Geoscience Reference
In-Depth Information
Finally, in order to avoid possible damage to historical building a modified
anticenter path location problem is used in Laporte et al. (
2009
) to design a metro
line as far away as possible from some patrimonial buildings to be protected.
The problem is solved with the help of a Voronoi diagram constructed around the
protected sites.
22.3.2
Rapid Transit Network Design
We now consider the problem of locating a rapid transit network from scratch, as
well as the problem of extending an already located network. The first attempt at
modeling and solving the general rapid transit network design problem is presented
in the paper by Laporte et al. (
2007
), which provides a computationally tractable
approach consisting of three stages. The first is the selection of key stations,
which are the main attraction points: railway or bus stations and airports, hospitals,
university campuses, large stores and commercial centers and densely populated
areas far away from the central area of the city, etc. The second stage is to connect
the key stations to form a core network. Finally, the intermediate stations are located
on the alignment resulting from the second stage. In the same paper, a linear
integer programming model aiming at maximizing the trip coverage is used in order
to solve the core network design problem in presence of an alternative mode of
transportation. Later, Marín (
2007
) relaxed some restrictions on the lines. In his
model the number of lines and the extremes of them are not fixed.
With the aim of modeling the user's behavior, Marín and García-Ródenas (
2009
)
introduced a logit function in order to distribute the travelers between the rapid
transit and private modes. In order to maintain the linear character of the program,
they consider a piecewise linear interpolation of the logit function. In the paper
of Escudero and Muñoz (
2009
) the problem is decomposed into two stages. The
first one consists of determining the infrastructure network, and the second one
determines the lines.
A methodological contribution to modeling and solving the transit network
design problem can be found in Gutiérrez-Jarpa et al. (
2013
). These authors take
into account the fact that the rapid transit networks are composed of line segments
which often have to be constructed within broad corridors. These segments are
later assembled into lines. The authors apply two criteria: minimizing construction
cost and maximizing origin-destination traffic capture and computed Pareto-optimal
solutions.
A multi-period capacity expansion problem was studied in Marín and Jaramillo
(
2008
). In this paper the lines to be opened in each period are determined by
taking into account an objective function which is a combination of community,
passenger and operator oriented objectives. Since the general problem cannot be
solved exactly, a heuristic procedure is designed to solve it.
Other approaches to solve the mathematical programming model for rapid
transit network design problems are based on Benders decomposition (Marín and
