ARTICULO ESPECIALIZADO DE INVESTIGACION-301

ARTICULO ESPECIALIZADO DE INVESTIGACION-301

REVISTA INVESTIGACIÓN OPERACIONAL
VOL. 36, NO. 2, 115-126, 2014
O–D MATRIX ADJUSTMENT FOR TRANSIT
NETWORKS BY CONJUGATE GRADIENT
ITERATIONS
L. Héctor Juárez and M. Victoria Chávez
Universidad Autónoma Metropolitana–Iztapalapa
Av. San Rafael Atlixco 186 Col. Vicentina, Mexico D.F., CP 09340
[email protected], [email protected]
ABSTRACT
The adjustment of an obsolete demand matrix, from some given known data, is an important issue
for transport research. In this article we introduce a penalized model, based on volume counts on
a given set of arcs or segments, to update the demand matrix. Also, we propose a multiplicative
conjugate gradient algorithm to solve the resultant convex optimization problem. This algorithm
has been programmed with the macro language of EMME and tested with a synthetic scenario
from the Winnipeg network. The numerical results show that the proposed algorithm improves the
performance of the traditional multiplicative steepest descent algorithm, introduced by Spiess.
KEYWORDS: O-D matrix, demand models, transit assignment, convex optimization, conjugate
gradient method, bilevel programming.
MSC:
RESUMEN
El ajuste de una matriz de demanda obsoleta, cuando se conocen ciertos datos, es un tema importante
en la investigación del transporte. En este artı́culo introducimos un modelo penalizado, basado en
el conteo de volúmenes sobre ciertos arcos o segmentos, para actualizar la matriz de demanda.
También, proponemos un algoritmo multiplicativo de gradiente conjugado para resolver el problema
resultante de optimización convexa. Este algoritmo ha sido programado utilizando el macro lenguage
de EMME y se ha aplicado a un escenario sintético, obtenido de la red de Winnipeg. Los resultados
numéricos muestran que el algoritmo propuesto mejora el desempeño del método tradicional de
descenso máximo, introducido por Spiess.
1.
INTRODUCTION
Public transport is becoming more relevant in modern societies, especially in large cities, where a good
transportation planning is extremely important for many obvious reasons. Therefore, a good knowledge of the
transit network and of the operation of the transportation system is necessary. In particular, mathematical
models for transit assignment are very useful to help understanding how users travel from their different
origins to their diverse destinations. These models must replicate realistic scenarios as close as possible,
and for this purpose it is necessary to collect field data. Data may be obtained based on surveys and other
complex and expensive studies, but unfortunately they are useful only for a limited short time, due to growth
in demand and change in infrastructure around big cities. To avoid making new comprehensive studies, there
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