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Traditional traffic counting location (TCL) problem is to determine the number and locations of counting stations that would best cover the network for the purpose of estimating origin-destination (O-D) trip tables. It is well noted that the quality of the estimated O-D trip table depends on the estimation methods, an appropriate set of links with...
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... total number of O-D pairs and A be the total number of links in the network. We define that the network is connected if there exists at least one directed simple path (a path that contains no repeated arcs and no repeated nodes) between each O-D pair w ∈ W starting at origin i and ending at destination j . Now, we introduce a binary integer variable: x a = ( 0 , 1 ), x a = 1 if a traffic counting station is located on link a , and 0 otherwise, x denotes the corresponding binary integer variable vector with element x a . Let t a be a virtual travel time on link a ∈ A . For the sake of our model formulation, we suppose t a is a function of x a and is simply defined as t a ( x a ) = x a , ∀ a ∈ A . (1) Since each link has a nonnegative value of travel time, we can use an appropriate shortest path algorithm to find the shortest path and its corresponding travel time from each origin i to each destination j within a finite number of iterations. Let u w be the shortest travel time between O-D pair w ∈ W determined by an appropriate shortest path algorithm such as Dijkstra method ( Ahuja et al., 1993; Bertsekas, 1998). Clearly, u w is a function of the binary integer variable vector x = ( ... , x a , ... ) , and we can easily understand that if u w ( x ) > 0 then the shortest path between O-D pair w ∈ W includes at least one counting link. In view of the definition of link travel time function (1), it is straightforward to see that if u w ( x ) > 0 then origin i and destination j of O-D pair w ∈ W is separated by at least one screen line. Otherwise, there exists at least one shorter path with zero travel time from i to j that does not go through any counting link or cross any screen line. To illustrate the concept of virtual travel time, consider the network depicted in Figure 1. This network consists of 9 nodes, 12 links, and 4 O-D pairs. Node 1 and node 4 are origins and node 6 and node 9 are destinations. Let us consider two sets of counting stations, [2,6,11] and [1,4,5], respectively forming screen lines A and B. Screen line A is able to intercept flows originating from ...
Citations
... Alternatively, the authors of [22] developed a comprehensive matrix tool that included all flow elements, representing O-D flows as binary variables (0 or 1). Reference [23] solved this problem by dispatching sensors to intercept all understudied O-D pairs using four BIP formulations. Subsequently, a genetic algorithm (GA) was presented to solve the formulations. ...
Traffic control and management applications require the full realization of traffic flow data. Frequently, such data are acquired by traffic sensors with two issues: it is not practicable or even possible to place traffic sensors on every link in a network; sensors do not provide direct information about origin–destination (O–D) demand flows. Therefore, it is imperative to locate the best places to deploy traffic sensors and then augment the knowledge obtained from this link flow sample to predict the entire traffic flow of the network. This article provides a resilient deep learning (DL) architecture combined with a global sensitivity analysis tool to solve O–D estimation and sensor location problems simultaneously. The proposed DL architecture is based on the stacked sparse autoencoder (SAE) model for accurately estimating the entire O–D flows of the network using link flows, thus reversing the conventional traffic assignment problem. The SAE model extracts traffic flow characteristics and derives a meaningful relationship between traffic flow data and network topology. To train the proposed DL architecture, synthetic link flow data were created randomly from the historical demand data of the network. Finally, a global sensitivity analysis was implemented to prioritize the importance of each link in the O–D estimation step to solve the sensor location problem. Two networks of different sizes were used to validate the performance of the model. The efficiency of the proposed method for solving the combination of traffic flow estimation and sensor location problems was confirmed from a low root-mean-square error with a reduction in the number of link flows required.
... Ehlert et al. (2006) addressed the problem intending to maximize the number of covered OD pairs assuming that the number of installable counting sensors is limited. Chen et al. (2007) assumed that some counting sensors have already been installed on the network and proposed a model to locate a limited number of additional sensors to maximize the coverage of OD pairs. Fei and Mahmassani (2011) addressed the problem of locating counting sensors so that the coverage of OD pairs is maximized while reducing the demand uncertainty. ...
This paper addresses the problem of locating vehicle-identification sensors along the arcs of the transportation network. The aim is to estimate the traffic volumes for a given set of routes under the assumption that the available sensors are insufficient to uniquely identify all route flows. We present a novel mixed-integer linear programming (MILP) model to determine the sensor locations so that in the system of linear equations solved in the path reconstruction phase, those routes whose volume cannot be uniquely determined, are linked to each other by equations involving a small number of unknowns. By this approach, experts’ opinions or historical information can be used to give a more precise estimation for those routes whose volumes are not uniquely observable. Since the direct resolution of the model via MILP solvers is time-consuming over moderate- and large-sized instances, by utilizing the problem structure, a genetic algorithm is adopted to find high-quality solutions to the model. Computational experiments over different instances, taken from the literature, confirm the effectiveness of the proposed model and algorithm.
... In contrast, Castillo et al. [41] created a complete matrix tool that incorporates all flow aspects and represents O-D flows as binary variables (0 or 1). Chen et al. [42] resolved the issue by deploying sensors to intercept all understudy O-D pairings using four BIP formulations. Then, the genetic algorithm (GA) used to solve the formulas was described. ...
Traffic management and control applications require comprehensive knowledge of traffic flow data. Typically, such information is gathered using traffic sensors, which have two basic challenges: First, it is impractical or impossible to install sensors on every arc in a network. Second, sensors do not provide direct information on origin-to-destination (O-D) demand flows. Consequently, it is essential to identify the optimal locations for deploying traffic sensors and then enhance the knowledge gained from this link flow sample to forecast the network's traffic flow. This article presents residual neural networks-a very deep set of neural networks to the problem for the first time. The suggested architecture reliably predicts the whole network's O-D flows utilizing link flows, hence inverting the standard traffic assignment problem. It deduces a relevant correlation between traffic flow statistics and network topology from traffic flow characteristics. To train the proposed deep learning architecture, random synthetic flow data was generated from the historical demand data of the network. A large-scale network was used to test and confirm the model's performance. Then, the Sioux Falls network was used to compare the results with the literature. The robustness of applying the proposed framework to this particular combined traffic flow problem was determined by maintaining superior prediction accuracy over the literature with a moderate number of traffic sensors.
... Ehlert et al. (2006) introduced binary integer linear programming (BIP) to the problem, where several different formulations were suggested to achieve either full O/D coverage or a partial one, subject to budget constraints. Chen et al. (2007) dispatched sensors to intercept the O/D pairs in a network through two BIP problems (in addition to two extension formulations). Next, they employed the genetic algorithm (GA) to solve the presented formulations. ...
... Exact solution methods ODE Passive Link √ £ Bi-level programming A distance-based GA (Gan et al., 2005) ODE Passive Link √ £ BIP Heuristics based on the TD (Eisenman et al., 2006) ODE Passive Link £ £ None Randomly Generated + Sensitivity Analysis (Bianco et al., 2006) OBS Active Nodes £ £ SLE Polynomial algorithms (Ma et al., 2006) ODE Passive Link £ £ BIP Heuristics based on improved coverage rules (Ehlert et al., 2006) ODE Passive Link √ £ BIP Linear Programming relaxation + Heuristics (Yang et al., 2006) SLP Passive Link √ £ BIP Linear Programming relaxation (Chen et al., 2007) ODE + SLP Fig. 5 also shows the disproportionate use of passive and active sensors. Studies on ODE, OBS, and LFI have focused on passive sensors. ...
Traffic flow data is a decisive element in transportation planning and traffic management. Over time, traffic sensors have been recognized as sources of such data. Despite their outstanding capabilities in measuring different traffic flow information types, they are not practical to apply across all transportation network streets or intersections. Thus, the traffic sensor location problem (TSLP) has emerged to answer two typical questions: how many sensors are needed, and what are the best locations for their deployment. This paper reviews the TSLP classes that have been extensively examined in the literature over the last three decades. This study tries to fulfill two major gaps in the existing literature. First, this is the only review article that summarizes the contributions made toward solving the TSLP spanning nearly 30 years. Second, it presents a comprehensive review and analysis of most TSLP studies with a new categorization system. This contribution clarifies the progress made and provides recommendations for further research.
... Hence, it can be used to develop methods for solving the optimal network sensor location problems (i.e. finding 'higher ratio' links for multiple O-D pairs), such as the classical traffic counting location problem for O-D matrix estimation (Bianco, Confessore, and Reverberi 2001;Chootinan, Chen, and Yang 2005;Chen et al. 2007;Larsson, Lundgren, and Peterson 2010) and the traffic detector location problem Pravinvongvuth 2004, 2010;Zhou and List 2010;Gentili and Mirchandani 2012;Castillo et al. 2015;Xu et al. 2016). Also, it can be used to identify the critical links/nodes for transportation network vulnerability analysis without assuming the disruption scenarios Jing, Xu, and Pu 2020). ...
The number of efficient paths between an origin-destination (O-D) pair provides the route diversity degree of possibly used paths in a transportation network, and it has many important applications in practice, e.g., network redundancy assessment, network sensor location problem, and vulnerable link/node identification problem. The existing counting method was based on the idea of the Bell loading method for the Logit route choice model to determine the number of efficient paths between any two nodes without the need of path enumeration. However, we observe that this method has a high computational time complexity and requires a lot of unnecessary computations. This high computational effort can significantly hinder its use, especially for large-scale networks. Inspired by the elegant Dial loading method for the Logit model, this paper develops a more computationally attractive method to count not only the number of efficient paths between each O-D pair, but also the number of efficient paths using each link/node between each O-D pair, and the total/average cost of these efficient paths between each O-D pair in a network. Besides circumventing path enumeration, the proposed method has a much lower time-complexity for computing the above three measures. Compared with the classical breadth-first and depth-first search algorithms, the proposed method avoids enumerating and storing path details, and traverses nodes more efficiently as it traverses each node only once to obtain the number of paths between O-D pairs. Numerical examples using ten transportation networks are then provided to demonstrate the validity and computational efficiency of the proposed method relative to the existing method. We find that the proposed method has a linear fitting relationship between the average computational time of each O-D pair and the number of nodes in a network, while the existing method has an exponential relationship.
... Initially, for a given scenario, a correspondence strictly determined matrix should be created. Then, based on the transport demand specified by this matrix, the traffic flow distribution in the network is carried out [6,10,11,12]. In accordance with the results of this procedure, micro-modeling of traffic is carried out. ...
The article discusses the methods’ development for determining the transport detectors location on the road network. In studying this problem, various approaches to collecting data on traffic flows are analyzed. The basic requirements for determining the number of data collection points and their location are formed. These requirements can be used in traffic monitoring systems. The proposed methods were tested using a model experiment on a test example. The simulation results showed the effectiveness of the considered methods.
... In this context, the traffic counting location problem (TCLP) emerges, in which the objective is to position traffic counters in highway segments to estimate O-D matrices. The TCLP is an NP-Hard combinatorial problem [2], and an approach to solve it is to enumerate all possible paths for each O-D pair. However, this procedure spends an infeasible computational time for large networks, since the number of paths between each O-D pair grows exponentially with respect to the size of the network. ...
... In an attempt to find good solutions for the TCLP, it was developed in [2] a Genetic Algorithm that finds feasible solutions for the TCLP, spending a reduced computational time. The strategy of [2] begins from a random population of individuals, which are represented by a sequence of binary integers (chromosomes) with a size equal to the number of segments in the network, and the value in each gene indicates the existence or not of a counter on its segment. ...
... In an attempt to find good solutions for the TCLP, it was developed in [2] a Genetic Algorithm that finds feasible solutions for the TCLP, spending a reduced computational time. The strategy of [2] begins from a random population of individuals, which are represented by a sequence of binary integers (chromosomes) with a size equal to the number of segments in the network, and the value in each gene indicates the existence or not of a counter on its segment. Some authors of the literature have developed mathematical models for TCLP and similar problems. ...
The traditional traffic counting location problem (TCLP) aims to determine the location of counting stations that would best cover a road network for the purpose of obtaining traffic flows. This information can be used, for example, to estimate origin-destination (O-D) trip tables. It is well noted that the quality of the estimated OD trip tables is related to an appropriate set of links with traffic counters and to the quality of the traffic counting. In this paper, we propose a Biased Random-key Genetic Algorithm to define the location of the traffic counters in a network, in order to count all flows between origins and destinations. A genetic algorithm of the literature was implemented, and its performance was compared to the proposed BRKGA. Computational experiments conducted on real-world instances, composed by the Brazilian states, have shown the benefit of the proposed method.
... Traffic surveys become even more complex when it is considered that the quality of an estimated OD matrix for road transport depends on different factors. These factors can be mainly related to: (1) methods used for estimation; (2) correct choice of segments (links) for vehicle counting (location and number of counting points); and (3) the quantity and reliability of the data used [9,15,47]. ...
... These papers seek to propose traffic counter locations aiming to obtain reliable data for the OD matrix estimation. The relationship between the number of traffic counters and the quality of the estimated OD matrix is detailed in [9]. ...
Large countries with extensive road networks, such as Brazil, require large volumes of financial resources to perform traffic surveys. In Brazil, the biggest road traffic survey was performed in 2011 with 120 counting survey stations. This survey was divided into three stages and 83 support units provided survey teams. A support unit is a place, such as a military organization, close to the survey stations. A stage indicates that only some survey stations must be considered at a time. In large scale traffic surveys with multi-stages, we must define which support unit will serve each survey station so that travel costs for the survey teams and the costs to use the support units are minimized. We present the Support Unit Location Problem to Assist Road Traffic Survey with Multi-Stages where, given a set of available support units, each one with a coverage area, and a set of multi-stage traffic survey stations, we must select units to serve stations so that the cost is minimized. Scenarios are evaluated for a real traffic survey with 300 counting stations and four stages in Brazil. Computational experiments show that large cost reductions can be found when a mathematical model is used.
... Assim, tomando como base o modelo matemático de Yang et al. (2006), González et al. (2017) apresentaram uma nova formulação matemática que incorpora uma restrição quanto ao número de faixas de rolamento por sentido. Além disso, como o problema de localização de sensores em redes é um problema combinatório NP-Difícil [Chen et al., 2007], os autores propuseram um algoritmo exato, Branch-and-Cut, para encontrar soluções ótimas para 26 instâncias reais, propostas por González et al. (2016), correspondentes aos estados brasileiros. Os testes computacionais, realizados com tempo limite de uma hora, mostraram que o algoritmo desenvolvido por González et al. (2017) é capaz de encontrar a solução ótima de algumas instâncias e fornecer boas soluções para outras. ...
O estudo do Problema de Localização dos Sensores de tráfego em Rede torna-se relevante ao fornecer ferramentas para localização ideal de sensores, considerando recurso limitado, para apoiar as atividades de controle e gestão de tráfego. Dessa forma, ao longo dos últimos, tem-se desenvolvido trabalhos que modelam matematicamente o problema, bem como propõem algoritmos para solucioná-lo. Nesse sentido, este artigo tem como objetivo identificar na literatura internacional quais são os estudos relevantes que desenvolvem metaheurísticas para solucionar o problema e realizar análises bibliométricas, cientométricas e sistemáticas desses artigos. Os resultados mostram que o Algoritmo Genético desponta-se como principal metaheurística aplicada ao problema e que a sua utilização para fornecimento de boas soluções iniciais para algoritmos exatos pode ser eficiente para encontrar soluções ótimas de grandes e complexas redes de transportes.
... Traffic counts are often used to monitor traffic circulation, measuring the number of vehicles passing through a station during a specified time period (Chen et al., 2007). This monitoring provides important traffic characteristics for the transportation planning such as critical flow time periods and average annual daily traffic. ...
... Travels between a given OD pair is considered to be observed if, and only if, no path between O and D is able to bypass the selected traffic count stations. However, TCLP is a combinatorial problem NP-Hard and solving it requires assigning a traffic count for each possible path between an OD pair (Chen et al., 2007). A possible approach to this problem is to list all possible paths for each OD pair, but this procedure spends a large computational time for road networks of real dimensions, since the number of paths between each OD pair grows exponentially with respect to the network size. ...
... In this context, Chen et al. (2007) developed a Genetic Algorithm (GA) that solves the TCLP, employing a reduced computational time. The strategy of the algorithm starts from a random population of individuals, which are represented by a sequence of binary numbers (chromosome) with size equals to the number of segments of the network, and the value in each gene indicates whether (or not) a traffic count exists on the corresponding segment. ...
The traditional traffic counting location problem (TCLP) aims to determine the location of counting stations that would best cover a road network for the purpose of obtaining traffic flows. This information can be used, for example, to estimate origin-destination (OD) trip tables. It is well noted that the quality of the estimated OD trip tables is related to an appropriate set of links with traffic counters and to the quality of the traffic counting. In this paper, we propose two methods (Branch-and-Cut algorithm and Clustering Search heuristic) to define the location of the traffic counters in a network, in order to count all flows between origins and destinations. A Genetic Algorithm heuristic presented in the literature is implemented in order to perform a fair comparison of results. Computational experiments conducted on real instances, composed by the Brazilian states, have shown the benefit of the proposed methods. Statistical tests show that Clustering Search heuristic has outperformed all other approaches.
