Algoritmos e formulações matemáticas para problemas de roteamento em arcos

Orientador: Fábio Luiz UsbertiTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Problemas de roteamento em arcos têm por objetivo determinar rotas de custo mínimo que visitam um subconjunto de arcos de um grafo, com uma ou mais restrições adicionais. Esta tese estuda três problemas NP-difíceis de roteamento em arcos: (1) o problema de roteamento em arcos capacitado (CARP); (2) o problema de roteamento em arcos capacitado e aberto (OCARP); e (3) o problema do carteiro chinês com cobertura (CCPP). Apresentamos formulações matemáticas e métodos exatos e heurísticos para tratar computacionalmente esses problemas: (i) uma heurística construtiva gulosa e randomizada é proposta para o CARP; (ii) uma metaheurística de algoritmos genéticos híbrido e dois métodos de limitantes inferiores por programação linear inteira, um branch-and-cut e um baseado em redes de fluxos, são propostos para o OCARP; e (iii) um método exato branch-and-cut com desigualdades válidas e uma heurística construtiva são propostos para o CCPP. Extensivos experimentos computacionais utilizando instâncias de benchmark foram executados para demonstrar o desempenho dos métodos propostos em relação aos métodos da literatura, considerando tanto a qualidade das soluções obtidas quanto o tempo de processamento. Nossos resultados mostram que os métodos propostos são estado da arte. Os problemas estudados apresentam aplicações práticas relevantes: o CARP tem aplicações em coleta de lixo urbano e remoção de neve de estradas; o OCARP tem aplicações em roteamento de leituristas e na definição de caminhos de corte em chapas metálicas; e o CCPP tem aplicações em roteamento de leituristas com o uso de tecnologia wireless. A solução desses problemas remete à diminuição de custos logísticos, melhorando a competitividade das empresasAbstract: Arc routing problems aim to find minimum cost routes that visit a subset of arcs of a graph, with one or more side constraints. This thesis studies three NP-hard arc routing problems: (1) the capacitated arc routing problem (CARP); (2) the open capacitated arc routing problem (OCARP); and (3) the covering Chinese postman problem (CCPP). We present mathematical formulations and heuristic and exact methods to computationally solve these problems: (i) a greedy and randomized constructive heuristic is proposed for the CARP; (ii) a hybrid genetic algorithm metaheuristic and two linear integer programming lower bound methods, one based on branch-and-cut and one based on flow networks, are proposed for the OCARP; and (iii) an exact branch-and-cut method with valid inequalities and a constructive heuristic are proposed for the CCPP. Extensive computational experiments using benchmark instances were performed to demonstrate the performance of the proposed methods in comparison to the previous methods, regarding both quality of solutions and processing time. Our results show that the proposed methods are state-of-the-art. The studied problems have many relevant practical applications: the CARP has applications on urban waste collection and snow removal; the OCARP has applications on the routing of meter readers and the cutting of metal sheets; and last, the CCPP has applications on automated meter readers routing. The solution of these problems leads to the reduction of logistics costs, improving businesses competitivenessDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação2016/00315-0FAPES

Implementing a multi-vehicle multi-route spatial decision support system for efficient trash collection in Portugal

More efficient vehicle routing can improve a firm's competitive advantage or increase the efficiency by which governmental agencies supply public services. More efficient routing can also reduce traffic congestion and air pollution which are growing problems in many urban areas. Unfortunately, the identification of the optimal solution to most vehicle routing problems is computationally intractable. This article presents a user-friendly spatial decision support system (SDSS) to generate vehicle routes for multiple-vehicle routing problems that serve demand located along arcs and at nodes of the transportation network. The SDSS incorporates a geographical information system (GIS) and heuristic solution procedures to generate routes, system-wide data, and maps, as well as individual vehicle route maps, directions, and data quickly. It accommodates realistic system specifics such as vehicle capacity and time constraints and network constraints such as one-way streets, and prohibited turns. The system was tested for trash collection in Coimbra, Portugal. In addition, the SDSS can be used for "what-if" analysis related to possible changes to input parameters such as vehicle capacity and maximum driving time.http://www.sciencedirect.com/science/article/B6VG7-4S094WG-1/1/a49767e3030ce208ad39a0f8ce2d119

The Agricultural Spraying Vehicle Routing Problem With Splittable Edge Demands

In horticulture, spraying applications occur multiple times throughout any crop year. This paper presents a splittable agricultural chemical sprayed vehicle routing problem and formulates it as a mixed integer linear program. The main difference from the classical capacitated arc routing problem (CARP) is that our problem allows us to split the demand on a single demand edge amongst robotics sprayers. We are using theoretical insights about the optimal solution structure to improve the formulation and provide two different formulations of the splittable capacitated arc routing problem (SCARP), a basic spray formulation and a large edge demands formulation for large edge demands problems. This study presents solution methods consisting of lazy constraints, symmetry elimination constraints, and a heuristic repair method. Computational experiments on a set of valuable data based on the properties of real-world agricultural orchard fields reveal that the proposed methods can solve the SCARP with different properties. We also report computational results on classical benchmark sets from previous CARP literature. The tested results indicated that the SCARP model can provide cheaper solutions in some instances when compared with the classical CARP literature. Besides, the heuristic repair method significantly improves the quality of the solution by decreasing the upper bound when solving large-scale problems.Comment: 25 pages, 8 figure

Efficient routing of snow removal vehicles

This research addresses the problem of finding a minimum cost set of routes for vehicles in a road network subject to some constraints. Extensions, such as multiple service requirements, and mixed networks have been considered. Variations of this problem exist in many practical applications such as snow removal, refuse collection, mail delivery, etc. An exact algorithm was developed using integer programming to solve small size problems. Since the problem is NP-hard, a heuristic algorithm needs to be developed. An algorithm was developed based on the Greedy Randomized Adaptive Search Procedure (GRASP) heuristic, in which each replication consists of applying a construction heuristic to find feasible and good quality solutions, followed by a local search heuristic. A simulated annealing heuristic was developed to improve the solutions obtained from the construction heuristic. The best overall solution was selected from the results of several replications. The heuristic was tested on four sets of problem instances (total of 115 instances) obtained from the literature. The simulated annealing heuristic was able to achieve average improvements of up to 26.36% over the construction results on these problem instances. The results obtained with the developed heuristic were compared to the results obtained with recent heuristics developed by other authors. The developed heuristic improved the best-known solution found by other authors on 18 of the 115 instances and matched the results on 89 of those instances. It worked specially better with larger problems. The average deviations to known lower bounds for all four datasets were found to range between 0.21 and 2.61%

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

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

A web spatial decision support system for vehicle routing using Google Maps

This article presents a user-friendly web-based Spatial Decision Support System (wSDSS) aimed at generating optimized vehicle routes for multiple vehicle routing problems that involve serving the demand located along arcs of a transportation network. The wSDSS incorporates Google Maps™ (cartography and network data), a database, a heuristic and an ant-colony meta-heuristic developed by the authors to generate routes and detailed individual vehicle route maps. It accommodates realistic system specifics, such as vehicle capacity and shift time constraints, as well as network constraints such as one-way streets and prohibited turns. The wSDSS can be used for “what-if” analysis related to possible changes to input parameters such as vehicle capacity, maximum driving shift time, seasonal variations of demand, network modifications, imposed arc orientations, etc. Since just a web browser is needed, it can be easily adapted to be widely used in many real-world situations. The system was tested for urban trash collection in Coimbra, Portugal

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