개미알고리즘을 이용한 드론의 제설 경로 최적화

학위논문(석사) -- 서울대학교대학원 : 공과대학 건설환경공학부, 2022.2. 김동규.Drones can overcome the limitation of ground vehicles by replacing the congestion time and allowing rapid service. For sudden snowfall with climate change, a quickly deployed drone can be a flexible alternative considering the deadhead route and the labor costs. The goal of this study is to optimize a drone arc routing problem (D-ARP), servicing the required roads for snow removal. A D-ARP creates computational burden especially in large network. The D-ARP has a large search space due to its exponentially increased candidate route, arc direction decision, and continuous arc space. To reduce the search space, we developed the auxiliary transformation method in ACO algorithm and adopted the random walk method. The contribution of the work is introducing a new problem and optimization approach of D-ARP in snow removal operation and reduce its search space. The optimization results confirmed that the drone travels shorter distance compared to the truck with a reduction of 5% to 22%. Furthermore, even under the length constraint model, the drone shows 4% reduction compared to the truck. The result of the test sets demonstrated that the adopted heuristic algorithm performs well in the large size networks in reasonable time. Based on the results, introducing a drone in snow removal is expected to save the operation cost in practical terms.드론은 혼잡시간대를 대체하고 빠른 서비스를 가능하게 함으로써 지상차량의 한계를 극복할 수 있다. 최근 기후변화에 따른 갑작스런 강설의 경우에, 드론과 같이 빠르게 투입할 수 있는 서비스는 운행 경로와 노동비용을 고려했을 때도 유연한 운영 옵션이 될 수 있다. 본 연구의 목적은 드론 아크 라우팅(D-ARP)을 최적화하는 것이며, 이는 제설에 필요한 도로를 서비스하는 경로를 탐색하는 것이다. 드론 아크 라우팅은 특히 큰 네트워크에서 컴퓨터 부하를 생성한다. 다시 말해D-ARP는 큰 검색공간을 필요로 하며, 이는 기하급수적으로 증가하는 후보 경로 및 호의 방향 결정 그리고 연속적인 호의 공간으로부터 기인한다. 검색공간을 줄이기 위해, 우리는 개미알고리즘에 보조변환방법을 적용하는 방안을 도입하였으며 또한 랜덤워크 기법을 채택하였다. 본 연구의 기여는 제설 운영에 있어 D-ARP라는 새로운 문제를 설정하고 최적화 접근법을 도입하였으며 검색공간을 최소화한 것이다. 최적화 결과, 드론은 지상트럭에 비해 약 5% ~ 22%의 경로 비용 감소를 보였다. 나아가 길이 제약 모델에서도 드론은 4%의 비용 감소를 보였다. 또한 실험결과는 적용한 휴리스틱 알고리즘이 큰 네트워크에서도 합리적 시간 내에 최적해를 찾음을 입증하였다. 이러한 결과를 바탕으로, 드론을 제설에 도입하는 것은 미래에 제설 운영 비용을 실질적으로 감소시킬 것으로 기대된다.Chapter 1. Introduction 4 1.1. Study Background 4 1.2. Purpose of Research 6 Chapter 2. Literature Review 7 2.1. Drone Arc Routing problem 7 2.2. Snow Removal Routing Problem 8 2.3. The Classic ARPs and Algorithms 9 2.4. Large Search Space and Arc direction 11 Chapter 3. Method 13 3.1. Problem Statement 13 3.2. Formulation 16 Chapter 4. Algorithm 17 4.1. Overview 17 4.2. Auxilary Transformation Method 18 4.3. Ant Colony Optimization (ACO) 20 4.4. Post Process for Arc Direction Decision 23 4.5. Length Constraint and Random Walk 24 Chapter 5. Results 27 5.1. Application in Toy Network 27 5.2. Application in Real-world Networks 29 5.3. Application of the Refill Constraint in Seoul 31 Chapter 6. Conclusion 34 References 35 Acknowledgment 40석

Genetic programming hyper-heuristic with vehicle collaboration for uncertain capacitated arc routing problem

Due to its direct relevance to post-disaster operations, meter reading and civil refuse collection, the Uncertain Capacitated Arc Routing Problem (UCARP) is an important optimisation problem. Stochastic models are critical to study as they more accurately represent the real world than their deterministic counterparts. Although there have been extensive studies in solving routing problems under uncertainty, very few have considered UCARP, and none consider collaboration between vehicles to handle the negative effects of uncertainty. This article proposes a novel Solution Construction Procedure (SCP) that generates solutions to UCARP within a collaborative, multi-vehicle framework. It consists of two types of collaborative activities: one when a vehicle unexpectedly expends capacity (route failure), and the other during the refill process. Then, we propose a Genetic Programming Hyper-Heuristic (GPHH) algorithm to evolve the routing policy used within the collaborative framework. The experimental studies show that the new heuristic with vehicle collaboration and GP-evolved routing policy significantly outperforms the compared state-of-the-art algorithms on commonly studied test problems. This is shown to be especially true on instances with larger numbers of tasks and vehicles. This clearly shows the advantage of vehicle collaboration in handling the uncertain environment, and the effectiveness of the newly proposed algorithm

Two-echelon freight transport optimisation: unifying concepts via a systematic review

Multi-echelon distribution schemes are one of the most common strategies adopted by the transport companies in an aim of cost reduction, but their identification in scientific literature is not always easy due to a lack of unification. This paper presents the main concepts of two-echelon distribution via a systematic review, in the specific a meta-narrative analysis, in order to identify and unify the main concepts, issues and methods that can be helpful for scientists and transport practitioners. The problem of system cost optimisation in two-echelon freight transport systems is defined. Moreover, the main variants are synthetically presented and discussed. Finally, future research directions are proposed.location-routing problems, multi-echelon distribution, cross-docking, combinatorial optimisation, systematic review.

Integrated network routing and scheduling problem for salt trucks with replenishment before snowfall

Kar yağışı öncesinde ve sırasında yolların zamanında tuzlanması, trafik güvenliğini iyileştirmek ve trafik sıkışıklığını önlemek için önemli bir önleyici faaliyettir. Bu çalışmada, bir şehir yolu ağındaki tuz kamyonlarının rotalama ve çizelgeleme problemi ele alınmıştır. Ele alınan problem İstanbul Büyükşehir Belediyesinin yoğun kar yağışı durumlarında karşılaştığı bir operasyonel problemdir ve periyodik olarak çözülmelidir. Problemde, araç filosu tuz kapasitesi açısından heterojen araçlardan oluşmaktadır ve birden fazla tuz ikmal noktası bulunmaktadır. Hava şartları gerektirdiğinde, tuzlanması gereken yollar ve bu yollar için öncelik seviyeleri belirlenmektedir. Amaç, ağın farklı noktalarında konumlanmış olan araçların, tuzlanması gereken tüm yolları tuzlayacak şekilde ve yolların ağırlıklı tamamlanma süresini en küçükleyerek rotalanması ve çizelgelenmesidir. Tuza ihtiyacı olan her yol tek bir araç tarafından tuzlanmalıdır. Araçlar tuzlanması gereken bir yolu tuzlama yapmadan sadece geçiş yapmak amacıyla da kullanılabilir. Araçlar, tuzları bittiğinde tuz ikmal noktalarını ziyaret etmelidir. Problemin çözümü için ilk olarak bir karma tam sayılı programlama modeli geliştirilmiştir. Problem büyüklüğü arttıkça modelin performansının hızla düştüğü gözlemlenmiş ve iki aşamalı bir sezgisel yöntem geliştirilmiştir. Sezgiselin ilk aşamasında yapıcı algoritma ile olurlu bir başlangıç çözümü elde edilmektedir, ikinci aşamasında bulunan başlangıç çözümü bir komşuluk arama algoritması ile geliştirilmektedir. Çözüm yaklaşımımızın verimliliği, gerçek hayat yol ağlarını yansıtan rastgele oluşturulmuş örnekler üzerinde analiz edilmiştir.Timely salting of roads before the snowfall is an important preventive activity for improving traffic safety and avoiding traffic congestions. We study the problem of routing and scheduling of salt trucks on a city road network. The problem is motivated by the operational problem that the Istanbul Metropolitan Municipality face in case of a heavy snowfall, and thereby should be solved in a periodic manner.In this problem, the vehicle fleet consists of heterogeneous vehicles that differ in salt capacity and there are multiple salt replenishment points. At the beginning of the current planning horizon, given a set of salt needing roads with different urgency levels, the vehicles start from different points of the network (i.e., their final locations at the end of the former planning horizon) and should cover all salt needing roads with the objective of minimizing the total weighted completion time of salting operation of each service needing arc. Each service needing arc should be serviced by exactly one vehicle, however, can be traversed for deadheading by a vehicle as part of its route.Vehicles visit replenishment points when they run out of salt. We first develop a Mixed-Integer Programming model for the problem. Since the performance of the model degrades rapidly as the problem size increases, we propose a simulated annealing metaheuristic, which obtains an initial solution by a constructive heuristic in the first phase, and then improves the solution in the next phase. The efficiency of our solution approach is evaluated on randomly generated instances reflecting real life road networks

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

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

Two-echelon freight transport optimisation: unifying concepts via a systematic review

Multi-echelon distribution schemes are one of the most common strategies adopted by the transport companies in an aim of cost reduction, but their identification in scientific literature is not always easy due to a lack of unification. This paper presents the main concepts of two-echelon distribution via a systematic review, in the specific a meta-narrative analysis, in order to identify and unify the main concepts, issues and methods that can be helpful for scientists and transport practitioners. The problem of system cost optimisation in two-echelon freight transport systems is defined. Moreover, the main variants are synthetically presented and discussed. Finally, future research directions are proposed

The Multi-Depot Minimum Latency Problem with Inter-Depot Routes

The Minimum Latency Problem (MLP) is a class of routing problems that seeks to minimize the wait times (latencies) of a set of customers in a system. Similar to its counterparts in the Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP), the MLP is NP-hard. Unlike these other problem classes, however, the MLP is customer-oriented and thus has impactful potential for better serving customers in settings where they are the highest priority. While the VRP is very widely researched and applied to many industry settings to reduce travel times and costs for service-providers, the MLP is a more recent problem and does not have nearly the body of literature supporting it as found in the VRP. However, it is gaining significant attention recently because of its application to such areas as disaster relief logistics, which are a growing problem area in a global context and have potential for meaningful improvements that translate into reduced suffering and saved lives. An effective combination of MLP\u27s and route minimizing objectives can help relief agencies provide aid efficiently and within a manageable cost. To further the body of literature on the MLP and its applications to such settings, a new variant is introduced here called the Multi-Depot Minimum Latency Problem with Inter-Depot Routes (MDMLPI). This problem seeks to minimize the cumulative arrival times at all customers in a system being serviced by multiple vehicles and depots. Vehicles depart from one central depot and have the option of refilling their supply at a number of intermediate depots. While the equivalent problem has been studied using a VRP objective function, this is a new variant of the MLP. As such, a mathematical model is introduced along with several heuristics to provide the first solution approaches to solving it. Two objectives are considered in this work: minimizing latency, or arrival times at each customer, and minimizing weighted latency, which is the product of customer need and arrival time at that customer. The case of weighted latency carries additional significance as it may correspond to a larger number of customers at one location, thus adding emphasis to the speed with which they are serviced. Additionally, a discussion on fairness and application to disaster relief settings is maintained throughout. To reflect this, standard deviation among latencies is also evaluated as a measure of fairness in each of the solution approaches. Two heuristic approaches, as well as a second-phase adjustment to be applied to each, are introduced. The first is based on an auction policy in which customers bid to be the next stop on a vehicle\u27s tour. The second uses a procedure, referred to as an insertion technique, in which customers are inserted one-by-one into a partial routing solution such that each addition minimizes the (weighted) latency impact of that single customer. The second-phase modification takes the initial solutions achieved in the first two heuristics and considers the (weighted) latency impact of repositioning nodes one at a time. This is implemented to remove potential inefficient routing placements from the original solutions that can have compounding effects for all ensuing stops on the tour. Each of these is implemented on ten test instances. A nearest neighbor (greedy) policy and previous solutions to these instances with a VRP objective function are used as benchmarks. Both heuristics perform well in comparison to these benchmarks. Neither heuristic appears to perform clearly better than the other, although the auction policy achieves slightly better averages for the performance measures. When applying the second-phase adjustment, improvements are achieved and lead to even greater reductions in latency and standard deviation for both objectives. The value of these latency reductions is thoroughly demonstrated and a call for further research regarding customer-oriented objectives and evaluation of fairness in routing solutions is discussed. Finally, upon conclusion of the results presented in this work, several promising areas for future work and existing gaps in the literature are highlighted. As the body of literature surrounding the MLP is small yet growing, these areas constitute strong directions with important relevance to Operations Research, Humanitarian Logistics, Production Systems, and more

Le problème périodique de tournées sur les arcs avec contraintes de capacité et de gestion de stocks

RÉSUMÉ : Dans cette thèse, on introduit le problème périodique de tournées sur les arcs avec contraintes de capacité et de gestion de stocks. Les arêtes d'un réseau représentent les clients qui nécessitent une certaine quantité de matériel. Ce matériel est mis en inventaire et consommé au cours du temps. Les besoins de réapprovisionnement indiquent la nature périodique du problème. Les exemples d'applications de ce problème sont l’arrosage des chemins de terre dans les mines à ciel ouvert pour supprimer la poussière, l'arrosage des routes dans les réseaux forestiers et l’arrosage des plantes sur les trottoirs des rues. On prend l’application de l'arrosage des routes dans les mines à ciel ouvert. Un camion-citerne se déplace le long des routes en arrosant de l'eau pour supprimer la poussière. À cause de sa capacité limitée, le camion doit retourner au dépôt avant de commencer une nouvelle tournée. À cause de l'évaporation de l’eau, l'humidité sur les routes diminue en fonction du temps. Les routes ont besoin d’un certain niveau d'humidité pour retenir efficacement les particules de poussière. Une pénurie arrive lorsque le niveau d'humidité se trouve en dessous du niveau requis. L'objectif de cette étude est de trouver un ensemble de tournées qui débutent et finissent au dépôt de telle façon que les coûts de pénalité liés à la pénurie, ainsi que les coûts de routage soient minimisés. Parce que l'ordre dans lequel les arêtes sont traversées et arrosées affecte le moment où l'humidité est restaurée, des décisions sur le routage et la gestion de l’inventaire sont prises simultanément. Ce problème a été traité pour les tournées sur les nœuds, i.e., les clients sont situés aux nœuds du réseau, et il est appelé Inventory Routing Problem. Cependant, il n'a pas été traité dans le domaine de tournées sur les arcs. Étant donné la capacité limitée du camion et la nature périodique du remplissage, on considère cette application comme un problème périodique de tournées sur les arcs avec contraintes de capacité (PCARP). Au début, on considère le cas du problème d’arrosage où il n'existe qu'un seul dépôt (réservoir d'eau) dans le réseau et un seul camion-citerne. On travaille sur un réseau mixte dans lequel, pour chaque arête, il y a deux arcs, un dans chaque direction de traverse. Il y a aussi une boucle artificielle au dépôt qui représente le remplissage du camion. L’horizon de temps est divisé en périodes de temps de même durée. Les coûts et les quantités en inventaire sont calculés pour chaque période de temps. On élabore un modèle de programmation linéaire en nombres entiers qui est testé pour des exemplaires connus du problème de tournées sur les arcs avec contraintes de capacité (CARP). La solution indique la séquence optimale de traverse et d’arrosage des arêtes, le remplissage du camion au dépôt, s’il a lieu, et les coûts totaux de routage et de pénalité pour la pénurie sur le niveau d’humidité. Les limites de ce modèle sont établies en fonction de la taille des réseaux et de la longueur de l’horizon de temps qu’on est capable de résoudre. On est capable de trouver la solution optimale pour des réseaux avec 40 à 55 arêtes pour 20 à 30 périodes de temps. Ce qui correspond à un horizon de temps de 30 minutes en réalité. Deux situations sont testées, lorsque la quantité d’eau arrosée aux arêtes est variable ou constante. Les résultats sont présentés pour valider les deux situations. La contribution de cette première approche est le modèle mathématique pour résoudre le problème d’arrosage des routes dans les mines à ciel ouvert. La deuxième approche a pour objectif de résoudre des exemplaires de plus grande taille et pour un horizon de temps plus long. On modifie le modèle mathématique pour inclure plus d’un véhicule et un seul dépôt. Avec ces modifications on est capable de trouver la solution optimale pour un exemplaire de petite taille, 11 arêtes, pour un horizon de temps de 20 minutes. Pour résoudre des exemplaires de plus grande taille et incrémenter l’horizon de temps, on utilise un algorithme heuristique appelé adaptive large neighborhood search (ALNS). L’ALNS se compose de huit opérateurs de destruction et de réparation choisis au hasard pour modifier la solution existante à chaque itération. La performance des opérateurs détermine la probabilité d'être choisi aux itérations suivantes. Une meilleure performance de l'opérateur, en termes d'amélioration de la solution existante, correspond à une plus grande probabilité d'être choisi. On utilise un ensemble d’exemplaires du CARP et un ensemble d’exemplaires créé à partir des réseaux de mines à ciel ouvert réels. Cette heuristique est capable de trouver une solution réalisable pour un horizon de temps de 300 minutes. Les opérateurs sont testés individuellement et en les combinant entre eux en utilisant un critère d’arrêt de 25000 itérations. On trouve la combinaison qui obtient la meilleure amélioration du coût total pour chaque ensemble d’exemplaires. Les contributions de cette approche sont la modification du modèle mathématique afin d'inclure plus d'un véhicule et l'application de l’heuristique ALNS pour obtenir une solution à ce nouveau problème. Finalement, un dernier problème est abordé. Il consiste à localiser un ou plusieurs dépôts (réservoirs d'eau) le long des nœuds du réseau pour réduire les coûts de pénurie et de routage du problème d'arrosage des routes dans les mines à ciel ouvert. Comme l’activité principale se trouve sur les arêtes du réseau, ce problème correspond à un problème de localisation et de tournées sur les arcs (LARP) avec une composante périodique. Ce problème a été traité pour les tournées sur les nœuds. Cependant, il n'y a pas une autre application dans laquelle la localisation des dépôts est faite dans le domaine des problèmes périodiques de tournées sur les arcs. On prend des décisions à long terme telles que la localisation des dépôts et des décisions à court terme telles que le routage et la gestion des stocks. Pour cette raison, plusieurs scénarios sont testés et leur coût moyen est ajouté aux coûts de localisation des dépôts afin d'obtenir un coût total pour le problème. Les scénarios sont le résultat de changements dans les paramètres du problème qui peuvent se produire sur un horizon de planification à long terme. Trois algorithmes de localisation sont utilisés pour obtenir une solution initiale à la localisation d’un et de plusieurs dépôts. Ces algorithmes suivent le processus Location, allocation and Routing (L-A-R), une méthode divisée en trois parties : premièrement, on place les dépôts sur les nœuds du réseau, puis on affecte les arêtes aux camions et finalement on trouve une tournée. L’heuristique ALNS développée pour l'approche précédente est adaptée et utilisée pour améliorer la solution. On compare la localisation d’un dépôt \`a différents endroits. On compare aussi les trois algorithmes de localisation. La contribution de cette partie est le développement d'un algorithme appliqué à la localisation de dépôts pour un problème périodique de tournées sur les arcs avec contraintes de capacité. ---------- ABSTRACT : This dissertation introduces the periodic capacitated arc routing problem with inventory constraints. The edges of a network act as customers that require a certain quantity of material. It is then held as inventory and consumed over time. The need for replenishment of the consumed material explains the periodic nature of the problem. Some examples of applications of this problem are the road watering in open-pit mine roads to suppress dust, road watering in forest roads and plant watering on street medians and sidewalks. This work focuses on the application of road watering in open-pit mines. A water truck travels along the roads of a mine spraying water to suppress dust. Because of its limited capacity, the truck needs to replenish at a water depot before starting a new route. Due to water evaporation, the humidity on the roads decreases over time. Roads require a certain amount of humidity to effectively retain dust particles. A shortage happens when the humidity level drops below the required level. The objective of this thesis is to find a set of routes that start and end at the depot so that the penalty costs associated with shortage, as well as the routing costs are minimized. Because the order in which roads are traversed and watered affects their humidity level, routing and inventory decisions are made simultaneously. This problem has been treated for node routing, i.e., the customers are located at the nodes of the network, and it is called the Inventory Routing Problem. However, it has not being addressed in the arc routing domain. This problem is modeled as a periodic capacitated arc routing problem due to capacity constraints and the frequency of service. The first case studied is where there is only one water depot and one vehicle to travel along the network. A mathematical model is developed using a mixed network. For each edge, there are two arcs that correspond to the direction in which the edge can be traversed. There is an artificial loop at the depot that represents the refill of the truck. The time horizon is divided in time periods of equal duration. Costs and inventory levels are calculated for each time period. The model is tested for known instances of the capacitated arc routing problem (CARP). It is able to solve to optimality networks of 40 to 55 edges for a time horizon of 20 to 30 periods. Two situations are considered where the quantity of water delivered to the edges is variable and constant. Results are reported to validate both situations. The contribution of this first approach is the mathematical model to solve the road watering problem. The mathematical model is then modified to include more than one vehicle. As the number of variables increases, it is capable of solving to optimality a network of 11 edges for a time horizon of less than 30 time periods. An adaptive large neighborhood search (ALNS) heuristic is developed to solve larger networks for a longer time horizon. It is able to provide a feasible solution for networks up to 55 edges and a time horizon of 300 time periods. The ALNS consists of an initial solution obtained using a construction algorithm and eight destroy-repair operators that are randomly selected to modify the initial solution at each iteration of the algorithm. The performance of these operators determines the probability of being selected for the next iteration. A better performance of the operator, in terms of improving the existing solution, corresponds to a higher probability of being selected. The operators are tested individually and in different combinations. The best combination is selected for each set of instances. Apart from the CARP instances, ten instances are created to test the algorithm. These new instances correspond to road networks of real open-pit mines. The contributions of this approach are the modification of the mathematical model to include more than one vehicle and the application of the ALNS to obtain a solution for this new problem. Finally, a new problem is addressed. It consists in the location of one or more water depots along the nodes of the network to reduce the shortage and routing costs. Because the solution is obtained by servicing the edges of a network, this problem corresponds to a location arc routing problem (LARP) with a periodic component. This problem has only been treated in the node routing domain. No other application has been studied for location in the arc routing domain. Long term decisions, such as depot location, are combined with short term decisions, such as routing and inventory replenishment. Several scenarios are tested and their average cost is added to the depot placement costs in order to obtain a total cost. These scenarios are the result of changes in the parameters of the problem that can occur over a long planning horizon. Three location algorithms are used to obtain an initial solution to the location of one and several depots. The algorithms follow a location, allocation and routing (L-A-R) approach in which, first the depots are placed, then the edges are assigned to the service trucks and finally, a route is formed. The ALNS developed for the previous approach is adapted and used to improve the solution. The contribution is an algorithm applied to the location of depots for a periodic capacitated arc routing problem