Applying min-max k postmen problems to the routing of security guards

The most essential and alluring characteristic of a security estate is the estate's ability to provide 24-h security to its residents, of which the continual patrolling of roads and paths is vital. The objective of this paper is to address the lack of sufficient patrol route design procedures by presenting a tabu search algorithm capable of generating multiple patrol routes for an estate's security guards. The paper shows that the problem of designing these routes can be modelled as an Arc Routing Problem, specifically as min-max k postmen problems. The algorithm is illustrated with a real problem instance from an estate in Gauteng, South Africa. The patrol routes generated by the algorithm provide a significant improvement in the even patrolling of the road network, and a more balanced work distribution among guards. The algorithm is also tested on several benchmark problems from literature.http://www.palgrave-journals.com/jors/index.htm

A Balanced Route Design for Min-Max Multiple-Depot Rural Postman Problem (MMMDRPP): a police patrolling case

Providing distributed services on road networks is an essential concern for many applications, such as mail delivery, logistics and police patrolling. Designing effective and balanced routes for these applications is challenging, especially when involving multiple postmen from distinct depots. In this research, we formulate this routing problem as a Min-Max Multiple-Depot Rural Postman Problem (MMMDRPP). To solve this routing problem, we develop an efficient tabu-search-based algorithm and propose three novel lower bounds to evaluate the routes. To demonstrate its practical usefulness, we show how to formulate the route design for police patrolling in London as an MMMDRPP and generate balanced routes using the proposed algorithm. Furthermore, the algorithm is tested on multiple adapted benchmark problems. The results demonstrate the efficiency of the algorithm in generating balanced routes

Developing Police Patrol Strategies Based on the Urban Street Network

In urban areas, crime and disorder have been long-lasting problems that spoil the economic and emotional well-being of residents. A significant way to deter crime, and maintain public safety is through police patrolling. So far, the deployment of police forces in patrolling has relied mainly on expert knowledge, and is usually based on two-dimensional spatial units, giving insufficient consideration to the underlying urban structure and collaboration among patrol officers. This approach has led to impractical and inefficient police patrol strategies, as well as a workload imbalance among officers. Therefore, it is of essential importance to devise advanced police patrol strategies that incorporate urban structure, the collaboration of the patrol officers, and a workload balance. This study aims to develop police patrol strategies that would make intelligent use of the street network layout in urban areas. The street network is a key component in urban structure and is the domain in which crime and policing take place. By explicitly considering street network configurations in their operations, police forces are enabled to provide timely responses to emergency calls and essential coverage to crime hotspots. Although some models have considered street networks in patrolling to some extent, challenges remain. First, most existing methods for the design of police districts use two-dimensional units, such as grid cells, as basic units, but using streets as basic units would lead to districts that are more accessible and usable. Second, the routing problem in police patrolling has several unique characteristics, such as patrollers potentially starting from different stations, but most existing routing strategies have failed to consider these. Third, police patrolling strategies should be validated using real-world scenarios, whilst most existing strategies in the literature have only been tested in small hypothetical instances without realistic settings. In this thesis, a framework for developing police patrol strategies based on the urban street network is proposed, to effectively cover crime hotspots, as well as the rest of the territory. This framework consists of three strategies, including a districting model, a patrol routing strategy for repeated coverage, and a patrol routing strategy for infrequent coverage. Various relevant factors have been considered in the strategy design, including the underlying structure of the street network and the collaboration among patrollers belonging to different stations. Moreover, these strategies have been validated by the patrolling scenarios in London. The results demonstrate that these strategies outperform the current corresponding benchmark strategies, which indicates that they may have considerable potential in future police operations

A Metaheuristic Genetic Algorithm for Routing Bridge Inspection Robots

The safety and integrity of transportation infrastructure relies heavily on bridge inspections which can be expensive and hazardous for inspectors. Recent advancements in robotics and autonomy has resulted in steel truss climbing robots for bridge inspection that can reduce these costs and improve safety. However, optimally routing multiple robots to traverse and inspect each member of a truss bridge remains a challenging NP-hard problem which we represent by the Min-Max k-Chinese Postman Problem. In this thesis we attack this problem by constructing routes with a Metaheuristic Genetic Algorithm. The results demonstrate that this approach provides high quality solutions in reasonable time. Specifically, on standard benchmarks from literature we reveal that the quality of solutions are statistically indistinguishable compared to a prior state-of-the-art Tabu Search method. Furthermore, our Metaheuristic Genetic Algorithm surpasses the prior best Direct Encoded Genetic Algorithm by producing routes that are on average 15.24% better quality in a fraction (0.05) of the time on 20 new benchmark problems representing four well-known bridge truss structures. We also investigate the impact of multiple robot starting points on the total inspection time in the multi-depot variant of the Min-Max k-Chinese Postman Problem. The Metaheuristic Genetic Algorithm multi-depot solutions outperforms the previous best Genetic Algorithm multi-depot solutions that are on average 41.72% better quality and 22 times faster with three different postman configurations on the 20 new benchmark problems. This thesis therefore indicates that Metaheuristic Genetic Algorithms are a viable approach to the Min-Max k-Chinese Postman Problem and thus for routing autonomous inspection robots for safer, most cost effective bridge inspection. More generally, Metaheuristic Genetic Algorithms may show promise for attacking other similar Arc Routing Problems

Multi-depot rural postman problems

The final publication is available at Springer via http://dx.doi.org/10.1007/s11750-016-0434-zThis paper studies multi-depot rural postman problems on an undirected graph. These problems extend the well-known undirected rural postman problem to the case where there are several depots instead of just one. Linear integer programming formulations that only use binary variables are proposed for the problem that minimizes the overall routing costs and for the model that minimizes the length of the longest route. An exact branch-and-cut algorithm is presented for each considered model, where violated constraints of both types are separated in polynomial time. Despite the difficulty of the problems, the numerical results from a series of computational experiments with various types of instances illustrate a quite good behavior of the algorithms. When the overall routing costs are minimized, over 43 % of the instances were optimally solved at the root node, and 95 % were solved at termination, most of them with a small additional computational effort. When the length of the longest route is minimized, over 25 % of the instances were optimally solved at the root node, and 99 % were solved at termination.Peer ReviewedPostprint (author's final draft

Modeling Correlation in Vehicle Routing Problems with Makespan Objectives and Stochastic Travel Times

The majority of stochastic vehicle routing models consider travel times to be independent. However, in reality, travel times are often stochastic and correlated, such as in urban areas. We examine a vehicle routing problem with a makespan objective incorporating both stochastic and correlated travel times. We develop an approach based on extreme-value theory to estimate the expected makespan (and standard deviation) and embed this within a routing heuristic. We present results that demonstrate the impact of different correlation patterns and levels of correlation on route planning

Optimisation de tournées de véhicules en viabilité hivernale

RÉSUMÉ : Cette thèse développe des outils mathématiques et informatiques pour améliorer les opérations de viabilité hivernale. En particulier, la confection des tournées de déneigement est traitée comme un problème de tournées sur les arcs avec plusieurs contraintes. Une métaheuristique est d’abord développée pour la confection de ces tournées. Par la suite, des modifications majeures sont apportées à cet algorithme pour tenir compte des caractéristiques spécifiques aux problèmes de tournées sur les arcs (arc routing problem) (ARP) sur des réseaux routiers réels. Finalement, un second problème combinant les tournées de déneigement et d’épandage avec la mise en commun de certains véhicules pour les opérations est traité. La solution développée permet de tirer parti des caractéristiques de chaque véhicule. Tout au long de la thèse, un accent particulier est porté sur l’utilisation des données réelles ainsi que sur le développement de méthodes pour faciliter l’importation et l’exportation de ces données. Les travaux entourant cette thèse débutent avec la confection de tournées de déneigement pour une ville au Québec, soit Dolbeau-Mistassini (DM). De nombreux problèmes ont été rencontrés avec l’utilisation d’une méthode tirée de la littérature. Parmi ceux-ci, on compte : — de nombreux demi-tours difficiles à exécuter par les véhicules ; — le faible respect des priorités accordées aux rues à l’échelle du réseau ; — de nombreux véhicules parcourent de longues distances pour se rendre dans les coins reculés du réseau ; — le déséquilibre des tâches de travail en raison des différentes vitesses d’opération des véhicules ; — le fait que la méthode ne tient pas compte des ruelles qui peuvent être traitées dans une direction ou dans l’autre en un seul passage. À la suite de nombreux ajustements manuels pour corriger les tournées obtenues, force a été de constater que des améliorations pouvaient être apportées à ce type de méthode. Les travaux concernant la première contribution de cette thèse ont donc porté sur le développement d’une méthode de création de tournées de déneigement. En raison du grand nombre de variables et de contraintes considérées dans le problème, le choix s’est porté sur une méthode heuristique. Ce type de méthode offre un bon équilibre entre le temps de traitement et la qualité des solutions obtenues. Plus précisément, le choix s’est arrêté sur une métaheuristique de type algorithme de recherche à voisinage adaptatif large (adaptive large neighborhood search) (ALNS), en raison du succès remporté récemment par ce type de méthode. Le premier article a permis de constater que l’algorithme développé permet de créer des tournées pour les véhicules de déneigement. Les contraintes suivantes sont respectées : équilibrage des tournées, couverture partielle du réseau, vitesses hétérogènes, restrictions de virages, restrictions rue/véhicule et hiérarchie du réseau. Pour la deuxième contribution de thèse, le problème a d’abord été formalisé par l’intermédiaire d’un programme linéaire en nombres entiers (mixed integer programming) (MIP). Le problème a été formulé comme un problème des k-postiers ruraux avec objectif minmax (min-max k-vehicles rural postman problem) (MM K-RPP) avec hiérarchies, pénalités sur virages, vitesses d’opération hétérogènes et tournées ouvertes sur un graphe mixte. Tel qu’anticipé, la résolution devient rapidement impossible à traiter avec un solveur commercial en utilisant seulement 20 segments de rue. Il a été décidé de poursuivre l’approfondissement de l’algorithme développé en première partie. Cette décision a été prise notamment en raison du très long temps de traitement qui réduit l’utilité du premier algorithme. Cette décision repose aussi sur le fait que visuellement, on constate que les tournées obtenues peuvent être améliorées. Dans cette optique, une collaboration a été initiée avec messieurs Fabien Lehuédé et Olivier Péton du laboratoire des sciences du numérique de Nantes (LS2N) à IMT Atlantique. Leur expertise avec la méthode ALNS a effectivement permis d’améliorer grandement les résultats obtenus. Parmi les améliorations apportées, on note une transformation du réseau permettant de tenir compte des pénalités sur virages lors du calcul des plus courts chemins. Cette transformation permet également de mieux prendre en compte les ruelles qui requièrent un seul passage dans une direction ou dans l’autre. De plus, la possibilité d’appliquer plusieurs fois un opérateur de destruction avant de passer à la construction est ajoutée. Cette contribution a également été l’occasion de développer et tester de nouveaux opérateurs de voisinage, développer une méthode de groupement des arcs et revoir et simplifier le code de la métaheuristique. L’algorithme a été appliqué à la première étude de cas ainsi qu’a deux nouvelles études de cas, Baie-Comeau (BC) et Plateau-Mont-Royal (PMR). Des tests ont également été exécutés en comparant les nouvelles tournées obtenues à des tournées conçues quelques années plus tôt ainsi qu’aux résultats obtenus par un solveur commercial. Les résultats obtenus démontrent que la méthodologie améliore les tournées conçues précédemment. Il est aussi possible de conclure que la méthode de groupage des arcs améliore la qualité des solutions obtenues et l’efficacité des nouveaux opérateurs développés varie selon le réseau utilisé. Pour la troisième contribution, nous sommes revenus sur le cas d’étude initial tel que décrit par les intervenants de la première étude de cas. Il a été dit que les charges de travail doivent être équilibrées, mais que certains véhicules doivent également épandre des fondants ou des abrasifs en plus de déneiger. Pour tenir compte de cette contrainte, certaines tournées avaient délibérément été gardées plus courtes dans les premières solutions. Pour le troisième article, il a été décidé de traiter cette problématique de front. Ce qu’il faut savoir est que certains véhicules sont équipés pour l’épandage et le déneigement alors que d’autres sont équipés pour le déneigement seulement. Lorsque les premiers traitent un segment de rue, ils exécutent les deux opérations simultanément. Lorsque les deuxièmes traitent un segment de rue, il faut planifier un second passage par les premiers véhicules pour qu’ils puissent épandre des fondants ou des abrasifs. L’algorithme développé précédemment a donc été modifié dans cette optique. En plus, la considération des contraintes de restrictions rue/véhicule a été ajoutée dans l’algorithme. Les résultats démontrent que l’algorithme permet effectivement de concevoir des tournées qui respectent les contraintes de la nouvelle étude de cas. Cet outil permet donc de tirer profit de l’interaction entre les divers types de véhicules. La contribution souligne également l’utilité d’un tel outil pour supporter l’analyse des besoins justifiant l’achat de nouveaux véhicules. En parallèle aux développements algorithmiques, des méthodes d’importation et d’exportation des données provenant des cas d’étude réels sont aussi développées. Dès le départ, il a été choisi d’utiliser des fichiers de type Shapefile comme source de données en raison de sa grande disponibilité et de la compatibilité avec les système d’information géographique (SIG). Une méthode pour passer du réseau géographique vers un réseau mathématique a donc été améliorée au cours des travaux. Alors qu’au début des travaux de la thèse, il fallait passer par un chiffrier Microsoft ExcelTM pour ensuite importer les données dans le code, à la fin, une méthode automatisée permet l’importation directe à partir des fichiers Shapefiles vers le code de la métaheuristique. Quant aux résultats obtenus, ils furent obtenus dans les premières étapes sous forment de représentations géographiques dans un SIG ainsi que des feuilles d’instructions indiquant les étapes, coin de rue par coin de rue, aux opérateurs de véhicules. De ce côté, les développements ont permis d’obtenir des fichiers de type KML. Ce type de fichier est compatible avec plusieurs logiciels et applications, dont Google EarthviewTM et des applications de guidage routier sur des appareils mobiles.----------ABSTRACT : In this thesis, we develop mathematical and computerized tools to improve winter viability operations. More precisely, the snow routing design problem is treated as an problème de tournée sur les arcs (arc routing problem) (ARP). In a first effort to solve the problem, a metaheuristic procedure is designed. Then, some major modifications are made to the algorithm to improve the consideration of specific characteristics of real road networks. Finally, a second problem combining the routing of the snowplow and the spreading vehicles are addressed. The objective is to fully take advantage of the characteristics of the different type of vehicles. In parallel with the algorithmic development, this thesis also develops some methodologies to facilitate the importation and exportation of the real world data. Works concerning this thesis were initiated with a mandate to design snowplow routes for a city in the province of Québec, namely DM. The problem was addressed by using a methodology found in the literature, however, several difficulties were encountered. Among others: — the routes contained several U-turns which are difficult to perform by the snow plowing vehicles; — little consideration of the priorities at the network level; — several vehicles have to travel to some remote streets in the same sector of the city where we would expect only one vehicle to go; — unbalanced sectors due to the different speeds of operation of the vehicles; — no consideration for back alleys that needs to be serviced only once in either direction. In respond to these problems, several manual modifications of the routes were undertaken to make them feasible. It was found that the methodology fails to solve the problem as it is encountered. Therefore, works concerning the first contribution of this thesis focused on the development of a methodology to design snowplow routing. Due to numerous variables and constraints, it was decided to develop a metaheuristic algorithm. This type of methodology offers a good balance between runtime and the quality of the solution obtained. In particular, an ALNS is selected because of its recent success cited in the literature. Thus, the first article concludes that the algorithm can design snowplow routing. The following constraints are considered: workload balance, partial area coverage, heterogeneous vehicle speeds, road/vehicle dependencies, network hierarchies and turn restrictions. In the second contribution of this thesis, the problem was modeled as a mixed integer program. It is formulated as a min-max k-rural postmen problem with hierarchies, turn penalties, open tours and heterogeneous speed on a mixed graph. As expected, the formulation is intractable even for a number of arcs as low as 20. It was then decided to pursue the development of the ALNS algorithm. This decision was taken considering the long runtime of the first algorithm and the fact that the routes obtained can be visually improved. A collaboration with Fabien Lehuédé and Olivier Péton from the Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique was undertaken. Their expertise with ALNS greatly helped to improve the results obtained. Among other improvements brought to the algorithm, one can cite the transformation of the graph which allows to better take into account turn penalties during the computation of the shortest paths. This transformation also allows to better take into account the back alleys which only need one service in either direction. This contribution also allowed to develop and test new neighborhood operators and an arc grouping methodology. Both of these innovations improve the quality of the solutions obtained. However the efficiency of the new operators varies with the network. For the third contribution, we took back the case study as it was described by the collaborator in DM. It was said that the workload needs to be balanced among the vehicles. However some vehicles must also perform winter spreading in addition to plowing. For the first set of routes produced, some of the routes were deliberately left with a lower workload to allow them to perform winter spreading. For the third article, it was decided to consider the spreading and the plowing directly during the construction and the improvement steps. Thus this problem was tackled more directly in the third article. It must be noted that some vehicles are equipped to perform both winter spreading and snow plowing and some others can only perform plowing. When the former service a street, they can perform both plowing and spreading at the same time. When the latter service a street, a second passage is required to spread salt or abrasives. The algorithm developed for the second contribution was then adapted for this new problem. Moreover, the street/vehicle restriction constraints were also added. The result shows that the algorithm can produce a set of routes respecting the constraints of the new problem. It can take advantage of the interaction between the various types of vehicles. The article also shows that such tool can be beneficial in analyzing the requirements for new vehicles. In parallel with the development of the algorithms, data importation and exportation techniques from real road networks are also developed. It was chosen to use Shapefiles because of its good relative availability and because of its compatibility with Geographic Information System (GIS). A method to transfer from a geographical to a mathematical network is improved during the thesis. At the beginning, a Microsoft ExcelTM datasheet is used to transfer the data from the GIS to the metaheuristic. At the end, it is possible to fetch the data directly from the Shapefiles to the metaheuristic. As for the results obtained, at the beginning, they were provided in the form of a Shapefile for visualization and indications on sheets of paper for the operators. At the end, the results can be exported to the KML format. This type of file is compatible with several software such as Google EarthviewTM and application Global Positioning System (GPS) applications on mobile devices

New models and algorithms for several families of Arc Routing Problems

Some of the most common decisions to be taken within a logistic systems at an operational level are related to the design of the vehicle routes. Vehicle Routing Problems and Arc Routing Problems are well-known families of problems addressing such decisions. Their main difference is whether service demand is located at the vertices or the edges of the operating network. In this thesis we focus on the study of several arc routing problems. We concentrate on three families of problems. The first family consists of Multi Depot Rural Postman Problems, which are an extension of Rural Postman Problems where there are several depots instead of only one. The second family of problems that we study are Location-Arc Routing Problems, in which the depots are not fixed in advance, so their location becomes part of the decisions of the problem. We finally study Target-Visitation Arc Routing Problems, where the service is subject to an ordering preference among the connected components induced by demand arcs. Different models are studied for each considered family. In particular, two different Multi Depot Rural Postman Problem models are considered, which differ in the objective function: the minimization of the overall transportation cost or the minimization of the makespan. Concerning Location-Arc Routing Problems, we study six alternative models that differ from each other in their objective function, whether there is an upper bound on the number of facilities to be located, or whether there are capacity constraints on the demand that can be served from selected facilities. Finally, two Target-Visitation Arc Routing Problem models are studied, which differ from each other in whether or not it is required that all the required edges in the same component are visited consecutively. The aim in this thesis is to provide quantitative tools to the decision makers to identify the best choices for the design of the routes. To this end and for each considered problem, we first study and analyze its characteristics and properties. Based on them we develop different Integer Linear Programming formulations suitable for being solved trough branch-and-cut. Finally, all formulations are tested trough extensive computational experience. In this sense, for Multi Depot Rural Postman Problems and Location-Arc Routing Problems we propose natural modeling formulations with three-index variables, where variables are associated with edges and facilities. For some of the models we also present alternative formulations with only two-index variables, which are solely associated with edges. Finally, for the Target-Visitation Arc Routing Problems we propose three different formulations, two alternative formulations for the general case, and one for the clustered version, where all the edges in the same components are served sequentially, which exploits some optimality conditions of the problem.Algunes de les decisions més habituals que es prenen en un sistema logístic a nivell operatiu estan relacionades amb el disseny de rutes de vehicles. Els coneguts Vehicle Routing Problems i Arc Routing Problems són famílies de problemes que s'ocupen d'aquest tipus de decisions. La principal diferència entre ambdós recau en si la demanda de servei es troba localitzada als vèrtexs o a les arestes de la xarxa. Aquesta tesi es centra en l'estudi de diversos problemes de rutes per arcs. Ens centrem en tres famílies de problemes. La primera família consisteix en els Multi Depot Rural Postman Problems, que són una extensió del Rural Postman Problem on hi ha diversos dipòsits en lloc d'un de sol. La segona família de problemes que estudiem són els Location-Arc Routing Problems, en els quals els dipòsits no estan fixats amb antelació i, per tant, la seva ubicació esdevé part de les decisions a prendre en el problema. Finalment, estudiem els Target-Visitation Arc Routing Problems, on el servei està subjecte a una preferència d'ordenació entre les components connexes induïdes pels arcs amb demanda. S'estudien diferents models per a cadascuna de les famílies considerades. En particular, es consideren dos models diferents per al Multi Depot Rural Postman Problem, que es diferencien en la funció objectiu: la minimització del cost general de transport o la minimització de la ruta més llarga. Pel que fa als Location-Arc Routing Problems, estudiem sis models alternatius que difereixen en la seva funció objectiu, considerant si hi ha un límit màxim sobre la quantitat de dipòsits a ubicar o si hi ha restriccions de capacitat sobre la demanda que es pot servir des dels dipòsits seleccionats. Finalment, s'estudien dos models de Target-Visitation Arc Routing Problem, que es diferencien en si es necessari que totes les arestes requerides en la mateixa component es visitin de forma consecutiva. L'objectiu d'aquesta tesi és proporcionar eines quantitatives als responsables, que permetin identificar les millors opcions de disseny de les rutes. Per això, i per a cadascundels problemes considerats, primer estudiem i analitzem les seves característiques i propietats. A partir d'aquestes, desenvolupem diferents formulacions de Programació Lineal Entera, adequades per a la seva solució mitjançant un branch-and-cut. Finalment, totes les formulacions són provades mitjançant un ampli testeig computacional. En aquest sentit, per als Multi Depot Rural Postman Problems i els Location-Arc Routing Problems, proposem formulacions naturals amb variables de tres índexs, on les variables estan associades a les arestes i als dipòsits. Per a alguns dels models també presentem formulacions alternatives, amb variables de només dos índexs, que només estan associades a les arestes. Finalment, per als Target-Visitation Arc Routing Problems proposem tres formulacions diferents, dues formulacions alternatives per al cas general i una per a la versió en clúster, on totes les arestes de la mateixa component es serveixen seqüencialment, cosa que explora algunes condicions d'optimització pròpies.Algunas de las decisiones más habituales que se toman en un sistema logístico a nivel operativo están relacionadas con el diseño de rutas de vehículos. Los conocidos Vehicle Routing Problems y Arc Routing Problems son familias de problemas que se ocupan de este tipo de decisiones. La principal diferencia entre ambas reside en si la demanda de servicios está localizada en los vértices o en las aristas de la red. Esta tesis se centra en el estudio de diversos problemas de rutas por arcos. Nos centramos en tres familias de problemas. La primera familia consiste en los Multi Depot Rural Postman Problems, que son una extensión del Rural Postman Problem donde hay varios depósitos en lugar de solamente uno. La segunda familia de problemas que estudiamos son los Location-Arc Routing Problems, en los que los depósitos no están fijados con antelación y, por lo tanto, su ubicación se convierte en parte de las decisiones a tomar en el problema. Finalmente, estudiamos los Target-Visitation Arc Routing Problems, donde el servicio está sujeto a una preferencia de ordenación entre las componentes conexas inducidas por los arcos con demanda. Se estudian diferentes modelos para cada una de las familias consideradas. En particular, se consideren dos modelos diferentes para el Multi Depot Rural Postman Problem que se diferencian en la función objetivo: la minimización del coste general de transporte o la minimización de la ruta más larga. En cuanto a los Location-Arc Routing Problems, estudiamos seis modelos alternativos que difieren en su función objetivo, en si hay un limite máximo sobre la cantidad de depósitos a ubicar, o en si hay restricciones de capacidad sobre la demanda que se puede servir desde los depósitos seleccionados. Finalmente, se estudian dos modelos de Target-Visitation Arc Routing Problem, que se diferencian en si es necesario que todas las aristas requeridas en la misma componente se visiten de forma consecutiva. El objetivo de esta tesis es proporcionar herramientas cuantitativas a los responsables, que permitan identificar las mejores opciones de diseño de las rutas. Por ello, y para cada uno de los problemas considerados, primero estudiamos y analizamos sus características y propiedades. A partir de estas, desarrollamos diferentes formulaciones de Programación Lineal Entera, adecuadas para su solución mediante un branch-and-cut. Finalmente, todas las formulaciones son probadas mediante un amplio testeo computacional. En este sentido, para los Multi Depot Rural Postman Problems y los Location-Arc Routing Problems, proponemos formulaciones naturales con variables de tres índices, donde las variables están asociadas a las aristas y a los depósitos. Para algunos de los modelos también presentamos formulaciones alternativas con variables de sólo dos índices, que sólo están asociadas a las aristas. Finalmente, para los Target-Visitation Arc Routing Problems proponemos tres formulaciones diferentes, dos formulaciones alternativas para el caso general y una para la versión en clúster, donde todas las aristas de la misma componente se sirven secuencialmente, lo que explora algunas condiciones de optimización propia

Towards high spatial resolution air quality mapping : a methodology to assess street-level exposure based on mobile monitoring

Exposure to air pollution has a severe impact on human health. Especially in urban areas, where most of the European population lives and which are typically hot-spots of air pollution, a lot of people are exposed to air pollution. However, the urban environment shows a high variability in air pollutant concentrations and available data are often lacking to accurately estimate the actual concentration levels citizens are exposed to. The emergence of lower-cost and portable sensors makes it possible to perform mobile measurements and to collect additional data at locations where stationary measurements are lacking. Further, this also makes it possible to engage citizens in participatory monitoring techniques. However, several issues on spatial and temporal representativeness can interfere with the real-life applicability of mobile monitoring. This thesis presents the possibilities and challenges of the use of mobile data to map the urban air quality. Based on an extensive targeted campaign, it is shown that mobile monitoring is a suitable approach to map the urban air quality at a high spatial resolution when using a carefully developed methodology. However, a large number of repeated measurements are still required to obtain representative results. A possible way to gather a large number of measurements is to make use of people’s common daily routines to move measurement devices around, which is defined as opportunistic measurements. An example case study with the collaboration of the city wardens of Antwerp is presented in this thesis. Mobile monitoring typically does not yet result in city-wide pollution maps. Based on the data, regression models can be built to predict the concentration levels at other locations. The results highlighted the potential to construct near-real-time pollution maps that can be used for providing personalized information about air quality to citizens

Winona Daily News

https://openriver.winona.edu/winonadailynews/1760/thumbnail.jp