A Submodular Approach for Optimal Sensor Placement in Traffic Networks

Mehr, Negar; Horowitz, Roberto

doi:10.23919/acc.2018.8431678

Cited by 11 publications

(16 citation statements)

References 21 publications

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“…For the detailed formulation of the greedy algorithm, we refer to [17]. The main idea of the greedy algorithm is at each iteration to simply add the element which maximizes the gain of f .…”

Section: A Submodularitymentioning

confidence: 99%

Priority Lists for Power System Investments: Locating Phasor Measurement Units

Murzakhanov

Pozo

2021

2021 IEEE Madrid PowerTech

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Power systems incrementally and continuously upgrade their components, such as transmission lines, reactive capacitors, or generating units. Decision-making tools often support the selection of the best set of components to upgrade. Optimization models are often used to support decision making at a given point in time. After certain time intervals, re-optimization is performed to find new components to add. In this paper, we propose a decision-making framework for incrementally updating power system components. This is an alternative approach to the classical sequential re-optimization decision making for an investment problem with modeled budget constraints. Our approach provides a priority list as a solution with a list of new components to upgrade. We show that i) our framework is consistent with the evolution of power system upgrades, and ii) in particular circumstances, both frameworks provide the same solution if the problem satisfies submodularity property.We have selected the problem of phasor measurement unit localization and compared the solution with the classical sequential re-optimization framework. For this particular problem, we show that the two approaches provide close results, while only our proposed algorithm is applicable in practice. The cases of 14 and 118 IEEE buses are used to illustrate the proposed methodology.

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Section: A Submodularitymentioning

confidence: 99%

Priority Lists for Power System Investments: Locating Phasor Measurement Units

Murzakhanov

Pozo

2021

2021 IEEE Madrid PowerTech

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“…The problem of placing traffic sensors on highway networks has been divided into two main categories in the literature, one involving estimation and the other involving observability. Under the former category, the objective is to determine the optimal placement of sensors that minimizes the estimation error for unmeasured quantities such as travel time [6]- [8], OD matrix [9], [10], link flows [11]. Under observability, the literature is further divided based on the type of observability that is considered, full or partial observability.…”

Section: Motivation and Paper Contributionsmentioning

confidence: 99%

“…Having described system (11) with sensor placement, we now state the paper's major computational objective: from a given possible set of traffic sensors G γ such that γ ∈ G γ , find the best (or optimal) sensor configuration γ * such that system (11) is observable, i.e., the system's initial state x 0 := x[0] can be uniquely determined from a finite set of measurements. In this paper, we opt to formulate the traffic sensor placement using the concept of observability through MHE framework developed in [42].…”

Section: Nonlinear Discrete-time Modeling Of Traffic Network With Rampsmentioning

confidence: 99%

“…First, as argued in [42], this approach is considerably more scalable than using empirical observability Gramian and second, we experience numerical issues in applying the method from [44]. With that in mind, we consider the first N observation window (or N discrete measurements) of system (11) expressed in the equation below…”

Section: Nonlinear Discrete-time Modeling Of Traffic Network With Rampsmentioning

confidence: 99%

“…Hence, for a fixed γ, the mapping g(•) maps the initial state into the N measurements output. The observability of system (11) with respect to g(•) is formally defined as follows [48].…”

Section: Nonlinear Discrete-time Modeling Of Traffic Network With Rampsmentioning

confidence: 99%

See 2 more Smart Citations

Where Should Traffic Sensors Be Placed on Highways?

Nugroho¹,

Vishnoi²,

Taha³

et al. 2021

Preprint

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This paper investigates the practical engineering problem of traffic sensors placement on stretched highways with ramps. Since it is virtually impossible to install bulky traffic sensors on each highway segment, it is crucial to find placements that result in optimized network-wide, traffic observability. Consequently, this results in accurate traffic density estimates on segments where sensors are not installed. The substantial contribution of this paper is the utilization of control-theoretic observability analysis-jointly with integer programming-to determine traffic sensor locations based on the nonlinear dynamics and parameters of traffic networks. In particular, the celebrated asymmetric cell transmission model is used to guide the placement strategy jointly with observability analysis of nonlinear dynamic systems through Gramians. Thorough numerical case studies are presented to corroborate the proposed theoretical methods and various computational research questions are posed and addressed. The presented approach can also be extended to other models of traffic dynamics.

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Distributed strategy selection: A submodular set function maximization approach

Rezazadeh

Kia

2023

Automatica

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A Submodular Approach for Optimal Sensor Placement in Traffic Networks

Cited by 11 publications

References 21 publications

Priority Lists for Power System Investments: Locating Phasor Measurement Units

Priority Lists for Power System Investments: Locating Phasor Measurement Units

Where Should Traffic Sensors Be Placed on Highways?

Distributed strategy selection: A submodular set function maximization approach

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