebler relative entropy (cross entropy) between two consecutive probability distributions.In this work, a hybrid algorithm is proposed by combing the multiagent cross entropy learning algorithm and the Hooke-Jeeves algorithm for solving the simulation-based transit network design problem. The proposed algorithm is derivative-free, convenient for solving the simulation-based TNDP.…”

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confidence: 99%

A Hybrid Multiagent Learning Algorithm for Solving the Dynamic Simulation-Based Continuous Transit Network Design Problem

2011

2011 International Conference on Technologies and Applications of Artificial Intelligence

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This paper proposes a hybrid multiagent learning algorithm for solving the dynamic simulation-based bilevel network design problem. The objective is to determine the optimal frequency of a multimodal transit network, which minimizes total users' travel cost and operation cost of transit lines. The problem is formulated as a bilevel programming problem with equilibrium constraints describing non-cooperative Nash equilibrium in a dynamic simulation-based transit assignment context. A hybrid algorithm combing the cross entropy multiagent learning algorithm and Hooke-Jeeves algorithm is proposed. Computational results are provided on the Sioux Falls network to illustrate the performance of the proposed algorithm. assignment problem to obtain a user-optimal equilibrium flow by Frank-Wolfe algorithm and then applied Hooke-Jeeves algorithm to iteratively derive optimal frequencies in a static transit network. Other solution techniques for the bilevel programming problem can be found in [6]. However, for dynamic simulation-based transit assignment, the above derivative-based methods cannot be applied since the functional form of the derivatives is generally unavailable. The simulation-based VI problem is generally difficult to solve in the dynamic transit system. For this issue, Ma and Lebacque [7][8] proposed a cross entropy (CE) based solution algorithm to iteratively derive optimal travel choice probabilities towards user equilibrium based on minimizing the Kullback-Liebler relative entropy (cross entropy) between two consecutive probability distributions.In this work, a hybrid algorithm is proposed by combing the multiagent cross entropy learning algorithm and the Hooke-Jeeves algorithm for solving the simulation-based transit network design problem. The proposed algorithm is derivative-free, convenient for solving the simulation-based TNDP. For the transit system simulation, a multiagent approach is proposed to capture explicitly the transit system dynamics. We propose a multi-layer network to effectively represent the transit network and simulate the movement of different agents (passengers and vehicles). Passenger's waiting time at stop is explicitly calculated subject to the capacity constraint of the vehicle.The rest of the paper is organized as follows. Section 2 describes the mathematical formulation of the bilevel programming problem for the TNDP. It follows in Section 3 the dynamic transit system description based on the multiagent approach along with the transit network model and travel cost formulation. Section 4 presents the proposed solution algorithm by combining the Hooke-Jeeves algorithm and the CE multiagent approach. A state-of-the-art algorithm based on the method of successive average (MSA) for solving simulation-based dynamic traffic assignment problem is proposed. Section 5 provides the computational results of the CE multagent approach and the MSA appraoch on the Sioux Falls network [2] to validate the obtained lower-level user euilibrium solution. Then we show the optimal transit frequency obt...

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A Cross Entropy Based Multi-Agent Approach to Traffic Assignment Problems

Cited by 9 publications

References 6 publications

The Spatial Variability of Vehicle Densities as Determinant of Urban Network Capacity

The Spatial Variability of Vehicle Densities as Determinant of Urban Network Capacity

Dynamic System Optimal Routing in Multimodal Transit Network

A Hybrid Multiagent Learning Algorithm for Solving the Dynamic Simulation-Based Continuous Transit Network Design Problem

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