Buttazzo, Giuseppe.
Optimal Urban Networks via Mass Transportation [electronic resource] / by Giuseppe Buttazzo, Aldo Pratelli, Eugene Stepanov, Sergio Solimini. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2009. - X, 150p. 15 illus. online resource. - Lecture Notes in Mathematics, 1961 0075-8434 ; . - Lecture Notes in Mathematics, 1961 .
Problem setting -- Optimal connected networks -- Relaxed problem and existence of solutions -- Topological properties of optimal sets -- Optimal sets and geodesics in the two-dimensional case.
Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and the short-term, "who goes where" optimization are considered. These models can also be adapted for the optimization of other types of networks, such as telecommunications, pipeline or drainage networks. In the monograph we study the most general problem settings, namely, when neither the shape nor even the topology of the network to be constructed is known a priori.
9783540857990
10.1007/978-3-540-85799-0 doi
Mathematics.
Mathematical optimization.
Operations research.
Cell aggregation--Mathematics.
Mathematics.
Calculus of Variations and Optimal Control; Optimization.
Operations Research, Mathematical Programming.
Manifolds and Cell Complexes (incl. Diff.Topology).
Optimal Urban Networks via Mass Transportation [electronic resource] / by Giuseppe Buttazzo, Aldo Pratelli, Eugene Stepanov, Sergio Solimini. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2009. - X, 150p. 15 illus. online resource. - Lecture Notes in Mathematics, 1961 0075-8434 ; . - Lecture Notes in Mathematics, 1961 .
Problem setting -- Optimal connected networks -- Relaxed problem and existence of solutions -- Topological properties of optimal sets -- Optimal sets and geodesics in the two-dimensional case.
Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and the short-term, "who goes where" optimization are considered. These models can also be adapted for the optimization of other types of networks, such as telecommunications, pipeline or drainage networks. In the monograph we study the most general problem settings, namely, when neither the shape nor even the topology of the network to be constructed is known a priori.
9783540857990
10.1007/978-3-540-85799-0 doi
Mathematics.
Mathematical optimization.
Operations research.
Cell aggregation--Mathematics.
Mathematics.
Calculus of Variations and Optimal Control; Optimization.
Operations Research, Mathematical Programming.
Manifolds and Cell Complexes (incl. Diff.Topology).