Exploring Graphs with Time Constraints by Unreliable Collections of Mobile Robots

A graph environment must be explored by a collection of mobile robots. Some of the robots, a priori unknown, may turn out to be unreliable. The graph is weighted and each node is assigned a deadline. The exploration is successful if each node of the graph is visited before its deadline by a reliable robot. The edge weight corresponds to the time needed by a robot to traverse the edge. Given the number of robots which may crash, is it possible to design an algorithm, which will always guarantee the exploration, independently of the choice of the subset of unreliable robots by the adversary? We find the optimal time, during which the graph may be explored. Our approach permits to find the maximal number of robots, which may turn out to be unreliable, and the graph is still guaranteed to be explored. We concentrate on line graphs and rings, for which we give positive results. We start with the case of the collections involving only reliable robots. We give algorithms finding optimal times needed for exploration when the robots are assigned to fixed initial positions as well as when such starting positions may be determined by the algorithm. We extend our consideration to the case when some number of robots may be unreliable. Our most surprising result is that solving the line exploration problem with robots at given positions, which may involve crash-faulty ones, is NP-hard. The same problem has polynomial solutions for a ring and for the case when the initial robots' positions on the line are arbitrary. The exploration problem is shown to be NP-hard for star graphs, even when the team consists of only two reliable robots

Spartan Daily, September 13, 1991

Volume 97, Issue 10https://scholarworks.sjsu.edu/spartandaily/8147/thumbnail.jp

Arc routing problems: A review of the past, present, and future

[EN] Arc routing problems (ARPs) are defined and introduced. Following a brief history of developments in this area of research, different types of ARPs are described that are currently relevant for study. In addition, particular features of ARPs that are important from a theoretical or practical point of view are discussed. A section on applications describes some of the changes that have occurred from early applications of ARP models to the present day and points the way to emerging topics for study. A final section provides information on libraries and instance repositories for ARPs. The review concludes with some perspectives on future research developments and opportunities for emerging applicationsThis research was supported by the Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional, Grant/Award Number: PGC2018-099428-B-I00. The Research Council of Norway, Grant/Award Numbers: 246825/O70 (DynamITe), 263031/O70 (AXIOM).Corberán, Á.; Eglese, R.; Hasle, G.; Plana, I.; Sanchís Llopis, JM. (2021). Arc routing problems: A review of the past, present, and future. Networks. 77(1):88-115. https://doi.org/10.1002/net.21965S8811577

Arc Routing Problems for Road Network Maintenance

RÉSUMÉ : Cette thèse présente deux problèmes rencontrés dans l’entretien des réseaux routiers, soit la surveillance des réseaux routiers pour la détection de verglas sur la chaussée et la reprogrammation des itinéraires pour les activités de déneigement et d’épandage de sel. Nous représentons ces problèmes par des modèles de tournées sur les arcs. La dépendance aux moments et la nature dynamique sont des caractéristiques propres de ces problèmes, par conséquence le cas de surveillance des réseaux routiers est modélisé comme un problème de postier rural avec fenêtres-horaires (RPPTW), tandis que le cas de la reprogrammation utilise des modèles obtenus à partir des formulations de problèmes de tournées sur les arcs avec capacité. Dans le cas du problème de surveillance, une patrouille vérifie l’état des chemins et des autoroutes, elle doit principalement détecter le verglas sur la chaussée dans le but d’assurer de bonnes conditions aux chauffeurs et aux piétons. Étant donné un réseau routier et des prévisions météo, le problème consiste à créer une tournée qui permette de détecter opportunément le verglas sur les rues et les routes. L’objectif poursuivi consiste à minimiser le coût de cette opération. En premier, on présente trois formulations basées sur la programmation linéaire en nombres entiers pour le problème de surveillance des réseaux qui dépend du moment et deux méthodes de résolution: un algorithme de coupes et un algorithme heuristique appelé adaptive large neighborhood search (ALNS). La méthode exacte inclut des inéquations valides tirées du problème du voyageur de commerce avec fenêtres-horaires et aussi du problème de voyageur du commerce avec contraintes de précédence. La méthode heuristique considère deux phases: en premier, on trouve une solution initiale et après dans la deuxième phase, l’algorithme essaie d’améliorer la solution initiale en utilisant sept heuristiques de destruction et deux heuristiques de réparation choisies au hasard. La performance des heuristiques est évaluée pendant les itérations. Une meilleure performance correspond à une plus grande probabilité de choisir une heuristique. Plusieurs tests ont été faits sur deux ensembles d’exemplaires de problèmes. Les résultats obtenus montrent que l’algorithme de coupes est capable de résoudre des réseaux avec 104 arêtes requises et des fenêtres-horaires structurées par tranches horaires ; l’algorithme peut aussi résoudre des réseaux avec 45 arêtes requises et des fenêtres-horaires structurées pour chaque arête requise. Pour l’algorithme ALNS, différentes versions de l’algorithme sont comparées. Les résultats montrent que cette méthode est efficace parce qu’elle est capable de résoudre à l’optimalité 224 des 232 exemplaires et de réduire le temps de calcul significativement pour les exemplaires les plus difficiles. La dernière partie de la thèse introduit le problème de la reprogrammation de tournées sur les arcs avec capacité (RCARP), lequel permet de modéliser la reprogrammation des itinéraires après une panne d’un véhicule lors de la phase d’exécution d’un plan initial des activités de déneigement ou d’épandage de sel. Le planificateur doit alors modifier le plan initial rapidement et reprogrammer les véhicules qui restent pour finir les activités. Dans ce cas, l’objectif poursuivi consiste à minimiser le coût d’opération et le coût de perturbation. La distance couverte par les véhicules correspond au coût d’opération, cependant une nouvelle métrique est développée pour mesurer le coût de perturbation. Les coûts considérés sont des objectifs en conflit. On analyse quatre politiques à la phase de re-routage en utilisant des formulations de programmation linéaire en nombres entiers. On propose une solution heuristique comme méthode pour résoudre le RCARP quand les coûts d’opération et de perturbation sont minimisés en même temps et quand une réponse rapide est nécessaire. La méthode consiste à fixer une partie de l’itinéraire initial et après à modifier seulement les itinéraires des véhicules les plus proches de la zone de l’interruption de la tournée du véhicule défaillant. La méthode a été testée sur des exemplaires obtenus d’un réseau réel. Nos tests indiquent que la méthode peut résoudre rapidement des exemplaires avec 88 arêtes requises et 10 véhicules actifs après la panne d’un véhicule. En conclusion, la principale contribution de cette thèse est de présenter des modèles de tournées sur les arcs et de proposer des méthodes de résolution d’optimisation qui incluent la dépendance aux temps et l’aspect dynamique. On propose des modèles et des méthodes pour résoudre le RPPTW, et on présente des résultats pour ce problème. On introduit pour la première fois le RCARP. Trois articles correspondant aux trois principaux chapitres ont été acceptés ou soumis à des revues avec comité de Lecture: “The rural postman problem with time windows” accepté dans Networks, “ALNS for the rural postman problem with time windows” soumis à Networks, and “The rescheduling capacitated arc routing problem” soumis à International Transactions in Operational Research.----------ABSTRACT : This dissertation addresses two problems related to road network maintenance: the road network monitoring of black-ice and the rescheduling of itineraries for snow plowing and salt spreading operations. These problems can naturally be represented using arc routing models. Timing-sensitive and dynamic nature are inherent characteristics of these problems, therefore the road network monitoring is modeled as a rural postman problem with time windows (RPPTW) and in the rescheduling case, models based on capacitated arc routing formulations are suggested for the rerouting phase. The detection of black-ice on the roads is carried out by a patrol to ensure safety conditions for drivers and pedestrians. Specific meteorological conditions cause black-ice on the roads; therefore the patrol must design a route covering part of the network in order to timely detect the black-ice according to weather forecasts. We look for minimum-cost solutions that satisfy the timing constraints. At first, three formulations based on mixed integer linear programming are presented for the timing-sensitive road network monitoring and two solution approaches are proposed: a cutting plane algorithm and an adaptive large neighborhood search (ALNS) algorithm. The exact method includes valid inequalities from the traveling salesman problem (TSP) with time windows and from the precedence constrained TSP. The heuristic method consists of two phases: an initial solution is obtained, and then in the second phase the ALNS method tries to improve the initial solution using seven removal and two insertion heuristics. The performance of the heuristics is evaluated during the iterations, and therefore the heuristics are selected depending on their performance (with higher probability for the better ones). Several tests are done on two sets of instances. The computational experiments performed show that the cutting plane algorithm is able to solve instances with up to 104 required edges and with time windows structured by time slots, and problems with up to 45 required edges and time windows structured by each required edge. For the ALNS algorithm, several versions of the algorithm are compared. The results show that this approach is efficient, solving to optimality 224 of 232 instances and significantly reducing the computational time on the hardest instances. The last part of the dissertation introduces the rescheduling capacitated arc routing problem (RCARP), which models the rescheduling of itineraries after a vehicle failure happens in the execution of an initial plan of snow plowing or salt spreading operations. A dispatcher must quickly adjust the remaining vehicles and modify the initial plan in order to complete the operations. In this case we look for solutions that minimize operational and disruption costs. The traveled distance represents the operational cost, and a new metric is discussed as disruption cost. The concerned objectives are in conflict. Four policies are analyzed in the rerouting phase using mixed integer linear programming formulations. A heuristic solution is developed to solve the RCARP when operational and disruption costs are minimized simultaneously and a quick response is needed. The idea is to fix part of the initial itinerary and only modify the itinerary of vehicles closer to the failure zone. The method is tested on a set of instances generated from a real network. Our tests indicate that the method can solve instances with up to 88 required edges and 10 active vehicles after the vehicle breakdown. In short the main contribution of this dissertation is to present arc routing models and optimization solution techniques that consider timing-sensitive and dynamic aspects. Formulations and solution methods with computational results are given for the RPPTW, and the RCARP is studied for the first time here. Three articles corresponding to the main three chapters have been accepted or submitted to peer review journals: “The rural postman problem with time windows” accepted in Networks, “ALNS for the rural postman problem with time windows” submitted to Networks, and “The rescheduling capacitated arc routing problem” submitted to International Transactions in Operational Research

1948, September 24, Friday

The Booster, Vol. XV, no. 11. Printed in Pittsburg, Kansas

Water truck routing optimization in open pit mines using the general algebraic modelling system approach

This paper presents a methodological approach for routing optimization in open pit mines which is a trending topic for dust emission reduction in mining process. In this context, the aim of the research and its contribution to the knowledge is firstly described based on a comprehensive literature survey in the field. Then, as an arc routing problem, the mathematical model for the process is generated including the objective function, minimizing the total distance traveled by the water truck fleets, practical constraints that should be met and the used assumptions. Finally, the formulated optimization problem solved employing General Algebraic Modelling System (GAMS) approach respect to the nature of the mathematical equations. The tested results by simulations discussed to confirm the effectiveness of the proposed method in dealing with the in-hand problem. This methodological approach could be used in optimization of other similar engineering problem as well

An updated annotated bibliography on arc routing problems

The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberán and Prins (Networks 56 (2010), 50–69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem (GRP) and Arc Routing Problems (ARPs) with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem (CARP) and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post-disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising.info:eu-repo/semantics/publishedVersio

Інформаційна система планування обслуговування доріг міста

Магістерська дисертація: 112 с., 12 рис., 20 табл., 1 додаток, 36 джерел. Актуальність. Проведені у Великобританії дослідження показали, що у вартості продукту, який потрапив до кінцевого споживача, до 70% складають витрати, що так чи інакше пов’язані з логістичними операціями. З огляду на це обслуговування доріг стає необхідним процесом, що спрямований на підтримання належного технічного стану доріг та надання можливості швидкого та безпечного переміщення транспортних засобів задля уникнення аварійних ситуацій і т. ін. Отже, обслуговування доріг потребує якісного планування маршрутів для спеціалізованої дорожньої техніки. Математичне формулювання цієї задачі відоме як задача маршрутизації по дугам (Arc Routing Problem), що є підмножиною задач маршрутизації транспортних засобів (Vehicle Routing Problem). Існує багато розроблених математичних моделей вищезазначеної задачі, проте врахування додаткових умов часто призводить до створення нової моделі і відповідно пошуку нового або модифікації існуючого методу розв’язання. Робота присвячена дослідженню та розробці методу розв’язання задачі ARP. Зв'язок роботи з науковими програмами, планами, темами. Робота виконувалась на кафедрі автоматизованих систем обробки інформації та управління Національного технічного університету України «Київський політехнічний інститут ім. Ігоря Сікорського» в рамках теми «Ефективні методи розв'язання задач теорії розкладів» (№ ДР 0117U000919). Мета і завдання дослідження. Метою є підвищення якості процесів обслуговування доріг міста за рахунок мінімізації часу проходження транспортними засобами запланованих шляхів сполучень (із врахуванням обмежень на директивні терміни виконання робіт та місткість машин). Для досягнення поставленої мети необхідно вирішити наступні завдання: – дослідити предметне середовище та особливості його функціонування; – провести аналіз відомих результатів розв’язання задачі маршрутизації транспортних засобів по дугам; – сформулювати постановку задачі мінімаксу k-китайських листонош з врахуванням директивних термінів виконання робіт та місткості машин; – розробити модифікований алгоритм сформульованої задачі та дослідити його ефективність; – розробити інформаційну систему планування обслуговування доріг міста. Об’єкт дослідження – логістичні процеси обслуговування доріг. Предмет дослідження – задачі побудови маршрутів транспортних засобів, що орієнтовані на проходження шляхів сполучень та враховують директивні терміни виконання робіт та місткість машин. Методи дослідження, застосовані в роботі, базуються на методах дослідження операцій, евристичних та метаевристичних алгоритмах. Наукова новизна отриманих результатів полягає у модифікації та використанні в складі інформаційної системи алгоритму розв’язання задачі маршрутизації по дугам. Публікації. Матеріали роботи опубліковані у науковому журналі «Paradigm of Knowledge» та тезах доповіді Тринадцятої міжнародної науково-практичної конференції «Математичне та імітаційне моделювання систем. МОДС 2018» та ІІІ Всеукраїнської науково-практичної конференції молодих вчених та студентів «Інформаційні системи та технології управління» (ІСТУ-2019).Master dissertation: 112 pp., 12 fig., 20 tab., 1 app., 36 sources. The relevance. Researchs in the UK have shown that up to 70% of the cost of a product that reaches the end consumer are the costs associated with logistics operations in one way or another. In view of this, road maintenance becomes a necessary process aimed to maintain the good condition of roads and enabling the rapid and safe movement of vehicles to avoid emergencies, etc. Therefore, road maintenance requires quality route planning for specialized road technics. The mathematical model of this problem is known as the Arc Routing Problem, which is a subset of Vehicle Routing Problems. There are many mathematical models developed for the above problem, but taking into account additional conditions often leads to the creation of a new model and, accordingly, finding a new one or modifying an existing method of solving. The work is devoted to researching and developing the algorithm for solving the ARP problem. Relationship of work with scientific programs, plans, themes. The work was done at the department of computer-aided management and data processing systems of the National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute» within the theme «Effective methods for solving problems of scheduling theory» (№ DR 0117U000919). Purpose and objects of the research. The goal of the research is to improve the quality of road maintenance processes in the city districts by minimizing the transit time of all routes and taking into account restrictions on car capacity and deadline classes of the work. The following tasks need be solved to achieve these tasks: – to investigate the subject environment and peculiarities of its functioning; – to analyze the known results of solving the arc routing problem; – create the formulation of the Min-Max Capacitated k-Chinese Postman Problem with Deadline Classes; – to develop the modified algorithm of the formulated problem and to investigate its effectiveness; – to develop the information system for city road maintenance planning. The object of the research – logistic processes of road maintenance. The subject of the research – vehicle routing problem, which is oriented on the passing of routes by vehicles and takes into account the deadline classes of the work and the capacity of cars. Methods of the research, used in the paper, are based on operations research methods, heuristic and metaheuristic algorithms. Scientific novelty of the results is the modification of the algorithm for solving the arc routing problem and the use of this algorithm within the information system. Publications. The results of the research were published in the scientific journal «Paradigm of Knowledge», at the materials of the XIII International scientific and practical conference «Mathematical Modeling and Simulation of Systems. MODS 2018» and III Ukrainian scientific and practical conference of young scientists and students "Information Systems and Management Technologies" (ISTU-2019)

Debris removal during disaster response phase : a case for Turkey

Ankara : The Department of Industrial Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 88-93.In this study, a methodology to provide emergency relief supplies to the disaster affected regions is developed. As a result of destructive effects of disasters, debris, which is the ruin and wreckage of the structures, occurs. Proper removal of debris has significant importance since it blocks the roads and prohibits emergency aid teams to access the disaster affected regions. Wrong disaster management, lack of efficiency and delays in debris removal cause disruptions in providing sheltering, nutrition, healthcare and communication services to the disaster victims, and more importantly they result in loss of lives. Due to the importance of a systematic and efficient way of debris removal from the point of improving disaster victims’ life quality and its contributions to transportation of emergency relief materials to the disaster affected regions, the focus of this study is providing emergency relief supplies to the disaster affected regions as soon as possible, by considering unblocking operations of roads through removing the accumulated debris. To come up with a scientific solution methodology to the problem, mathematical models that select the paths in order to transport emergency aid materials in the presence of debris to the pre-determined disaster affected regions are developed. The performances of the models are tested on two distinct data sets from İstanbul. Since it is crucial to act quickly in an emergency case, a constructive and an improvement heuristic are also proposed.Şahin, HalenurM.S