Locating leak detecting sensors in a water distribution network by solving prize-collecting Steiner arborescence problems

Prodon, Alain; DeNegre, Scott; Liebling, Th. M.

doi:10.1007/s10107-010-0368-4

Cited by 12 publications

(8 citation statements)

References 9 publications

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“…Finally, for relevant studies on prize-collecting problems with disconnected, directed or generalized spanning subgraphs, which do not belong to the scope of this work, we refer the reader to [1,4,8,18,46].…”

Section: Related Literaturementioning

confidence: 99%

Exact algorithms for budgeted prize-collecting covering subgraph problems

Morandi¹,

Leus²,

Yaman³

2021

Preprint

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We introduce a class of budgeted prize-collecting covering subgraph problems. For an input graph with prizes on the vertices and costs on the edges, the aim of these problems is to find a connected subgraph such that the cost of its edges does not exceed a given budget and its collected prize is maximum. A vertex prize is collected when the vertex is visited, but the price can also be partially collected if the vertex is covered, where an unvisited vertex is covered by a visited one if the latter belongs to the former's neighbourhood. A capacity limit is imposed on the number of vertices that can be covered by the same visited vertex. Potential application areas include network design and intermodal transportation. We develop a branch-and-cut framework and a Benders decomposition for the exact solution of the problems in this class. We validate our algorithmic frameworks for the cases where the subgraph is a tour and a tree, and for these two cases we also identify novel symmetry-breaking inequalities.

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Section: Related Literaturementioning

confidence: 99%

Exact algorithms for budgeted prize-collecting covering subgraph problems

Morandi¹,

Leus²,

Yaman³

2021

Preprint

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“…Frequently, network design and location decisions are combined. So, for example Prodon et al [190] used the PCSTP to locate sensors for leak detection in water distribution networks. In the design of local access networks, the facility location problem and the STP are combined and the underlying optimization problem is known as the connected facility location problem (ConFLP).…”

Section: Old and New Applications Of The Stpmentioning

confidence: 99%

Solving Steiner trees: Recent advances, challenges, and perspectives

Ljubić

2020

Networks

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The Steiner tree problem (STP) in graphs is one of the most studied problems in combinatorial optimization. Since its inception in 1970, numerous articles published in the journal Networks have stimulated new theoretical and computational studies on Steiner trees: from approximation algorithms, heuristics, metaheuristics, all the way to exact algorithms based on (mixed) integer linear programming, fixed parameter tractability, or combinatorial branch‐and‐bounds. The pervasive applicability and relevance of Steiner trees have been reinforced by the recent 11th DIMACS Implementation Challenge in 2014 and the PACE 2018 Challenge. This article provides an overview of the rich developments from the last three decades for the STP in graphs and highlights the most recent computational studies for some of its closely related variants.

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“…The design of a leakage detection system using the PCStT is performed in [34]. The problem consists of finding the optimal location of detectors in an urban water distribution network so that, given a budget constraint, a desired coverage is provided.…”

Section: The Prize Collecting Steiner Tree Problemmentioning

confidence: 99%

Exact approaches for solving robust prize-collecting Steiner tree problems

Álvarez-Miranda

Ljubić

Toth

2013

European Journal of Operational Research

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In the Prize-Collecting Steiner Tree Problem (PCStT) we are given a set of customers with potential revenues and a set of possible links connecting these customers with fixed installation costs. The goal is to decide which customers to connect into a tree structure so that the sum of the link costs plus the revenues of the customers that are left out is minimized. The problem, as well as some of its variants, is used to model a wide range of applications in telecommunications, gas distribution networks, protein-protein interaction networks, or image segmentation. In many applications it is unrealistic to assume that the revenues or the installation costs are known in advance. In this paper we consider the well-known Bertsimas and Sim (B&S) robust optimization approach, in which the input parameters are subject to interval uncertainty, and the level of robustness is controlled by introducing a control parameter, which represents the perception of the decision maker regarding the number of uncertain elements that will present an adverse behavior. We propose branch-and-cut approaches to solve the robust counterparts of the PCStT and the Budget Constraint variant and provide an extensive computational study on a set of benchmark instances that are adapted from the deterministic PCStT inputs. We show how the Price of Robustness influences the cost of the solutions and the algorithmic performance. Finally, we adapt our recent theoretical results regarding algorithms for a general class of B&S robust optimization problems for the robust PCStT and its budget and quota constrained variants

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Locating leak detecting sensors in a water distribution network by solving prize-collecting Steiner arborescence problems

Cited by 12 publications

References 9 publications

Exact algorithms for budgeted prize-collecting covering subgraph problems

Exact algorithms for budgeted prize-collecting covering subgraph problems

Solving Steiner trees: Recent advances, challenges, and perspectives

Exact approaches for solving robust prize-collecting Steiner tree problems

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