The demand adjustment problem via inexact restoration method
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The demand adjustment problem via inexact restoration method Jorgelina Walpen1
· Pablo A. Lotito2 · Elina M. Mancinelli1 · Lisandro Parente3
Received: 30 October 2018 / Revised: 26 November 2019 / Accepted: 2 December 2019 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract In this work, the demand adjustment problem (DAP) associated with urban traffic planning is studied. The framework for the formulation of the DAP is mathematical programming with equilibrium constraints. In particular, if the optimization program associated with the equilibrium constraint is considered, the DAP results in a bilevel optimization problem. In this approach, the DAP via the inexact restoration method is treated. Keywords Traffic · Origin–destination matrix adjustment · Inexact restoration method · Bilevel problem Mathematics Subject Classification 90B20 · 90C26
1 Introduction Transport planning is a developing science and many interesting problems arise from it. Most of them require to have information about the needs of the community to travel from some point to another. Usually this information is stored in a matrix called the origin– destination matrix (OD matrix) or demand matrix. Different points over the transport network are considered as the origin–destination pairs (od pairs) and the OD matrix saves the number of trips originating and terminating in each of them (demands).
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Jorgelina Walpen [email protected] Pablo A. Lotito [email protected] Elina M. Mancinelli [email protected] Lisandro Parente [email protected]
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FCEIA, Universidad Nacional de Rosario, Pellegrini 250, 2000 Rosario, Argentina
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CONICET, Pladema, Universidad Nacional del Centro de la Provincia de Buenos Aires, Campus Universitario Paraje Arroyo Seco, B7000 Tandil, Argentina
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CIFASIS, FCEIA UNR, CONICET, Ocampo y Esmeralda, 2000 Rosario, Argentina 0123456789().: V,-vol
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Od pairs may be connected by paths, flows on each path of the network, for a deterministic and stationary state of it, are obtained as a result of affecting the demands to the specific network. That is to say, trips are assigned to different available paths so that all of them can be carried out. The availability of the OD matrix is not always guaranteed. In general, it is expensive and difficult to obtain as it cannot be built by simple observation, in fact, direct interviews of measurements of high cost must be carried out to build the OD matrix. The Demand Adjustment Problem (DAP) consists in the estimation of the origin– destination matrix (OD matrix) of a congested transport network, based on the information of some observed flows in the network and an available target OD matrix (probably an outdated one). The problem of adjusting the OD matrix can be modelled as an optimization problem with equilibrium constraints and reformulated as a bilevel problem. Among its drawbacks it has bad mathematical properties which make it difficult to solve it. Some of them are: non-con
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