Iterative Backpropagation Method for Efficient Gradient Estimation in Bilevel Network Equilibrium Optimization Problems

Patwary A.U.z (), Shuling Wang () and Hong K. Lo ()
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Patwary A.U.z: Department of Civil, Geological and Mining Engineering, Polytechnique Montreal, Montréal, Québec H3T 1J4, Canada; Department of Civil Engineering, The Hong Kong University of Science and Technology, Hong Kong, China
Shuling Wang: Department of Civil Engineering, The Hong Kong University of Science and Technology, Hong Kong, China; Key Laboratory of Road and Traffic Engineering of Ministry of Education, Tongji University, Shanghai 201804, China
Hong K. Lo: Department of Civil Engineering, The Hong Kong University of Science and Technology, Hong Kong, China

Transportation Science, 2023, vol. 57, issue 5, 1134-1159

Abstract: Network optimization or network design with an embedded traffic assignment (TA) to model user equilibrium principle, sometimes expressed as bilevel problems or mathematical programs with equilibrium constraints (MPEC), is at the heart of transportation planning and operations. For applications to large-scale multimodal networks with high dimensional decision variables, the problem is nontrivial, to say the least. General-purpose algorithms and problem-specific bilevel formulations have been proposed in the past to solve small problems for demonstration purposes. Research gap, however, exists in developing efficient solution methods for large-scale problems in both static and dynamic contexts. This paper proposes an efficient gradient estimation method called Iterative Backpropagation (IB) for network optimization problems with an embedded static TA model. IB exploits the iterative structure of the TA solution procedure and simultaneously calculates the gradients while the TA process converges. IB does not require any additional function evaluation and consequently scales very well with higher dimensions. We apply the proposed approach to origin-destination (OD) estimation, an MPEC problem, of the Hong Kong multimodal network with 49,806 decision variables, 8,797 nodes, 18,207 links, 2,684 transit routes, and 165,509 OD pairs. The calibrated model performs well in matching the link counts. Specifically, the IB-gradient based optimization technique reduces the link volume squared error by 98%, mean absolute percentage error (MAPE) from 95.29% to 21.23%, and the average GEH statistics from 24.18 to 6.09 compared with the noncalibrated case. The framework, even though applied to OD estimation in this paper, is applicable to a wide variety of optimization problems with an embedded TA model, opening up an efficient way to solve large-scale MPEC or bilevel problems.

Keywords: Iterative backpropagation; IB; gradient; OD estimation (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:57:y:2023:i:5:p:1134-1159

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