In the framework of transport theory, we are interested in the following optimization problem: given the distributions of working people and of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of from with respect to a metric which depends on the transportation network....
In the framework of transport theory, we are interested in the following optimization problem: given the distributions µ of working people and µ of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of µ from µ with respect to a metric which depends on the transportation network.
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Given a metric space we consider a general class of functionals which measure the cost of a path in joining two given points and , providing abstract existence results for
optimal paths. The results are then applied to the case when is aWasserstein space of probabilities
on a given set and the cost of a path depends on the value of classical functionals over measures. Conditions for linking arbitrary extremal measures and by means of finite cost paths are given.
Given the probability measure over the given region , we consider the optimal location of a set composed by points in in order to minimize the average distance (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving...
Given the probability measure over the given region
, we consider the optimal location of a set
composed by points in in order to minimize the
average distance (the
classical optimal facility location problem). The paper compares two
strategies to find optimal configurations: the long-term one which
consists in
placing all points at once in an optimal position, and the
short-term one which consists in placing the points one by one adding
at each step at most one point and preserving the...
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