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Optimal networks for mass transportation problems

Alessio Brancolini; Giuseppe Buttazzo — 2005

ESAIM: Control, Optimisation and Calculus of Variations

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....

Optimal networks for mass transportation problems

Alessio Brancolini; Giuseppe Buttazzo — 2010

ESAIM: Control, Optimisation and Calculus of Variations

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. ...

Path functionals over Wasserstein spaces

Alessio Brancolini; Giuseppe Buttazzo; Filippo Santambrogio — 2006

Journal of the European Mathematical Society

Given a metric space $X$ we consider a general class of functionals which measure the cost of a path in $X$ joining two given points $x_{0}$ and $x_{1}$ , providing abstract existence results for optimal paths. The results are then applied to the case when $X$ is aWasserstein space of probabilities on a given set $Ω$ and the cost of a path depends on the value of classical functionals over measures. Conditions for linking arbitrary extremal measures $μ_{0}$ and $μ_{1}$ by means of finite cost paths are given.

Long-term planning versus short-term planning in the asymptotical location problem

Alessio Brancolini; Giuseppe Buttazzo; Filippo Santambrogio; Eugene Stepanov — 2009

ESAIM: Control, Optimisation and Calculus of Variations

Given the probability measure $ν$ over the given region $Ω \subset ℝ^{n}$ , we consider the optimal location of a set $Σ$ composed by $n$ points in $Ω$ in order to minimize the average distance $Σ \mapsto \int_{Ω} dist (x, Σ) d ν$ (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all $n$ 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...

Long-term planning short-term planning in the asymptotical location problem

Alessio Brancolini; Giuseppe Buttazzo; Filippo Santambrogio; Eugene Stepanov — 2008

ESAIM: Control, Optimisation and Calculus of Variations

Given the probability measure over the given region $Ω \subset ℝ^{n}$ , we consider the optimal location of a set composed by points in in order to minimize the average distance $Σ \mapsto \int_{Ω} dist (x, Σ) d ν$ (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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Currently displaying 1 – 5 of 5

Optimal networks for mass transportation problems

Optimal networks for mass transportation problems

Path functionals over Wasserstein spaces

Long-term planning versus short-term planning in the asymptotical location problem

Long-term planning short-term planning in the asymptotical location problem