Stability of optimal traffic plans in the irrigation problem

Colombo, Maria; Rosa, Antonio; Marchese, Andrea; Pegon, Paul; Prouff, Antoine

doi:10.3934/dcds.2021167

Cited by 4 publications

(1 citation statement)

References 17 publications

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“…Existence results and some regularity properties of minimizers have been established for instance in [1,5,23,30,31]. Recently, another helpful wellposedness property of the problem was established in [14]: the stability of minimizers with respect to variations of the boundary, see [15] for the Lagrangian counterpart. Slightly improving upon the main result of [14], see Theorem A.1, we advance on the study of the well-posedness properties of the branched transportation problem, as we establish the first result on the generic uniqueness of minimizers, in full generality, namely in every dimension d and for every exponent α ∈ (0, 1).…”

Section: Introductionmentioning

confidence: 99%

Generic uniqueness of optimal transportation networks

Caldini¹,

Marchese²,

Steinbrüchel³

2022

Preprint

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Section: Introductionmentioning

confidence: 99%

Generic uniqueness of optimal transportation networks

Caldini¹,

Marchese²,

Steinbrüchel³

2022

Preprint

Self Cite

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Generic uniqueness of optimal transportation networks

Caldini,

Marchese,

Steinbrüchel

2023

Calc. Var.

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Informed-TRRT*: An improved sampling-based path planning algorithm

Shi,

2024

DCDS-S

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Path planning involves finding the optimal path in a known environment, allowing robots or vehicles to reach the destination as quickly and safely as possible from the starting point. In this domain, the RRT* (Rapidlyexploring Random Tree Star) algorithm has emerged as an advanced path planning approach, in handling challenges in complex environments. However, due to the slow convergence rate of RRT*, and the significant uncertainty in the generated paths, achieving stability in generating optimal paths within a fixed number of iterations poses challenges for the RRT* algorithm. This paper develops a novel algorithm, Informed-TRRT*, which combines the Theta* algorithm with the Informed-RRT* algorithm. The algorithm proposed in this paper rapidly obtains a short initial solution using the Theta* algorithm, narrows the sampling region based on this initial solution to improve sampling efficiency, and incorporates pruning algorithms to further enhance path optimality. Through comparative simulation experiments in environments of increasing complexity, the proposed algorithm generates paths with lengths optimized by 1.23% and 3.56% compared to the Theta* algorithm and Informed-RRT* algorithm, respectively, in environments with gradually increasing complexity; 19.53% and 8.76%; 6.45% and 9.07%.

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Stability of optimal traffic plans in the irrigation problem

Cited by 4 publications

References 17 publications

Generic uniqueness of optimal transportation networks

Generic uniqueness of optimal transportation networks

Generic uniqueness of optimal transportation networks

Informed-TRRT*: An improved sampling-based path planning algorithm

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