CD
C. De Bacco
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Designing efficient transportation and communication infrastructures that reflect population distribution and travel demand is an important problem in both theory and practice. In a newly developed city, for example, one must determine how many rail lines or other transport connections are needed to satisfy daily commuting demand while keeping construction and operating costs as low as possible. Traditionally, such network layouts are designed with the help of expert knowledge and heuristic choices. In this thesis, we study a framework that aims to reduce this dependence by automatically generating a network from the spatial distribution and movement rates of different groups of users, or commodities. The resulting model balances the cost of transporting these commodities with the cost of constructing and maintaining the network itself.
The mathematical basis of this work is the Monge--Kantorovich framework for optimal transport, which has been used to describe adaptive transport phenomena inspired by the behavior of the slime mold \textit{Physarum polycephalum} \cite{Tero2007}. This organism is known for its ability to find efficient paths in complex environments, such as mazes, by adapting the thickness of its transport tubes according to the flux they carry. Such behavior has motivated dynamical models in which transport costs and network conductivities evolve over time until an optimal configuration is reached. These models are naturally defined on graphs, but they can also be extended to continuous state spaces \cite{Facca_2018_math}, which may be viewed as very fine discretizations of the underlying domain.
Most existing formulations are restricted to the single-commodity case, meaning that only one type of flow is considered. In many real-world applications, however, different commodities may travel through the same infrastructure and may exhibit different spatial distributions and movement patterns. This multi-commodity setting is significantly more realistic for applications such as passenger transport, freight logistics, and communication systems. It also introduces additional complexity, since the interaction between different flows may affect the optimal network structure in a nontrivial way. ...
The mathematical basis of this work is the Monge--Kantorovich framework for optimal transport, which has been used to describe adaptive transport phenomena inspired by the behavior of the slime mold \textit{Physarum polycephalum} \cite{Tero2007}. This organism is known for its ability to find efficient paths in complex environments, such as mazes, by adapting the thickness of its transport tubes according to the flux they carry. Such behavior has motivated dynamical models in which transport costs and network conductivities evolve over time until an optimal configuration is reached. These models are naturally defined on graphs, but they can also be extended to continuous state spaces \cite{Facca_2018_math}, which may be viewed as very fine discretizations of the underlying domain.
Most existing formulations are restricted to the single-commodity case, meaning that only one type of flow is considered. In many real-world applications, however, different commodities may travel through the same infrastructure and may exhibit different spatial distributions and movement patterns. This multi-commodity setting is significantly more realistic for applications such as passenger transport, freight logistics, and communication systems. It also introduces additional complexity, since the interaction between different flows may affect the optimal network structure in a nontrivial way. ...
Designing efficient transportation and communication infrastructures that reflect population distribution and travel demand is an important problem in both theory and practice. In a newly developed city, for example, one must determine how many rail lines or other transport connections are needed to satisfy daily commuting demand while keeping construction and operating costs as low as possible. Traditionally, such network layouts are designed with the help of expert knowledge and heuristic choices. In this thesis, we study a framework that aims to reduce this dependence by automatically generating a network from the spatial distribution and movement rates of different groups of users, or commodities. The resulting model balances the cost of transporting these commodities with the cost of constructing and maintaining the network itself.
The mathematical basis of this work is the Monge--Kantorovich framework for optimal transport, which has been used to describe adaptive transport phenomena inspired by the behavior of the slime mold \textit{Physarum polycephalum} \cite{Tero2007}. This organism is known for its ability to find efficient paths in complex environments, such as mazes, by adapting the thickness of its transport tubes according to the flux they carry. Such behavior has motivated dynamical models in which transport costs and network conductivities evolve over time until an optimal configuration is reached. These models are naturally defined on graphs, but they can also be extended to continuous state spaces \cite{Facca_2018_math}, which may be viewed as very fine discretizations of the underlying domain.
Most existing formulations are restricted to the single-commodity case, meaning that only one type of flow is considered. In many real-world applications, however, different commodities may travel through the same infrastructure and may exhibit different spatial distributions and movement patterns. This multi-commodity setting is significantly more realistic for applications such as passenger transport, freight logistics, and communication systems. It also introduces additional complexity, since the interaction between different flows may affect the optimal network structure in a nontrivial way.
The mathematical basis of this work is the Monge--Kantorovich framework for optimal transport, which has been used to describe adaptive transport phenomena inspired by the behavior of the slime mold \textit{Physarum polycephalum} \cite{Tero2007}. This organism is known for its ability to find efficient paths in complex environments, such as mazes, by adapting the thickness of its transport tubes according to the flux they carry. Such behavior has motivated dynamical models in which transport costs and network conductivities evolve over time until an optimal configuration is reached. These models are naturally defined on graphs, but they can also be extended to continuous state spaces \cite{Facca_2018_math}, which may be viewed as very fine discretizations of the underlying domain.
Most existing formulations are restricted to the single-commodity case, meaning that only one type of flow is considered. In many real-world applications, however, different commodities may travel through the same infrastructure and may exhibit different spatial distributions and movement patterns. This multi-commodity setting is significantly more realistic for applications such as passenger transport, freight logistics, and communication systems. It also introduces additional complexity, since the interaction between different flows may affect the optimal network structure in a nontrivial way.