Line coverage is the task of servicing a given set of one-dimensional features in an environment. It is important for the inspection of linear infrastructure such as road networks, power lines, and oil and gas pipelines. This paper addresses the single robot line coverage problem for aerial and ground robots by modeling it as an optimization problem on a graph. The problem belongs to the broad class of arc routing problems and is closely related to the rural postman problem (RPP) on asymmetric graphs. The paper presents an integer linear programming formulation with proofs of correctness. Using the minimum cost flow problem, we develop approximation algorithms with guarantees on the solution quality. These guarantees also improve the existing results for the asymmetric RPP. The main algorithm partitions the problem into three cases based on the structure of the required graph, that is, the graph induced by the features that require servicing. We evaluate our algorithms on road networks from the 50 most populous cities in the world, consisting of up to 730 road segments. The algorithms, augmented with improvement heuristics, run within 3 s and generate solutions that are within 10% of the optimum. We experimentally demonstrate our algorithms with commercial UAVs on the UNC Charlotte campus road network.
{"title":"The single robot line coverage problem: Theory, algorithms, and experiments","authors":"Saurav Agarwal, Srinivas Akella","doi":"10.1002/net.22171","DOIUrl":"https://doi.org/10.1002/net.22171","url":null,"abstract":"Line coverage is the task of servicing a given set of one-dimensional features in an environment. It is important for the inspection of linear infrastructure such as road networks, power lines, and oil and gas pipelines. This paper addresses the single robot line coverage problem for aerial and ground robots by modeling it as an optimization problem on a graph. The problem belongs to the broad class of arc routing problems and is closely related to the rural postman problem (RPP) on asymmetric graphs. The paper presents an integer linear programming formulation with proofs of correctness. Using the minimum cost flow problem, we develop approximation algorithms with guarantees on the solution quality. These guarantees also improve the existing results for the asymmetric RPP. The main algorithm partitions the problem into three cases based on the structure of the <i>required graph</i>, that is, the graph induced by the features that require servicing. We evaluate our algorithms on road networks from the 50 most populous cities in the world, consisting of up to 730 road segments. The algorithms, augmented with improvement heuristics, run within 3 s and generate solutions that are within 10% of the optimum. We experimentally demonstrate our algorithms with commercial UAVs on the UNC Charlotte campus road network.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"124 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138534114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article we introduce a preprocessing technique to solve the Segment Routing Traffic Engineering Problem optimally using significantly fewer computational resources than previously introduced methods. Segment routing is a recently developed interior gateway routing protocol to be used on top of existing protocols that introduces more flexibility in traffic engineering. In practice, segment routing allows to deviate traffic from its original path by specifying a list of intermediate nodes or links, called segments, to visit before going to its destination. The issue we tackle in this article is that the number of segment paths scales exponentially with the maximum number of segments allowed leading to scalability issues in mathematical formulations. This article introduces the notion of dominated segment paths, these are paths that can be eliminated from the solution space when searching for an optimal solution. We propose a dynamic programming algorithm eliminating dominated paths for any number of segments. Numerical results show that respectively 50%, 90%, and 97% of paths are dominated when considering up to 2, 3, and 4 segments on benchmark network topologies.
{"title":"Preprocessing for segment routing optimization","authors":"Hugo Callebaut, Jérôme De Boeck, B. Fortz","doi":"10.1002/net.22165","DOIUrl":"https://doi.org/10.1002/net.22165","url":null,"abstract":"In this article we introduce a preprocessing technique to solve the Segment Routing Traffic Engineering Problem optimally using significantly fewer computational resources than previously introduced methods. Segment routing is a recently developed interior gateway routing protocol to be used on top of existing protocols that introduces more flexibility in traffic engineering. In practice, segment routing allows to deviate traffic from its original path by specifying a list of intermediate nodes or links, called segments, to visit before going to its destination. The issue we tackle in this article is that the number of segment paths scales exponentially with the maximum number of segments allowed leading to scalability issues in mathematical formulations. This article introduces the notion of dominated segment paths, these are paths that can be eliminated from the solution space when searching for an optimal solution. We propose a dynamic programming algorithm eliminating dominated paths for any number of segments. Numerical results show that respectively 50%, 90%, and 97% of paths are dominated when considering up to 2, 3, and 4 segments on benchmark network topologies.","PeriodicalId":54734,"journal":{"name":"Networks","volume":" ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47327402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
James Campbell, Á. Corberán, Isaac Plana, J. Sanchis, Paula Segura
In this article, we present and solve the multi‐purpose K$$ K $$ ‐drones general routing problem (MP K$$ K $$ ‐DGRP). In this optimization problem, a fleet of multi‐purpose drones, aerial vehicles that can both make deliveries and conduct sensing activities (e.g., imaging), have to jointly visit a set of nodes to make deliveries and map one or more continuous areas. This problem is motivated by global healthcare applications that deploy multipurpose drones that combine delivery trips with collection of aerial imaging data for use in emergency preparedness and resilience planning. The continuous areas that have to be mapped may correspond to terrain surfaces (e.g., flooded areas or regions with a disease outbreak) or to infrastructure networks to be inspected. The continuous areas can be modeled as a set of lines so that each area is completely serviced if all the lines covering it are traversed. Thus, given a set of nodes and a set of lines, the problem is to design drone routes of shortest total duration traversing the lines and visiting the nodes, while not exceeding the range limit (flight time) and capacity (loading) of the drones. Unlike ground vehicles in classical routing problems, drones can enter a line through any of its points, service only a part of that line and then exit through another of its points. The possibility of flying directly between any two points of the network offered by drones can lead to reduced costs, but it increases the difficulty of the problem. To deal with this problem, the lines are discretized, allowing drones to enter and exit each line only at a finite set of points, thus obtaining an instance of the K$$ K $$ ‐vehicles general routing problem ( K$$ K $$ ‐GRP). We present in this article an integer programming formulation for the K$$ K $$ ‐GRP and propose a matheuristic algorithm and a branch‐and‐cut procedure for its solution. Results are provided for problems with up to 20 deliveries and up to 28 continuous areas.
{"title":"The multi‐purpose K‐drones general routing problem","authors":"James Campbell, Á. Corberán, Isaac Plana, J. Sanchis, Paula Segura","doi":"10.1002/net.22176","DOIUrl":"https://doi.org/10.1002/net.22176","url":null,"abstract":"In this article, we present and solve the multi‐purpose K$$ K $$ ‐drones general routing problem (MP K$$ K $$ ‐DGRP). In this optimization problem, a fleet of multi‐purpose drones, aerial vehicles that can both make deliveries and conduct sensing activities (e.g., imaging), have to jointly visit a set of nodes to make deliveries and map one or more continuous areas. This problem is motivated by global healthcare applications that deploy multipurpose drones that combine delivery trips with collection of aerial imaging data for use in emergency preparedness and resilience planning. The continuous areas that have to be mapped may correspond to terrain surfaces (e.g., flooded areas or regions with a disease outbreak) or to infrastructure networks to be inspected. The continuous areas can be modeled as a set of lines so that each area is completely serviced if all the lines covering it are traversed. Thus, given a set of nodes and a set of lines, the problem is to design drone routes of shortest total duration traversing the lines and visiting the nodes, while not exceeding the range limit (flight time) and capacity (loading) of the drones. Unlike ground vehicles in classical routing problems, drones can enter a line through any of its points, service only a part of that line and then exit through another of its points. The possibility of flying directly between any two points of the network offered by drones can lead to reduced costs, but it increases the difficulty of the problem. To deal with this problem, the lines are discretized, allowing drones to enter and exit each line only at a finite set of points, thus obtaining an instance of the K$$ K $$ ‐vehicles general routing problem ( K$$ K $$ ‐GRP). We present in this article an integer programming formulation for the K$$ K $$ ‐GRP and propose a matheuristic algorithm and a branch‐and‐cut procedure for its solution. Results are provided for problems with up to 20 deliveries and up to 28 continuous areas.","PeriodicalId":54734,"journal":{"name":"Networks","volume":" ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47972253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a modeling framework for stochastic rider‐driver matching in many‐to‐one ridesharing systems, in which drivers have to be selected before the exact rider demand is known. The modeling framework allows for the use of driver booking fees and penalties for unmatched drivers, therefore supporting different system operating modes. We model this problem as a two‐stage stochastic set packing problem. To tackle the intractability of the stochastic problem, we introduce three model approximations and evaluate them on a large set of benchmark instances for three different system operating modes. Our computational experiments show the superiority of some model approximations over others and provide valuable insights on the impact of penalties and booking fees on the system's profitability and user satisfaction.
{"title":"Two‐stage stochastic one‐to‐many driver matching for ridesharing","authors":"Gabriel Homsi, B. Gendron, S. D. Jena","doi":"10.1002/net.22170","DOIUrl":"https://doi.org/10.1002/net.22170","url":null,"abstract":"We introduce a modeling framework for stochastic rider‐driver matching in many‐to‐one ridesharing systems, in which drivers have to be selected before the exact rider demand is known. The modeling framework allows for the use of driver booking fees and penalties for unmatched drivers, therefore supporting different system operating modes. We model this problem as a two‐stage stochastic set packing problem. To tackle the intractability of the stochastic problem, we introduce three model approximations and evaluate them on a large set of benchmark instances for three different system operating modes. Our computational experiments show the superiority of some model approximations over others and provide valuable insights on the impact of penalties and booking fees on the system's profitability and user satisfaction.","PeriodicalId":54734,"journal":{"name":"Networks","volume":" ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47603773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the benefit of introducing split deliveries in the inventory routing problem (IRP), both when the order‐up‐to level (OU) and the maximum level replenishment policies are applied. We first propose a mathematical formulation and solve it by implementing a branch‐and‐cut algorithm. Then, we carry out a worst‐case analysis to show the cost increase we have in the worst case by using unsplit deliveries instead of split deliveries, both for the OU and the maximum‐level replenishment policies. Extensive computational results on benchmark instances allow us to evaluate the benefit of introducing split deliveries. Finally, a sensitivity analysis on customer demands, initial inventory levels, maximum inventory levels and distance to the depot allows us to understand the instance features that make split deliveries effective in IRPs.
{"title":"The inventory routing problem with split deliveries","authors":"Nho Minh Dinh, C. Archetti, L. Bertazzi","doi":"10.1002/net.22175","DOIUrl":"https://doi.org/10.1002/net.22175","url":null,"abstract":"We study the benefit of introducing split deliveries in the inventory routing problem (IRP), both when the order‐up‐to level (OU) and the maximum level replenishment policies are applied. We first propose a mathematical formulation and solve it by implementing a branch‐and‐cut algorithm. Then, we carry out a worst‐case analysis to show the cost increase we have in the worst case by using unsplit deliveries instead of split deliveries, both for the OU and the maximum‐level replenishment policies. Extensive computational results on benchmark instances allow us to evaluate the benefit of introducing split deliveries. Finally, a sensitivity analysis on customer demands, initial inventory levels, maximum inventory levels and distance to the depot allows us to understand the instance features that make split deliveries effective in IRPs.","PeriodicalId":54734,"journal":{"name":"Networks","volume":" ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46096962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pedro Maristany de las Casas, Luitgard Kraus, A. Sedeño-Noda, R. Borndörfer
We introduce the Targeted Multiobjective Dijkstra Algorithm (T‐MDA), a label setting algorithm for the One‐to‐One Multiobjective Shortest Path (MOSP) Problem. It is based on the recently published Multiobjective Dijkstra Algorithm (MDA) and equips it with A*‐like techniques. For any explored subpath, a label setting MOSP algorithm decides whether the subpath can be discarded or must be stored as part of the output. A major design choice is how to store subpaths from the moment they are first explored until the mentioned final decision can be made. The T‐MDA combines the polynomially bounded size of the priority queue used in the MDA and a lazy management of paths that are not in the queue. The running time bounds from the MDA remain valid. In practice, the T‐MDA outperforms known algorithms from the literature and the increased memory consumption is negligible. In this paper, we benchmark the T‐MDA against an improved version of the state of the art NAMOAdr∗$$ {mathrm{NAMOA}}_{mathrm{dr}}^{ast } $$ One‐to‐One MOSP algorithm from the literature on a standard testbed.
{"title":"Targeted multiobjective Dijkstra algorithm","authors":"Pedro Maristany de las Casas, Luitgard Kraus, A. Sedeño-Noda, R. Borndörfer","doi":"10.1002/net.22174","DOIUrl":"https://doi.org/10.1002/net.22174","url":null,"abstract":"We introduce the Targeted Multiobjective Dijkstra Algorithm (T‐MDA), a label setting algorithm for the One‐to‐One Multiobjective Shortest Path (MOSP) Problem. It is based on the recently published Multiobjective Dijkstra Algorithm (MDA) and equips it with A*‐like techniques. For any explored subpath, a label setting MOSP algorithm decides whether the subpath can be discarded or must be stored as part of the output. A major design choice is how to store subpaths from the moment they are first explored until the mentioned final decision can be made. The T‐MDA combines the polynomially bounded size of the priority queue used in the MDA and a lazy management of paths that are not in the queue. The running time bounds from the MDA remain valid. In practice, the T‐MDA outperforms known algorithms from the literature and the increased memory consumption is negligible. In this paper, we benchmark the T‐MDA against an improved version of the state of the art NAMOAdr∗$$ {mathrm{NAMOA}}_{mathrm{dr}}^{ast } $$ One‐to‐One MOSP algorithm from the literature on a standard testbed.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"82 1","pages":"277 - 298"},"PeriodicalIF":2.1,"publicationDate":"2023-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44751417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nowadays, truck‐and‐drone problems represent one of the most studied classes of vehicle routing problems. The Flying Sidekick Traveling Salesman Problem (FS‐TSP) is the first optimization problem defined in this class. Since its definition, several variants have been proposed differing for the side constraints related to the operating conditions and for the structure of the hybrid truck‐and‐drone delivery system. However, regardless the specific problem under investigation, determining the optimal solution of most of these routing problems is a very challenging task, due to the vehicle synchronization issue. On this basis, this work provides a new arc‐based integer linear programming formulation for the FS‐TSP. The solution of such formulation required the development of a branch‐and‐cut solution approach based on new families of valid inequalities and variable fixing strategies. We tested the proposed approach on different sets of benchmark instances. The experimentation shows that the proposed method is competitive or outperforms the state‐of‐the‐art approaches, providing either the optimal solution or improved bounds for several instances unsolved before.
{"title":"A new MILP formulation for the flying sidekick traveling salesman problem","authors":"M. Boccia, A. Mancuso, A. Masone, C. Sterle","doi":"10.1002/net.22172","DOIUrl":"https://doi.org/10.1002/net.22172","url":null,"abstract":"Nowadays, truck‐and‐drone problems represent one of the most studied classes of vehicle routing problems. The Flying Sidekick Traveling Salesman Problem (FS‐TSP) is the first optimization problem defined in this class. Since its definition, several variants have been proposed differing for the side constraints related to the operating conditions and for the structure of the hybrid truck‐and‐drone delivery system. However, regardless the specific problem under investigation, determining the optimal solution of most of these routing problems is a very challenging task, due to the vehicle synchronization issue. On this basis, this work provides a new arc‐based integer linear programming formulation for the FS‐TSP. The solution of such formulation required the development of a branch‐and‐cut solution approach based on new families of valid inequalities and variable fixing strategies. We tested the proposed approach on different sets of benchmark instances. The experimentation shows that the proposed method is competitive or outperforms the state‐of‐the‐art approaches, providing either the optimal solution or improved bounds for several instances unsolved before.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"82 1","pages":"254 - 276"},"PeriodicalIF":2.1,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47983343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marilena Jianu, L. Dăuş, Vlad Drăgoi, Valeriu Beiu
This article studies the roots of the reliability polynomials of linear consecutive‐k‐out‐of‐n:F systems. We prove that these roots are unbounded in the complex plane, for any fixed k≥2$$ kge 2 $$ . In the particular case k=2$$ k=2 $$ , we show that the reliability polynomials have only real roots and highlight the closure of these roots by establishing their explicit formulas. We also point out that in this case, for any fixed n, the nonzero roots of the reliability polynomial are distinct numbers.
本文研究了线性连续- k - out - of - n:F系统的可靠性多项式的根。我们证明了这些根在复平面上无界，对于任意固定k≥2 $$ kge 2 $$。在k=2 $$ k=2 $$的特殊情况下，我们证明了可靠性多项式只有实数根，并通过建立它们的显式公式来突出这些根的闭包性。我们还指出，在这种情况下，对于任意固定的n，可靠性多项式的非零根是不同的数。
{"title":"Reliability polynomials of consecutive‐k‐out‐of‐n:F systems have unbounded roots","authors":"Marilena Jianu, L. Dăuş, Vlad Drăgoi, Valeriu Beiu","doi":"10.1002/net.22168","DOIUrl":"https://doi.org/10.1002/net.22168","url":null,"abstract":"This article studies the roots of the reliability polynomials of linear consecutive‐k‐out‐of‐n:F systems. We prove that these roots are unbounded in the complex plane, for any fixed k≥2$$ kge 2 $$ . In the particular case k=2$$ k=2 $$ , we show that the reliability polynomials have only real roots and highlight the closure of these roots by establishing their explicit formulas. We also point out that in this case, for any fixed n, the nonzero roots of the reliability polynomial are distinct numbers.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"82 1","pages":"222 - 228"},"PeriodicalIF":2.1,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46598005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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