Suppose that m$$ m $$ mobile service units are located at a base station (depot) in a transportation network with n$$ n $$ nodes. On any day, the nodes of the network may generate calls for service independently with known probabilities. The calls are centrally allocated to the service units who then visit the allocated customers on shortest open tours, that is, for each service unit, the way back to the depot from the last served customer is not counted towards the length of the tour. It is required to find an optimal location for the depot to minimize the expected travel distance. We obtain bounds on the approximation ratios for two simple and fast heuristics for the problem on a general network. For the problem on a tree, we present an O(nm+1)$$ Oleft({n}^{m+1}right) $$ exact algorithm.
{"title":"The probabilistic uncapacitated open vehicle routing location problem","authors":"I. Averbakh, Wei Yu","doi":"10.1002/net.22147","DOIUrl":"https://doi.org/10.1002/net.22147","url":null,"abstract":"Suppose that m$$ m $$ mobile service units are located at a base station (depot) in a transportation network with n$$ n $$ nodes. On any day, the nodes of the network may generate calls for service independently with known probabilities. The calls are centrally allocated to the service units who then visit the allocated customers on shortest open tours, that is, for each service unit, the way back to the depot from the last served customer is not counted towards the length of the tour. It is required to find an optimal location for the depot to minimize the expected travel distance. We obtain bounds on the approximation ratios for two simple and fast heuristics for the problem on a general network. For the problem on a tree, we present an O(nm+1)$$ Oleft({n}^{m+1}right) $$ exact algorithm.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"82 1","pages":"68 - 83"},"PeriodicalIF":2.1,"publicationDate":"2023-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45603209","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 article considers the base station deployment problem in a wireless network. The natural formulation of this problem usually leads to numerical and memory issues, preventing users from dealing with real‐world cases. We provide a compact reformulation that allows us to get beyond the drawbacks of the natural formulation. Tests are done on ten instances derived from realistic LTE scenarios. The computational results show that the proposed reformulation enables mixed‐integer programming solvers to provide an optimal solution in a short amount of time.
{"title":"A compact formulation for the base station deployment problem in wireless networks","authors":"P. Avella, Alice Calamita, L. Palagi","doi":"10.1002/net.22146","DOIUrl":"https://doi.org/10.1002/net.22146","url":null,"abstract":"This article considers the base station deployment problem in a wireless network. The natural formulation of this problem usually leads to numerical and memory issues, preventing users from dealing with real‐world cases. We provide a compact reformulation that allows us to get beyond the drawbacks of the natural formulation. Tests are done on ten instances derived from realistic LTE scenarios. The computational results show that the proposed reformulation enables mixed‐integer programming solvers to provide an optimal solution in a short amount of time.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"82 1","pages":"52 - 67"},"PeriodicalIF":2.1,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47074339","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}
Given a bi‐directed graph modeling a telecommunication network, and a set of origin‐destination pairs representing traffic requests (commodities) along with their associated Service Function Chains (SFCs), the Virtual Network Function Placement and Routing Problem (VNFPRP) aims to find, for each commodity, one latency‐constrained routing path that visits the required Virtual Network Functions in a specific order. The function installation costs together with the node activation costs have to be minimized. In this paper, we present two extended Mixed Integer Programming (MIP) formulations to model the VNFPRP. For each formulation we define the master problem, the pricing problem, the associated Lagrangian bound and a specific branching scheme, in order to derive an efficient Branch‐and‐Price algorithm. We also provide several families of valid inequalities to strengthen the LP‐relaxation bounds. Computational results are reported comparing the performance of the two Branch‐and‐Price algorithms with a compact MIP formulation and its Branch‐and‐Benders‐cut implementation on a set of SNDlib instances representing telecommunication networks.
{"title":"Two extended formulations for the virtual network function placement and routing problem","authors":"Ahlam Mouaci, É. Gourdin, Ivana Ljubic, N. Perrot","doi":"10.1002/net.22144","DOIUrl":"https://doi.org/10.1002/net.22144","url":null,"abstract":"Given a bi‐directed graph modeling a telecommunication network, and a set of origin‐destination pairs representing traffic requests (commodities) along with their associated Service Function Chains (SFCs), the Virtual Network Function Placement and Routing Problem (VNFPRP) aims to find, for each commodity, one latency‐constrained routing path that visits the required Virtual Network Functions in a specific order. The function installation costs together with the node activation costs have to be minimized. In this paper, we present two extended Mixed Integer Programming (MIP) formulations to model the VNFPRP. For each formulation we define the master problem, the pricing problem, the associated Lagrangian bound and a specific branching scheme, in order to derive an efficient Branch‐and‐Price algorithm. We also provide several families of valid inequalities to strengthen the LP‐relaxation bounds. Computational results are reported comparing the performance of the two Branch‐and‐Price algorithms with a compact MIP formulation and its Branch‐and‐Benders‐cut implementation on a set of SNDlib instances representing telecommunication networks.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"82 1","pages":"32 - 51"},"PeriodicalIF":2.1,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46153470","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}
C. Bentz, Marie-Christine Costa, Pierre-Louis Poirion, Thomas Ridremont
We are interested in the design of robust (or resilient) capacitated rooted Steiner networks in the case of terminals with uniform demands. Formally, we are given a graph, capacity, and cost functions on the edges, a root, a subset of vertices called terminals, and a bound k$$ k $$ on the number of possible edge failures. We first study the problem where k=1$$ k=1 $$ and the network that we want to design must be a tree covering the root and the terminals: we give complexity results and propose models to optimize both the cost of the tree and the number of terminals disconnected from the root in the worst case of an edge failure, while respecting the capacity constraints on the edges. Secondly, we consider the problem of computing a minimum‐cost survivable network, that is, a network that covers the root and terminals even after the removal of any k$$ k $$ edges, while still respecting the capacity constraints on the edges. We also consider the possibility of protecting a given number of edges. We propose three different formulations: a bilevel formulation (with an attacker and a defender), a cutset‐based formulation and a flow‐based one. We compare the formulations from a theoretical point of view, and we propose algorithms to solve them and compare their efficiency in practice.
{"title":"Robust capacitated Steiner trees and networks with uniform demands","authors":"C. Bentz, Marie-Christine Costa, Pierre-Louis Poirion, Thomas Ridremont","doi":"10.1002/net.22143","DOIUrl":"https://doi.org/10.1002/net.22143","url":null,"abstract":"We are interested in the design of robust (or resilient) capacitated rooted Steiner networks in the case of terminals with uniform demands. Formally, we are given a graph, capacity, and cost functions on the edges, a root, a subset of vertices called terminals, and a bound k$$ k $$ on the number of possible edge failures. We first study the problem where k=1$$ k=1 $$ and the network that we want to design must be a tree covering the root and the terminals: we give complexity results and propose models to optimize both the cost of the tree and the number of terminals disconnected from the root in the worst case of an edge failure, while respecting the capacity constraints on the edges. Secondly, we consider the problem of computing a minimum‐cost survivable network, that is, a network that covers the root and terminals even after the removal of any k$$ k $$ edges, while still respecting the capacity constraints on the edges. We also consider the possibility of protecting a given number of edges. We propose three different formulations: a bilevel formulation (with an attacker and a defender), a cutset‐based formulation and a flow‐based one. We compare the formulations from a theoretical point of view, and we propose algorithms to solve them and compare their efficiency in practice.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"82 1","pages":"3 - 31"},"PeriodicalIF":2.1,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44569732","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}
Given a wireless sensor network, we consider the problem to minimize its total energy consumption over consecutive time slots with respect to communication activities. Nonempty and disjoint subsets of nodes are required to be active and connected under a tree topology configuration in the different time slots, and each network node must be active in a unique time slot. Moreover, the power required by the same pair of network nodes to communicate on the associated direct channel may vary in the different time slots. The problem has been recently introduced in the literature under the name Sub‐Tree Scheduling for Wireless Sensor Networks with Partial Coverage. We focus on the exact solution of the problem. We present a branch‐and‐cut (BC) algorithm based on a novel integer linear programming formulation which allows avoiding the introduction of symmetries in the solution space. In particular, the algorithm relies on an efficient and nontypical separation algorithm for known valid inequalities, and on an easy‐to‐implement primal bound heuristic. The effectiveness of the BC algorithm is empirically shown through an extensive experimental analysis involving 300 newly generated benchmark instances with up to 200 network nodes and 8 time slots. Additionally, the experimental results show that the BC algorithm represents a valid computational tool to benchmark the performance of heuristics addressing the problem, and can be used in practice, as an heuristic solver, to tackle problem instances that are not too large.
{"title":"On optimally solving sub‐tree scheduling for wireless sensor networks with partial coverage: A branch‐and‐cut algorithm","authors":"Nicola Bianchessi","doi":"10.1002/net.22145","DOIUrl":"https://doi.org/10.1002/net.22145","url":null,"abstract":"Given a wireless sensor network, we consider the problem to minimize its total energy consumption over consecutive time slots with respect to communication activities. Nonempty and disjoint subsets of nodes are required to be active and connected under a tree topology configuration in the different time slots, and each network node must be active in a unique time slot. Moreover, the power required by the same pair of network nodes to communicate on the associated direct channel may vary in the different time slots. The problem has been recently introduced in the literature under the name Sub‐Tree Scheduling for Wireless Sensor Networks with Partial Coverage. We focus on the exact solution of the problem. We present a branch‐and‐cut (BC) algorithm based on a novel integer linear programming formulation which allows avoiding the introduction of symmetries in the solution space. In particular, the algorithm relies on an efficient and nontypical separation algorithm for known valid inequalities, and on an easy‐to‐implement primal bound heuristic. The effectiveness of the BC algorithm is empirically shown through an extensive experimental analysis involving 300 newly generated benchmark instances with up to 200 network nodes and 8 time slots. Additionally, the experimental results show that the BC algorithm represents a valid computational tool to benchmark the performance of heuristics addressing the problem, and can be used in practice, as an heuristic solver, to tackle problem instances that are not too large.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"499 - 513"},"PeriodicalIF":2.1,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47919336","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 article studies the Hazardous Orienteering Problem (HOP), a variant of the more famous Orienteering Problem (OP). In the OP, a vehicle earns a profit for each customer it visits (e.g., to pick up a parcel) subject to an upper bound on the tour time. In the HOP, the parcels picked up at some customers have a probability of triggering a catastrophic event. The probability depends on how long the parcels travel on the vehicle. If any catastrophic event triggers, the entire collected profit is lost. The goal is to determine the tour that maximizes the expected profit. The problem has interesting applications in routing of hazardous material, cash‐in‐transit, and law enforcement. We propose a mixed‐integer nonlinear formulation and techniques both to obtain dual bounds and to produce primal solutions. Computational tests investigate the efficacy of the methods proposed and allow to gain insights into solution features.
{"title":"The hazardous orienteering problem","authors":"Alberto Santini, C. Archetti","doi":"10.1002/net.22129","DOIUrl":"https://doi.org/10.1002/net.22129","url":null,"abstract":"This article studies the Hazardous Orienteering Problem (HOP), a variant of the more famous Orienteering Problem (OP). In the OP, a vehicle earns a profit for each customer it visits (e.g., to pick up a parcel) subject to an upper bound on the tour time. In the HOP, the parcels picked up at some customers have a probability of triggering a catastrophic event. The probability depends on how long the parcels travel on the vehicle. If any catastrophic event triggers, the entire collected profit is lost. The goal is to determine the tour that maximizes the expected profit. The problem has interesting applications in routing of hazardous material, cash‐in‐transit, and law enforcement. We propose a mixed‐integer nonlinear formulation and techniques both to obtain dual bounds and to produce primal solutions. Computational tests investigate the efficacy of the methods proposed and allow to gain insights into solution features.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"235 - 252"},"PeriodicalIF":2.1,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43021607","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}
F. Carrabs, R. Cerulli, Federica Laureana, Domenico Serra, Carmine Sorgente
This article addresses the 2‐edge‐connected minimum branch vertices problem, a variant of the minimum branch vertices problem in which the spanning subgraph is required to be 2‐edge‐connected for survivability reasons. The problem has been recently introduced and finds application in optical networks design scenarios, where branch vertices are associated to switch devices that allow to split the entering light signals and send them to several adjacent vertices. An exact approach to the problem has been proposed in the literature. In this paper, we formally prove its NP‐completeness and propose a genetic algorithm, which exploits some literature‐provided procedures for efficiently checking and restoring solutions feasibility, and makes use of novel ad‐hoc designed operators aiming to improve their values, reducing the number of branch vertices. The computational tests show that, on the benchmark instances, the genetic algorithm very often finds the optimal solution. Moreover, in order to further investigate the effectiveness and the performance of our algorithm, we generated a new set of random instances where the optimal solution is known a priori.
{"title":"A genetic approach for the 2‐edge‐connected minimum branch vertices problem","authors":"F. Carrabs, R. Cerulli, Federica Laureana, Domenico Serra, Carmine Sorgente","doi":"10.1002/net.22142","DOIUrl":"https://doi.org/10.1002/net.22142","url":null,"abstract":"This article addresses the 2‐edge‐connected minimum branch vertices problem, a variant of the minimum branch vertices problem in which the spanning subgraph is required to be 2‐edge‐connected for survivability reasons. The problem has been recently introduced and finds application in optical networks design scenarios, where branch vertices are associated to switch devices that allow to split the entering light signals and send them to several adjacent vertices. An exact approach to the problem has been proposed in the literature. In this paper, we formally prove its NP‐completeness and propose a genetic algorithm, which exploits some literature‐provided procedures for efficiently checking and restoring solutions feasibility, and makes use of novel ad‐hoc designed operators aiming to improve their values, reducing the number of branch vertices. The computational tests show that, on the benchmark instances, the genetic algorithm very often finds the optimal solution. Moreover, in order to further investigate the effectiveness and the performance of our algorithm, we generated a new set of random instances where the optimal solution is known a priori.","PeriodicalId":54734,"journal":{"name":"Networks","volume":" ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42303704","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 generalizations of stochastic network interdiction problem with distributional ambiguity. Specifically, we consider a distributionally risk‐averse (or robust) network interdiction problem (DRA‐NIP) and a distributionally risk‐receptive network interdiction problem (DRR‐NIP) where a leader maximizes a follower's minimal expected objective value for either the worst‐case or the best‐case, respectively, probability distribution belonging to ambiguity set (a set of distributions). The DRA‐NIP arises in applications where a risk‐averse leader interdicts a follower to cause delays in their supply convoy. In contrast, the DRR‐NIP provides network vulnerability analysis where a network‐user seeks to identify vulnerabilities in the network against potential disruptions by an adversary (or leader) who is receptive to risk for improving the expected objective values. We present finitely convergent algorithms for solving DRA‐NIP and DRR‐NIP with a general ambiguity set. To evaluate their performance, we provide results of our extensive computational experiments performed on instances known for (risk‐neutral) stochastic NIP.
{"title":"Distributionally risk‐receptive and risk‐averse network interdiction problems with general ambiguity set","authors":"Sumin Kang, M. Bansal","doi":"10.1002/net.22114","DOIUrl":"https://doi.org/10.1002/net.22114","url":null,"abstract":"We introduce generalizations of stochastic network interdiction problem with distributional ambiguity. Specifically, we consider a distributionally risk‐averse (or robust) network interdiction problem (DRA‐NIP) and a distributionally risk‐receptive network interdiction problem (DRR‐NIP) where a leader maximizes a follower's minimal expected objective value for either the worst‐case or the best‐case, respectively, probability distribution belonging to ambiguity set (a set of distributions). The DRA‐NIP arises in applications where a risk‐averse leader interdicts a follower to cause delays in their supply convoy. In contrast, the DRR‐NIP provides network vulnerability analysis where a network‐user seeks to identify vulnerabilities in the network against potential disruptions by an adversary (or leader) who is receptive to risk for improving the expected objective values. We present finitely convergent algorithms for solving DRA‐NIP and DRR‐NIP with a general ambiguity set. To evaluate their performance, we provide results of our extensive computational experiments performed on instances known for (risk‐neutral) stochastic NIP.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"22 - 3"},"PeriodicalIF":2.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42795363","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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