Pricing routines for vehicle routing with time windows on road networks

Several very effective exact algorithms have been developed for vehicle routing problems with time windows. Unfortunately, most of these algorithms cannot be applied to instances that are defined on road networks, because they implicitly assume that the cheapest path between two customers is equal to the quickest path. Garaix and coauthors proposed to tackle this issue by first storing alternative paths in an auxiliary multi-graph, and then using that multi-graph within a branch-and-price algorithm. We show that, if one works with the original road network rather than the multi-graph, then one can solve the pricing subproblem more quickly, in both theory and practice

Pricing routines for vehicle routing with time windows on road networks

Several very effective exact algorithms have been developed for vehicle routing problems with time windows. Unfortunately, most of these algorithms cannot be applied to instances that are defined on road networks, because they implicitly assume that the cheapest path between two customers is equal to the quickest path. Garaix and coauthors proposed to tackle this issue by first storing alternative paths in an auxiliary multi-graph, and then using that multi-graph within a branch-and-price algorithm. We show that, if one works with the original road network rather than the multi-graph, then one can solve the pricing subproblem more quickly, in both theory and practice

Vehicle routing on real road networks

The vehicle routing problem (VRP) has received particular attention, in the field of transportation and logistics. Producing good solutions for the problem is of interest both commercially and theoretically. Reliable solutions to real life applications require an approach based on realistic assumptions that resemble real-world conditions. In that respects, this thesis studies vehicle routing problems on real road networks addressing aspects of the problem that need to be modelled on the original road network graph and aims to provide appropriate modelling techniques for solving them. As a preliminary step, chapter 2 studies the travelling salesman problem (TSP) on real road networks, referred to as the Steiner TSP (STSP) and proposes alternative integer programming formulations for the problem and some other related routing problems. The performances of formulations is examined both theoretically and computationally. Chapter 3 highlights the fact that travel speeds on road networks are correlated and uses a real traffic dataset to explore the structure of this correlation. In conclusion, it is shown that there is still significant spatial correlations between speeds on roads that are up to twenty links apart, in our congested road network. Chapter 4 extends chapter 2 and incorporates the findings of chapter 3 into a modelling framework for VRP. The STSP with correlated costs is defined as a potentially useful variant of VRP that considers the costs in the STSP to be stochastic random variables with correlation. The problem is then formulated as a single-objective problem with eight different integer programming formulations presented. It is then shown how to account for three different correlation structures in each of the formulations. Chapter 5 considers the VRPs with time windows and shows how most of the exact algorithms proposed for them, might not be applicable if the problem is defined on the original road network graph due to the underlying assumption of these algorithms that the cheapest path between a pair of customers is the same as the quickest path. This assumption is not always true on a real road network. Instead some alternative pricing routines are proposed that can solve the problem directly on the original graph

Improved bounds for large scale capacitated arc routing problem

AbstractThe Capacitated Arc Routing Problem (CARP) stands among the hardest combinatorial problems to solve or to find high quality solutions. This becomes even more true when dealing with large instances. This paper investigates methods to improve on lower and upper bounds of instances on graphs with over 200 vertices and 300 edges, dimensions that, today, can be considered of large scale. On the lower bound side, we propose to explore the speed of a dual ascent heuristic to generate capacity cuts. These cuts are next improved with a new exact separation enchained to the linear program resolution that follows the dual heuristic. On the upper bound, we implement a modified Iterated Local Search procedure to Capacitated Vehicle Routing Problem (CVRP) instances obtained by applying a transformation from the CARP original instances. Computational experiments were carried out on the set of large instances generated by Brandão and Eglese and also on the regular size sets. The experiments on the latter allow for evaluating the quality of the proposed solution approaches, while those on the former present improved lower and upper bounds for all instances of the corresponding set

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

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 with Time Duration Constraints and Uncertainty

RÉSUMÉ : Le problème résolu dans cette thèse est divisé en deux parties: 1) la localisation-affectation pour les tournées sur les arcs en tenant compte des caractéristiques des secteurs, c’est-à-dire le problème de conception des secteurs (SDP), 2) le routage robuste sur les arcs avec contraintes de durée (RARPTD). Les objectifs de cette recherche sont les suivants: 1) développer une formulation mathématique pour la conception des secteurs en considérant le temps de passage sur les arcs et le niveau de service requis. Le résultat du modèle mathématique donne une solution optimale pour le problème de localisation-affectation pour les tournées sur les arcs, 2) proposer un algorithme heuristique efficace, qui assure à la fois des coûts acceptables et de bonnes caractéristiques des secteurs. L'algorithme heuristique donne une solution applicable pour le problème de conception des secteurs, 3) développer une formulation mathématique déterministe pour le problème de tournées sur les arcs avec contraintes de durée et concevoir un jeu de données d'incertitude des temps de parcours et de service, 4) proposer une formulation résoluble pour le problème de tournées robustes sur les arcs avec contraintes de durée. Les essais sont conduits avec des données générées aléatoirement et avec un cas réel de réseau. L'analyse des résultats démontre que l'algorithme heuristique en trois étapes est plus facile à utiliser que l'algorithme branch-and-cut. De plus, l'algorithme heuristique en trois étapes peut générer une bonne solution avec des secteurs concis et bien conçus. En ce qui concerne le RARPTD, les essais montrent que les réseaux de petite taille peuvent être résolus rapidement. L’analyse de sensibilité indique que: 1) il existe toujours deux façons d'améliorer la robustesse de la solution optimale: payer le prix de la robustesse ou ajuster l'allocation des arcs aux secteurs, 2) lorsque le nombre de véhicules augmente, la solution optimale sous faible niveau d'incertitude peut être plus robuste, mais le coût des solutions optimales sous le même niveau d'incertitude augmente.----------ABSTRACT : The problem solved in this thesis is divided into two parts: 1) location-allocation arc routing with considering the characteristics of sectors, namely, the sector design problem (SDP), 2) robust arc routing with time duration based on the sectoring result of sector design (RARPTD). The objectives of this research are: 1) to develop a location-allocation arc routing mathematical formulation with considering the deadheading time and required service level. The result of the mathematical model provides an optimal solution for the location-allocation arc routing problem, 2) to design an effective and efficient heuristic algorithm, which ensures both acceptable cost and good sector characteristics. The heuristic algorithm provides an applicable solution for the sector design problem, 3) to develop the deterministic mathematical formulation for the arc routing problem with time duration and deadheading time and design the uncertainty support set of the service time and deadheading time, 4) to propose a solvable formulation for the robust arc routing problem. The result of the robust formulation provides the robust optimal solution for the robust arc routing problem with time duration. Experiments are conducted with randomly generated instances and a real network case. The results analysis demonstrates that the three-stage heuristic algorithm is computationally more tractable than the branch-and-cut algorithm and could yield high quality solution with compact and good shaped sectors. As for the part of RARPTD, experiments demonstrate that small-sized networks can be solved to optimality quickly and sensitivity analysis indicates: 1) there are always two ways to improve the robustness of the optimal solution: pay the price of robustness or adjust the allocation of required edges, 2) when the number of vehicles increases, the optimal solution under low uncertainty level can be more robust but the cost of the optimal solutions under the same uncertainty level increases