On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

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

Workload Equity in Vehicle Routing Problems: A Survey and Analysis

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature. However, there has been only limited discussion about how workload equity should be modeled in VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences. This article addresses this gap with an analysis of classical and alternative equity functions for biobjective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs. In the analysis, we identify a set of axiomatic properties that an ideal equity measure should satisfy, collect six common measures, and point out important connections between their properties and those of the resulting Pareto-optimal solutions. To gauge the extent of these implications, we also conduct a numerical study on small biobjective VRP instances solvable to optimality. Our study reveals two undesirable consequences when optimizing equity with nonmonotonic functions: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent, i.e. composed of tours whose workloads are all equal to or longer than those of other Pareto-optimal solutions. We show that the extent of these phenomena should not be underestimated. The results of our biobjective analysis are valid also for weighted sum, constraint-based, or single-objective models. Based on this analysis, we conclude that monotonic equity functions are more appropriate for certain types of VRP models, and suggest promising avenues for further research.Comment: Accepted Manuscrip

Genetic algorithm for the continuous location-routing problem

This paper focuses on the continuous location-routing problem that comprises of the location of multiple depots from a given region and determining the routes of vehicles assigned to these depots. The objective of the problem is to design the delivery system of depots and routes so that the total cost is minimal. The standard location-routing problem considers a finite number of possible locations. The continuous location-routing problem allows location to infinite number of locations in a given region and makes the problem much more complex. We present a genetic algorithm that tackles both location and routing subproblems simultaneously.Web of Science29318717

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

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

Robust Branch-Cut-and-Price for the Capacitated Minimum Spanning Tree Problem over a Large Extended Formulation

This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arbores- cence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms. Powerful new cuts expressed over a very large set of variables could be added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very signi¯cant improvements over previous algorithms. Several open instances could be solved to optimalityNo keywords;

HEURISTIC FOR ASYMMETRIC CAPACITATED VEHICLE ROUTING PROBLEM

The vehicle routing problem (VRP) is commonly defined as the problem of designing optimal delivery or collection routes from one or several depots to a set of geographically scattered customers, under a variety of side conditions. This problem is generally described through a graph, whose arcs represent the road sections and vertices correspond to the depot and customer locations. The arcs (and consequently the corresponding graph) can be directed or undirected, depending on whether they can be traversed in only one direction or in both directions. Since each arc is associated with a cost then if the graph is directed, the cost matrix is asymmetric and the corresponding problem is called asymmetric vehicle routing problem (AVRP). Although the symmetric problems are special cases of the asymmetric ones, the latter were much less studied in the literature. In this paper, a type of problem, called the Asymmetric Capacitated Vehicle Routing Problem (ACVRP) is discussed and a heuristic algorithm is proposed to solve the problem. Keywords: Vehicle Routing, Asymmetric, Capacitated, Heuristi

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