A heuristic method for a congested capacitated transit assignment model with strategies

•The capacitated congested strategy-based transit assignment is solved using an MSA method as result of its VI reformulation.•At each iteration a capacitated linear problem is solved using Lagrangian relaxation, generating the hyperpaths of the solution.•Solutions are always capacity feasible, even...

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Vydané v:	Transportation research. Part B: methodological Ročník 106; s. 293 - 320
Hlavní autori:	Codina, Esteve, Rosell, Francisca
Médium:	Journal Article Publikácia
Jazyk:	English
Vydavateľské údaje:	Elsevier Ltd 01.12.2017
Predmet:	49 Calculus of variations and optimal control; optimization 49R50 Variational methods for eigenvalues of operators 65 Numerical analysis 65C Probabilistic methods, simulation and stochastic differential equations 90 Operations research, mathematical programming 90C Mathematical programming Anàlisi matemàtica Anàlisi numèrica Calculus of variations Classificació AMS Congested transit assignment Càlcul de variacions Heuristic methods Investigació operativa Matemàtiques i estadística Numerical analysis Probabilitat Programació (Matemàtica) Programming (Mathematics) Simulation methods Strategy-based transit equilibrium Variational inequalities Àrees temàtiques de la UPC Congested transit assignment Strategy-based transit equilibrium Heuristic methods Variational inequalities
ISSN:	0191-2615, 1879-2367
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Popis
Shrnutí:	•The capacitated congested strategy-based transit assignment is solved using an MSA method as result of its VI reformulation.•At each iteration a capacitated linear problem is solved using Lagrangian relaxation, generating the hyperpaths of the solution.•Solutions are always capacity feasible, even under very high demand levels.•The method behaves better and is computationally as efficient as the one in Cepeda et al. (2001), in any congestion level.•Passenger delay models at stops, derivated from queueing theory, with infinite delays, can be integrated. This paper addresses the problem of solving the congested transit assignment problem with strict capacities. The model under consideration is the extension made by Cominetti and Correa (2001), for which the only solution method capable of resolving large transit networks is the one proposed by Cepeda et al. (2006). This transit assignment model was recently formulated by the authors as both a variational inequality problem and a fixed point inclusion problem. As a consequence of these results, this paper proposes an algorithm for solving the congested transit assignment problem with strict line capacities. The proposed method consists of using an MSA-based heuristic for finding a solution for the fixed point inclusion formulation. Additionally, it offers the advantage of always obtaining capacity-feasible flows with equal computational performance in cases of moderate congestion and with greater computational performance in cases of highly congested networks. A set of computational tests on realistic small- and large-scale transit networks under various congestion levels are reported, and the characteristics of the proposed method are analyzed.
ISSN:	0191-2615 1879-2367
DOI:	10.1016/j.trb.2017.07.008