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

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

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%

Solving the hierarchical windy postman problem with variable service costs using a math-heuristic algorithm

The Hierarchical Windy Postman Problem (HWPP) is an arc routing problem in which an order relation is imposed on the arcs/edges of the graph, and one has to pass through each edge at least once while adhering to the hierarchical priority relations. The tour starts from and ends at a specific node and the aim is to minimize the length of the tour. We consider a variant of the HWPP in which (i) the precedence order of the edge hierarchies is linear and edges within each hierarchy are connected and (ii) the cost of serving each edge decreases with the number of times it is traversed, and we refer to it as HWPP with variable service costs. An integer non-heuristic linear mathematical formulation is proposed, and a solution approach is designed. Our solution heuristic adapts the layer algorithm of Dror et al. (Networks 17:283–294, 1987) but employs an integer mathematical formulation as a sub-procedure instead of the blossom algorithm to find the least cost path between the nodes of the graph. This choice is based on the fact that the blossom algorithm requires a symmetric cost structure while we deal here with the general case of asymmetric cost structure, which makes our problem a windy variant of the postman problem. It should be noted that our problem is not asymmetric in the sense that there are no opposite arcs with different costs but there are edges which have different costs depending on the traversal direction. In order to compare the performance of our heuristic algorithm with respect to the performance of the mathematical model that is solved by the commercial solver Gurobi, 84 test instances are generated having varying sizes and densities and with different number of hierarchies. These test instances are solved by both methods and the generated results show that the proposed heuristic method is much faster and generates better quality solutions

On the periodic hierarchical Chinese postman problem

This paper presents a mathematical formulation and a heuristic approach for a new variant of the Hierarchical Chinese Postman Problem (HCPP). Indeed, we introduce the concept of periodicity, and we define and solve, for the first time, the Periodic-HCPP, denoted as P-HCPP. Given that the resulting integer programming model makes use of a big number of binary variables and given the extended time horizon considered, 30 days in our case, the problem is characterized by a high level of complexity. However, our developed heuristic is able to solve instances having up to 40 nodes, 520 arcs and hierarchies, whereas a general-purpose solver like Gurobi was not able to provide solutions for instances having more than 10 nodes. While the collected results are very encouraging, we provide at the end of this paper a set of possible future extensions of this work

Cutting path as a Rural Postman Problem: solutions by Memetic Algorithms

The Rural Postman Problem (RPP) is a particular Arc Routing Problem (ARP) which consistsof determining a minimum cost circuit on a graph so that a given subset of required edges is traversed. TheRPP is an NP-hard problem with significant real-life applications. This paper introduces an originalapproach based on Memetic Algorithms - the MARP algorithm - to solve the RPP and, also deals with aninteresting Industrial Application, which focuses on the path optimization for component cuttingoperations. Memetic Algorithms are a class of Metaheuristics which may be seen as a population strategythat involves cooperation and competition processes between population elements and integrates "socialknowledge", using a local search procedure. The MARP algorithm is tested with different groups ofinstances and the results are compared with those gathered from other publications. MARP is also used inthe context of various real-life applications

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

Waste Collection Vehicle Routing Problem: Literature Review

Waste generation is an issue which has caused wide public concern in modern societies, not only for the quantitative rise of the amount of waste generated, but also for the increasing complexity of some products and components. Waste collection is a highly relevant activity in the reverse logistics system and how to collect waste in an efficient way is an area that needs to be improved. This paper analyzes the major contribution about Waste Collection Vehicle Routing Problem (WCVRP) in literature. Based on a classification of waste collection (residential, commercial and industrial), firstly the key findings for these three types of waste collection are presented. Therefore, according to the model (Node Routing Problems and Arc Routing problems) used to represent WCVRP, different methods and techniques are analyzed in this paper to solve WCVRP. This paper attempts to serve as a roadmap of research literature produced in the field of WCVRP