A graph G$$ G $$ is stronger than a graph H$$ H $$ if G$$ G $$ has at least as many connected spanning subgraphs of size k$$ k $$ as H$$ H $$ for any positive integer k$$ k $$ . Counting the number of connected spanning subgraphs of fixed size allows us to compute the reliability of a graph. Formally, the reliability polynomial of a graph is the probability that the graph is connected when each edge is deleted independently with the same fixed probability. A graph G$$ G $$ is uniformly more reliable than H$$ H $$ if its reliability polynomial is greater than or equal to the reliability polynomial of H$$ H $$ for all probabilities. As a direct consequence of the definition, a sufficient condition for G$$ G $$ to be uniformly more reliable than H$$ H $$ is for G$$ G $$ to be stronger than H$$ H $$ . In this paper, we show that the sufficient condition is not necessary by providing an example of two infinite families of graphs, Gk$$ {G}_k $$ and Hk$$ {H}_k $$ , such that Gk$$ {G}_k $$ is uniformly more reliable than Hk$$ {H}_k $$ but is not stronger than Hk$$ {H}_k $$ .
对于任意正整数k $$ k $$，如果G $$ G $$具有至少与H $$ H $$相同数量的大小为k $$ k $$的连通生成子图，则图G $$ G $$比图H $$ H $$强。计算固定大小的连接生成子图的数量使我们能够计算图的可靠性。图的可靠性多项式的形式是图的每条边以相同的固定概率被独立删除时，图连通的概率。对于所有概率，如果图G $$ G $$的可靠度多项式大于等于H $$ H $$的可靠度多项式，则图G 一致地比H $$ H $$更可靠。作为定义的直接结果，G $$ G $$比H $$ H $$一致更可靠的一个充分条件是G $$ G $$比H $$ H $$更强。本文通过给出两个无限族图Gk $$ {G}_k $$和Hk $$ {H}_k $$的例子，证明了Gk $$ {G}_k $$比Hk $$ {H}_k $$一致更可靠，但不强于Hk $$ {H}_k $$的充分条件是不必要的。
{"title":"More reliable graphs are not always stronger","authors":"Christina M. Graves","doi":"10.1002/net.22141","DOIUrl":"https://doi.org/10.1002/net.22141","url":null,"abstract":"A graph G$$ G $$ is stronger than a graph H$$ H $$ if G$$ G $$ has at least as many connected spanning subgraphs of size k$$ k $$ as H$$ H $$ for any positive integer k$$ k $$ . Counting the number of connected spanning subgraphs of fixed size allows us to compute the reliability of a graph. Formally, the reliability polynomial of a graph is the probability that the graph is connected when each edge is deleted independently with the same fixed probability. A graph G$$ G $$ is uniformly more reliable than H$$ H $$ if its reliability polynomial is greater than or equal to the reliability polynomial of H$$ H $$ for all probabilities. As a direct consequence of the definition, a sufficient condition for G$$ G $$ to be uniformly more reliable than H$$ H $$ is for G$$ G $$ to be stronger than H$$ H $$ . In this paper, we show that the sufficient condition is not necessary by providing an example of two infinite families of graphs, Gk$$ {G}_k $$ and Hk$$ {H}_k $$ , such that Gk$$ {G}_k $$ is uniformly more reliable than Hk$$ {H}_k $$ but is not stronger than Hk$$ {H}_k $$ .","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"490 - 498"},"PeriodicalIF":2.1,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45671449","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}
The Weighted Safe Set Problem requires to partition an undirected graph into two families of connected components, respectively denoted as safe and unsafe, in such a way that each safe component dominates the unsafe adjacent components with respect to a weight function. We introduce a combinatorial branch and bound approach, whose main strength is a refined relaxation that combines graph manipulations and the solution of an auxiliary problem. We also propose fixing procedures to reduce the number of branching nodes. The algorithm solves all weighted instances available in the literature and most unweighted ones, up to 50 vertices, with computational times orders of magnitude smaller than the competing algorithms. In order to investigate the limits of the approach, we introduce a benchmark of graphs with 60 vertices, solving to optimality the denser instances.
{"title":"A combinatorial branch and bound for the safe set problem","authors":"Alberto Boggio Tomasaz, R. Cordone, P. Hosteins","doi":"10.1002/net.22140","DOIUrl":"https://doi.org/10.1002/net.22140","url":null,"abstract":"The Weighted Safe Set Problem requires to partition an undirected graph into two families of connected components, respectively denoted as safe and unsafe, in such a way that each safe component dominates the unsafe adjacent components with respect to a weight function. We introduce a combinatorial branch and bound approach, whose main strength is a refined relaxation that combines graph manipulations and the solution of an auxiliary problem. We also propose fixing procedures to reduce the number of branching nodes. The algorithm solves all weighted instances available in the literature and most unweighted ones, up to 50 vertices, with computational times orders of magnitude smaller than the competing algorithms. In order to investigate the limits of the approach, we introduce a benchmark of graphs with 60 vertices, solving to optimality the denser instances.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"445 - 464"},"PeriodicalIF":2.1,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42701267","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 focus on an extension of the maximum weight perfect matching problem with additional disjunctive conflict constraints in conjunction with the degree and binary restrictions. Given a simple graph with a nonnegative weight associated with each edge and a set of conflicting edges, the perfect matching problem with conflict constraints consists of finding a maximum weight perfect matching without any conflicting edge pair. Unlike the well‐known ordinary maximum weight perfect matching problem this one is strongly 𝒩𝒫 ‐hard. We propose two branch‐and‐bound algorithms for the exact solution of the problem. The first one is based on an equivalent maximum weight stable set formulation with an additional cardinality restriction obtained on the graph representing conflict relations and uses the information coming from its maximal stable sets. The second one is essentially a recursive depth first search scheme that benefits from simple upper bounds incorporated with a fast infeasibility detection procedure to prune the branch‐and‐bound tree. According to the extensive computational tests it is possible to say that they are both very efficient.
{"title":"Maximum weight perfect matching problem with additional disjunctive conflict constraints","authors":"M. Akyüz, I. K. Altinel, T. Öncan","doi":"10.1002/net.22139","DOIUrl":"https://doi.org/10.1002/net.22139","url":null,"abstract":"We focus on an extension of the maximum weight perfect matching problem with additional disjunctive conflict constraints in conjunction with the degree and binary restrictions. Given a simple graph with a nonnegative weight associated with each edge and a set of conflicting edges, the perfect matching problem with conflict constraints consists of finding a maximum weight perfect matching without any conflicting edge pair. Unlike the well‐known ordinary maximum weight perfect matching problem this one is strongly 𝒩𝒫 ‐hard. We propose two branch‐and‐bound algorithms for the exact solution of the problem. The first one is based on an equivalent maximum weight stable set formulation with an additional cardinality restriction obtained on the graph representing conflict relations and uses the information coming from its maximal stable sets. The second one is essentially a recursive depth first search scheme that benefits from simple upper bounds incorporated with a fast infeasibility detection procedure to prune the branch‐and‐bound tree. According to the extensive computational tests it is possible to say that they are both very efficient.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"465 - 489"},"PeriodicalIF":2.1,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44448137","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}
Nicolau Andrés-Thió, M. Brazil, C. Ras, Doreen A. Thomas
We introduce a formal framework for the study of augmenting networks in the plane for disaster‐resilience, where a disaster is modeled by a straight‐line segment. We generalize various graph structures from classical 2‐edge‐connectivity, including minimal cuts and blocks. The key concept that we introduce is that of an l$$ l $$ ‐leaf, which builds on the fundamental “leaf‐block” concept from classical augmentation. We present a number of algorithms for constructing the above‐mentioned graph structures, including a sweep‐line algorithm that finds all edge‐cuts that can be destroyed by a single disaster. We also present an algorithm which optimally adds a single edge between a pair of l$$ l $$ ‐leaves or blocks while avoiding certain disaster regions. Finally, we present a number of heuristic schemes for solving the disaster‐resilient network augmentation problem and perform extensive experiments to demonstrate the power of the l$$ l $$ ‐leaf concept within heuristic design.
我们引入了一个正式的框架来研究灾难恢复平面上的扩展网络，其中灾难是由直线段建模的。我们从经典的2边连通性中推广了各种图结构，包括最小切割和块。我们引入的关键概念是l $$ l $$‐叶，它建立在经典增广的基本“叶块”概念之上。我们提出了许多用于构建上述图结构的算法，包括一种扫描线算法，该算法可以找到所有可能被一次灾难破坏的边缘切割。我们还提出了一种算法，该算法在一对l $$ l $$‐叶或块之间最佳地添加一条边，同时避免某些灾难区域。最后，我们提出了一些启发式方案来解决灾难弹性网络增强问题，并进行了广泛的实验来证明l $$ l $$‐leaf概念在启发式设计中的力量。
{"title":"Network augmentation for disaster‐resilience against geographically correlated failure","authors":"Nicolau Andrés-Thió, M. Brazil, C. Ras, Doreen A. Thomas","doi":"10.1002/net.22138","DOIUrl":"https://doi.org/10.1002/net.22138","url":null,"abstract":"We introduce a formal framework for the study of augmenting networks in the plane for disaster‐resilience, where a disaster is modeled by a straight‐line segment. We generalize various graph structures from classical 2‐edge‐connectivity, including minimal cuts and blocks. The key concept that we introduce is that of an l$$ l $$ ‐leaf, which builds on the fundamental “leaf‐block” concept from classical augmentation. We present a number of algorithms for constructing the above‐mentioned graph structures, including a sweep‐line algorithm that finds all edge‐cuts that can be destroyed by a single disaster. We also present an algorithm which optimally adds a single edge between a pair of l$$ l $$ ‐leaves or blocks while avoiding certain disaster regions. Finally, we present a number of heuristic schemes for solving the disaster‐resilient network augmentation problem and perform extensive experiments to demonstrate the power of the l$$ l $$ ‐leaf concept within heuristic design.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"419 - 444"},"PeriodicalIF":2.1,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46241509","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 mean‐standard deviation minimum cost flow (MSDMCF) problem, where the objective is minimizing a linear combination of the mean and standard deviation of flow costs. Due to the nonlinearity and nonseparability of the objective, the problem is not amenable to the standard algorithms developed for network flow problems. We prove that the solution for the MSDMCF problem coincides with the solution for a particular mean‐variance minimum cost flow (MVMCF) problem. Leveraging this result, we propose bisection (BSC), Newton–Raphson (NR), and a hybrid (NR‐BSC)—method seeking to find the specific MVMCF problem whose optimal solution coincides with the optimal solution for the given MSDMCF problem. We further show that this approach can be extended to solve more generalized nonseparable parametric minimum cost flow problems under certain conditions. Computational experiments show that the NR algorithm is about twice as fast as the CPLEX solver on benchmark networks generated with NETGEN.
{"title":"Mean‐standard deviation model for minimum cost flow problem","authors":"C. Gokalp, S. Boyles, A. Unnikrishnan","doi":"10.1002/net.22135","DOIUrl":"https://doi.org/10.1002/net.22135","url":null,"abstract":"We study the mean‐standard deviation minimum cost flow (MSDMCF) problem, where the objective is minimizing a linear combination of the mean and standard deviation of flow costs. Due to the nonlinearity and nonseparability of the objective, the problem is not amenable to the standard algorithms developed for network flow problems. We prove that the solution for the MSDMCF problem coincides with the solution for a particular mean‐variance minimum cost flow (MVMCF) problem. Leveraging this result, we propose bisection (BSC), Newton–Raphson (NR), and a hybrid (NR‐BSC)—method seeking to find the specific MVMCF problem whose optimal solution coincides with the optimal solution for the given MSDMCF problem. We further show that this approach can be extended to solve more generalized nonseparable parametric minimum cost flow problems under certain conditions. Computational experiments show that the NR algorithm is about twice as fast as the CPLEX solver on benchmark networks generated with NETGEN.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"378 - 398"},"PeriodicalIF":2.1,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48255060","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 propose graph‐based models for several vehicle routing problems with intermediate stops: the capacitated multi‐trip vehicle routing problem with time windows, the multi‐depot vehicle routing problem with inter‐depot routes, the arc routing problem with intermediate facilities under capacity and length restrictions and the green vehicle routing problem. In these models, the set of feasible routes is represented by a set of resource constrained paths in one or several graphs. Intermediate stops are supported by the possibility to define negative resource consumption for some arcs. The models that we propose are then solved by VRPSolver, which implements a generic branch‐cut‐and‐price exact algorithm. Thus, a simple parameterization enables us to use several state‐of‐the‐art algorithmic components: automatic stabilization by dual price smoothing, limited‐memory rank‐1 cuts, reduced cost‐based arc elimination, enumeration of elementary routes, and hierarchical strong branching. For each problem, we numerically compare the proposed methodology with the best exact approach found in the literature. State‐of‐the‐art computational results were obtained for all problems except one.
{"title":"Solving vehicle routing problems with intermediate stops using VRPSolver models","authors":"M. C. Roboredo, R. Sadykov, Eduardo Uchoa","doi":"10.1002/net.22137","DOIUrl":"https://doi.org/10.1002/net.22137","url":null,"abstract":"In this article, we propose graph‐based models for several vehicle routing problems with intermediate stops: the capacitated multi‐trip vehicle routing problem with time windows, the multi‐depot vehicle routing problem with inter‐depot routes, the arc routing problem with intermediate facilities under capacity and length restrictions and the green vehicle routing problem. In these models, the set of feasible routes is represented by a set of resource constrained paths in one or several graphs. Intermediate stops are supported by the possibility to define negative resource consumption for some arcs. The models that we propose are then solved by VRPSolver, which implements a generic branch‐cut‐and‐price exact algorithm. Thus, a simple parameterization enables us to use several state‐of‐the‐art algorithmic components: automatic stabilization by dual price smoothing, limited‐memory rank‐1 cuts, reduced cost‐based arc elimination, enumeration of elementary routes, and hierarchical strong branching. For each problem, we numerically compare the proposed methodology with the best exact approach found in the literature. State‐of‐the‐art computational results were obtained for all problems except one.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"399 - 416"},"PeriodicalIF":2.1,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46703993","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}
Pouria Arsalani, M. Reisi, Vahid Dardashti, G. Moslehi
Railcars are known as the heart of the freight rail transportation industry. Hence, any improvements in their operations can lead to sharp reductions in various operating costs. One of the most critical operations on railcars is blocking and routing their transportation. Railway companies face continuous challenged about what blocks should be formed to carry shipments across different origin–destination pairs (O–D pairs) and reclassify them in intermediate yards to minimize transportation reclassification costs. In addition, it is necessary to determine train service between O–D pairs and the number of trains. Along with the shipment routing plans, this problem is called train formation and shipment path optimization (TFSP). In TFSP, some substructure and rail network operational constraints should be considered, including link capacity, classification capacity, the number of sorting tracks, and path length. This paper presents two arc‐based mixed‐integer linear programming (MILP) models to formulate the TFSP problem. To the best of the authors' knowledge, no MILP arc‐based model has been published for the problem that does not need any preprocess before solving. Computational results of solving models on the datasets showed that the first model could obtain a feasible solution with a maximum 0.05% gap up to 48 yards instance. The second model also could find a solution with a small gap compared to the optimal solution in a reasonable time for instances up to 128 yards. Also, the proposed models were compared to the best methods in the literature, and their superiority was shown.
{"title":"Two new mixed‐integer programming models for the integrated train formation and shipment path optimization problem","authors":"Pouria Arsalani, M. Reisi, Vahid Dardashti, G. Moslehi","doi":"10.1002/net.22133","DOIUrl":"https://doi.org/10.1002/net.22133","url":null,"abstract":"Railcars are known as the heart of the freight rail transportation industry. Hence, any improvements in their operations can lead to sharp reductions in various operating costs. One of the most critical operations on railcars is blocking and routing their transportation. Railway companies face continuous challenged about what blocks should be formed to carry shipments across different origin–destination pairs (O–D pairs) and reclassify them in intermediate yards to minimize transportation reclassification costs. In addition, it is necessary to determine train service between O–D pairs and the number of trains. Along with the shipment routing plans, this problem is called train formation and shipment path optimization (TFSP). In TFSP, some substructure and rail network operational constraints should be considered, including link capacity, classification capacity, the number of sorting tracks, and path length. This paper presents two arc‐based mixed‐integer linear programming (MILP) models to formulate the TFSP problem. To the best of the authors' knowledge, no MILP arc‐based model has been published for the problem that does not need any preprocess before solving. Computational results of solving models on the datasets showed that the first model could obtain a feasible solution with a maximum 0.05% gap up to 48 yards instance. The second model also could find a solution with a small gap compared to the optimal solution in a reasonable time for instances up to 128 yards. Also, the proposed models were compared to the best methods in the literature, and their superiority was shown.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"359 - 377"},"PeriodicalIF":2.1,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42953095","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 a network interdiction problem involving two agents: a defender and an evader. The evader seeks to traverse a path from a source node to a terminus node in a directed network without being detected. The game takes place in two stages. In the first stage, the defender removes a set of arcs in the network. In the second stage, the defender and evader play a simultaneous game. The defender monitors a set of arcs, thus increasing the probability that the evader will be detected on that arc (if the evader uses the arc). The evader selects a source‐terminus path. Because the second stage is played simultaneously, both agents use mixed‐strategy solutions. We approach the solution of the second‐stage problem by proposing a constraint‐and‐column generation algorithm. We show that both the constraint‐generation and column‐generation problems are NP‐hard. Accordingly, we prescribe approximate versions of these problems that can be solved more efficiently. Our algorithm relies on solving the approximate versions until it is necessary to obtain an exact solution of the constraint‐generation and column‐generation problems. Then, to link the first‐ and second‐stage problems, we model the original problem using an epigraph reformulation, which we solve using a Benders‐decomposition based approach. The efficacy of our approach is demonstrated on a set of randomly generated test instances.
{"title":"A two‐stage network interdiction‐monitoring game","authors":"D. Nguyen, Yongjia Song, J. Smith","doi":"10.1002/net.22136","DOIUrl":"https://doi.org/10.1002/net.22136","url":null,"abstract":"We study a network interdiction problem involving two agents: a defender and an evader. The evader seeks to traverse a path from a source node to a terminus node in a directed network without being detected. The game takes place in two stages. In the first stage, the defender removes a set of arcs in the network. In the second stage, the defender and evader play a simultaneous game. The defender monitors a set of arcs, thus increasing the probability that the evader will be detected on that arc (if the evader uses the arc). The evader selects a source‐terminus path. Because the second stage is played simultaneously, both agents use mixed‐strategy solutions. We approach the solution of the second‐stage problem by proposing a constraint‐and‐column generation algorithm. We show that both the constraint‐generation and column‐generation problems are NP‐hard. Accordingly, we prescribe approximate versions of these problems that can be solved more efficiently. Our algorithm relies on solving the approximate versions until it is necessary to obtain an exact solution of the constraint‐generation and column‐generation problems. Then, to link the first‐ and second‐stage problems, we model the original problem using an epigraph reformulation, which we solve using a Benders‐decomposition based approach. The efficacy of our approach is demonstrated on a set of randomly generated test instances.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"334 - 358"},"PeriodicalIF":2.1,"publicationDate":"2022-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45791463","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}
A. Casado, N. Mladenović, J. Sánchez-Oro, A. Duarte
Several problems are emerging in the context of communication networks and most of them must be solved in reduced computing time since they affect to critical tasks. In this research, the monitor placement problem is tackled. This problem tries to cover the communications of an entire network by locating a monitor in specific nodes of the network, in such a way that every link remains surveyed. In case that a solution cannot be generated in the allowed computing time, a penalty will be assumed for each link uncovered. The problem is addressed by considering the variable neighborhood search framework, proposing a novel constructive method, an intelligent local search to optimize the improvement phase, and an intensified shake to guide the search to more promising solutions. The proposed algorithm is compared with a hybrid search evolutionary algorithm over a set of instances derived from real‐life networks to prove its performance.
{"title":"Variable neighborhood search approach with intensified shake for monitor placement","authors":"A. Casado, N. Mladenović, J. Sánchez-Oro, A. Duarte","doi":"10.1002/net.22134","DOIUrl":"https://doi.org/10.1002/net.22134","url":null,"abstract":"Several problems are emerging in the context of communication networks and most of them must be solved in reduced computing time since they affect to critical tasks. In this research, the monitor placement problem is tackled. This problem tries to cover the communications of an entire network by locating a monitor in specific nodes of the network, in such a way that every link remains surveyed. In case that a solution cannot be generated in the allowed computing time, a penalty will be assumed for each link uncovered. The problem is addressed by considering the variable neighborhood search framework, proposing a novel constructive method, an intelligent local search to optimize the improvement phase, and an intensified shake to guide the search to more promising solutions. The proposed algorithm is compared with a hybrid search evolutionary algorithm over a set of instances derived from real‐life networks to prove its performance.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"319 - 333"},"PeriodicalIF":2.1,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42965473","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}
This work focuses on the capacitated dispersion problem for which we study several mathematical formulations in different spaces using variables associated with nodes, edges, and costs. The relationships among the presented formulations are investigated by comparing the projections of the feasible sets of the LP relaxations onto the subspace of natural variables. These formulations are then strengthened with families of valid inequalities and variable‐fixing procedures. The separation problems associated with the valid inequalities that are exponential in number are shown to be polynomially solvable by reducing them to longest path problems in acyclic graphs. The dual bounds obtained from stronger but larger formulations are used to improve the strength of weaker but smaller formulations. Several sets of computational experiments are conducted to illustrate the usefulness of the findings, as well as the aptness of the formulations for different types of instances.
{"title":"Formulations and valid inequalities for the capacitated dispersion problem","authors":"M. Landete, Juanjo Peiró, H. Yaman","doi":"10.1002/net.22132","DOIUrl":"https://doi.org/10.1002/net.22132","url":null,"abstract":"This work focuses on the capacitated dispersion problem for which we study several mathematical formulations in different spaces using variables associated with nodes, edges, and costs. The relationships among the presented formulations are investigated by comparing the projections of the feasible sets of the LP relaxations onto the subspace of natural variables. These formulations are then strengthened with families of valid inequalities and variable‐fixing procedures. The separation problems associated with the valid inequalities that are exponential in number are shown to be polynomially solvable by reducing them to longest path problems in acyclic graphs. The dual bounds obtained from stronger but larger formulations are used to improve the strength of weaker but smaller formulations. Several sets of computational experiments are conducted to illustrate the usefulness of the findings, as well as the aptness of the formulations for different types of instances.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"294 - 315"},"PeriodicalIF":2.1,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45689750","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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