ID: cond-mat/0608208

Structure of Optimal Transport Networks Subject to a Global Constraint

August 9, 2006

View on ArXiv

Similar papers 2

Optimal boundary control of the isothermal semilinear Euler equation for gas dynamics on a network

April 12, 2023

84% Match
Marcelo Bongarti, Michael Hintermüller
Optimization and Control
Analysis of PDEs

The analysis and boundary optimal control of the nonlinear transport of gas on a network of pipelines is considered. The evolution of the gas distribution on a given pipe is modeled by an isothermal semilinear compressible Euler system in one space dimension. On the network, solutions satisfying (at nodes) the so called Kirchhoff flux continuity conditions are shown to exist in a neighborhood of an equilibrium state. The associated nonlinear optimization problem then aims at ...

Find SimilarView on arXiv

Robust network formation with biological applications

November 29, 2023

84% Match
Jan Haskovec, Jan Vybiral
Optimization and Control

We provide new results on the structure of optimal transportation networks obtained as minimizers of an energy cost functional consisting of a kinetic (pumping) and material (metabolic) cost terms, constrained by a local mass conservation law. In particular, we prove that every tree (i.e., graph without loops) represents a local minimizer of the energy with concave metabolic cost. For the linear metabolic cost, we prove that the set of minimizers contains a loop-free structur...

Find SimilarView on arXiv

Optimizing intermittent water supply in urban pipe distribution networks

September 10, 2015

84% Match
Anna M. Lieb, Chris H. Rycroft, Jon Wilkening
Fluid Dynamics

In many urban areas of the developing world, piped water is supplied only intermittently, as valves direct water to different parts of the water distribution system at different times. The flow is transient, and may transition between free-surface and pressurized, resulting in complex dynamical features with important consequences for water suppliers and users. Here, we develop a computational model of transition, transient pipe flow in a network, accounting for a wide variet...

Find SimilarView on arXiv

Designing optimal networks for multi-commodity transport problem

October 27, 2020

84% Match
Alessandro Lonardi, Enrico Facca, ... , De Bacco Caterina
Physics and Society
Social and Information Netwo...
Systems and Control
Systems and Control
Adaptation and Self-Organizi...

Designing and optimizing different flows in networks is a relevant problem in many contexts. While a number of methods have been proposed in the physics and optimal transport literature for the one-commodity case, we lack similar results for the multi-commodity scenario. In this paper we present a model based on optimal transport theory for finding optimal multi-commodity flow configurations on networks. This model introduces a dynamics that regulates the edge conductivities ...

Find SimilarView on arXiv

Theory and Approximate Solvers for Branched Optimal Transport with Multiple Sources

October 14, 2022

84% Match
Peter Lippmann, Enrique Fita Sanmartín, Fred A. Hamprecht
Machine Learning
Combinatorics
Optimization and Control

Branched Optimal Transport (BOT) is a generalization of optimal transport in which transportation costs along an edge are subadditive. This subadditivity models an increase in transport efficiency when shipping mass along the same route, favoring branched transportation networks. We here study the NP-hard optimization of BOT networks connecting a finite number of sources and sinks in $\mathbb{R}^2$. First, we show how to efficiently find the best geometry of a BOT network for...

Find SimilarView on arXiv

Modeling Minimum Cost Network Flows With Port-Hamiltonian Systems

March 23, 2023

84% Match
Onur Tanil Doganay, Kathrin Klamroth, Bruno Lang, ... , Totzeck Claudia
Optimization and Control

We give a short overview of advantages and drawbacks of the classical formulation of minimum cost network flow problems and solution techniques, to motivate a reformulation of classical static minimum cost network flow problems as optimal control problems constrained by port-Hamiltonian systems (pHS). The first-order optimality system for the port-Hamiltonian system-constrained optimal control problem is formally derived. Then we propose a gradient-based algorithm to find opt...

Find SimilarView on arXiv

Economic Topology Optimization of District Heating Networks using a Pipe Penalization Approach

May 24, 2022

84% Match
Yannick Wack, Martine Baelmans, ... , Blommaert Maarten
Computational Engineering, F...

In the presented study, a pipe penalization approach for the economic topology optimization of District Heating Networks is proposed, drawing inspiration from density-based topology optimization. For District Heating Networks, the upfront investment is a crucial factor for the rollout of this technology. Today, the pipe routing is usually designed relying on a linearization of the underlying heat transport problem. This study proposes to solve the optimal pipe routing problem...

Find SimilarView on arXiv

Structure, Scaling and Phase Transition in the Optimal Transport Network

July 31, 2006

83% Match
Steffen Bohn, Marcelo O. Magnasco
Disordered Systems and Neura...

We minimize the dissipation rate of an electrical network under a global constraint on the sum of powers of the conductances. We construct the explicit scaling relation between currents and conductances, and show equivalence to a a previous model [J. R. Banavar {\it et al} Phys. Rev. Lett. {\bf 84}, 004745 (2000)] optimizing a power-law cost function in an abstract network. We show the currents derive from a potential, and the scaling of the conductances depends only locally ...

Find SimilarView on arXiv

Graphical Models and Belief Propagation-hierarchy for Optimal Physics-Constrained Network Flows

February 7, 2017

83% Match
Michael Chertkov, Sidhant Misra, Marc Vuffray, ... , Van Hentenryck Pascal
Systems and Control
Applications

In this manuscript we review new ideas and first results on application of the Graphical Models approach, originated from Statistical Physics, Information Theory, Computer Science and Machine Learning, to optimization problems of network flow type with additional constraints related to the physics of the flow. We illustrate the general concepts on a number of enabling examples from power system and natural gas transmission (continental scale) and distribution (district scale)...

Find SimilarView on arXiv

Principled network extraction from images

December 23, 2020

83% Match
Diego Baptista, Bacco Caterina De
Computer Vision and Pattern ...
Adaptation and Self-Organizi...
Physics and Society

Images of natural systems may represent patterns of network-like structure, which could reveal important information about the topological properties of the underlying subject. However, the image itself does not automatically provide a formal definition of a network in terms of sets of nodes and edges. Instead, this information should be suitably extracted from the raw image data. Motivated by this, we present a principled model to extract network topologies from images that ...

Find SimilarView on arXiv