Ramification Algorithm for Transporting Routes in R2

Piersa, Jarosław

doi:10.1109/ictai.2014.104

Cited by 2 publications

(2 citation statements)

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“…It was shown in [38] and [39] that, although not necessarily leading to a global minimizer, this optimization algorithm provides an approximately optimal transport network and is applicable even in case of a large number of sinks (N ≈ 400). Two heuristic approaches based on stochastic optimization techniques on graphs were presented in [25] and [30]. As before, these method are capable of providing almost optimal network structures, but cannot guarantee global optimality either.…”

Section: Existing Numerical Methods For Branched Transport-type Problemsmentioning

confidence: 99%

An adaptive finite element approach for lifted branched transport problems

Dirks¹,

Wirth²

2020

Preprint

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We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to Mumford-Shah-type image processing problems, which in turn can be related to certain higher-dimensional convex optimization problems via so-called functional lifting. We examine the relation between these different models and exploit it to solve the branched transport model numerically via convex optimization. To this end we develop an efficient numerical treatment based on a specifically designed class of adaptive finite elements. This method allows the computation of finely resolved optimal transportation networks despite the high dimensionality of the convex optimization problem and its complicated set of nonlocal constraints. In particular, by design of the discretization the infinite set of constraints reduces to a finite number of inequalities.

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Section: Existing Numerical Methods For Branched Transport-type Problemsmentioning

confidence: 99%

An adaptive finite element approach for lifted branched transport problems

Dirks¹,

Wirth²

2020

Preprint

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“…In [6,7] we proposed a randomized search algorithm for the optimal solution. In this work we refine this algorithm, inspect its theoretical backgrouds using Markov chain Monte Carlo (MCMC) theory and generalise it, so it can be applied to 'indistinguishable goods' variant.…”

Section: Introductionmentioning

confidence: 99%

Branching Optimization for Transporting Tasks in the Plane

Piersa

2016

Int. J. Artif. Intell. Tools

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In this work we propose a simulated annealing based search algorithm for optimal ramified or branched transportation route in [Formula: see text]. The cost function of the transport network allows the system to merge small roads into larger highways, carry the goods together and separate them near the destination. As a result the transportation route has multiple branching-in and -out points, to some extent similar to nerve system of the tree leaf. The problem is known to be NP-complete even for finite set of branching points and metric spaces.

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Ramification Algorithm for Transporting Routes in R2

Cited by 2 publications

References 10 publications

An adaptive finite element approach for lifted branched transport problems

An adaptive finite element approach for lifted branched transport problems

Branching Optimization for Transporting Tasks in the Plane

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