Connectivity Upgrade Models for Survivable Network Design

Balakrishnan, Anantaram; Mirchandani, Pitu B.; Natarajan, Harihara Prasad

doi:10.2139/ssrn.876488

Cited by 6 publications

(6 citation statements)

References 22 publications

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“…On the other hand, the second type of fractionality may affect the path-based formulation as well, as shown in Figure 2. In this example, there are three commodities, no flow costs and activation costs equal to one for arcs (3,6), (4, 7), (5,8) and zero for the remaining arcs. The figure shows an optimal solution of the linear relaxation of the path-based formulation, where the flow of each commodity is split into two paths, the costly arcs are activated at value 0.5 and the resulting cost is 3/2.…”

Section: Observation 2 Any Feasible Solution For the Linear Relaxatio...mentioning

confidence: 99%

“…Under a stochastic paradigm, the network is required to remain operative either with a large probability ( [26], [9]) or after some recourse action has been implemented ( [23]). Alternatively, more conservative approaches, imposing explicit redundancy in the definition of the network, have been considered in the literature; typically, one is required to design a network having two (edge) disjoint paths for each commodity ( [24], [1], [2], and [5]), while [18] considered the case in which higher connectivity requirements are imposed.…”

Section: Introductionmentioning

confidence: 99%

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Network Design with Service Requirements: Scaling-up the Size of Solvable Problems

Gudapati¹,

Malaguti²,

Monaci³

2021

Preprint

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Network design, a cornerstone of mathematical optimization, is about defining the main characteristics of a network satisfying requirements on connectivity, capacity, and level-of-service. It finds applications in logistics and transportation, telecommunications, data sharing, energy distribution, and distributed computing. In multi-commodity network design, one is required to design a network minimizing the installation cost of its arcs and the operational cost to serve a set of point-to-point connections. The definition of this prototypical problem was recently enriched by additional constraints imposing that each origin-destination of a connection is served by a single path satisfying one or more level-of-service requirements, thus defining the Network Design with Service Requirements [Balakrishnan, Li, and Mirchandani. Operations Research, 2017]. These constraints are crucial, e.g., in telecommunications and computer networks, in order to ensure reliable and low-latency communication. In this paper we provide a new formulation for the problem, where variables are associated with paths satisfying the end-to-end service requirements. We present a fast algorithm for enumerating all the exponentially-many feasible paths and, when this is not viable, we provide a column generation scheme that is embedded into a branch-and-cutand-price algorithm. Extensive computational experiments on a large set of instances show that our approach is able to move a step further in the solution of the Network Design with Service Requirements, compared with the current state-of-the-art.

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Section: Observation 2 Any Feasible Solution For the Linear Relaxatio...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Network Design with Service Requirements: Scaling-up the Size of Solvable Problems

Gudapati¹,

Malaguti²,

Monaci³

2021

Preprint

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“…Problems related with designing rings of bounded size are studied by Fortz and Labbé [7] and Fortz et al [8][9][10]. Generalizations of 2EC networks are studied by Magnanti and Raghavan [22] and Balakrishnan et al [2].…”

Section: Introductionmentioning

confidence: 99%

A branch-and-cut algorithm for two-level survivable network design problems

Rodríguez-Martín

Salazar-González

Yaman

2016

Computers & Operations Research

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This paper approaches the problem of designing a two-level network protected against single-edge failures. The problem simultaneously decides on the partition of the set of nodes into terminals and hubs, the connection of the hubs through a backbone network (first network level), and the assignment of terminals to hubs and their connection through access networks (second network level). We consider two survivable structures in both network levels. One structure is a two-edge connected network, and the other structure is a ring. There is a limit on the number of nodes in each access network, and there are fixed costs associated with the hubs and the access and backbone links. The aim of the problem is to minimize the total cost. We give integer programming formulations and valid inequalities for the different versions of the problem, solve them using a branch-and-cut algorithm, and discuss computational results. Some of the new inequalities can be used also to solve other problems in the literature, like the plant cycle location problem and the hub location routing problem. © 2015 Elsevier Ltd. All rights reserved

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“…The number of customers that a plant can serve is limited. Magnanti and Raghavan and Balakrishnan et al consider more general survivability requirements. Klincewicz reviews combined hub location and network design problems.…”

Section: Introductionmentioning

confidence: 99%

The ring/κ‐rings network design problem: Model and branch‐and‐cut algorithm

2016

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This article considers the problem of designing a two‐level network where the upper level consists of a backbone ring network connecting the so‐called hub nodes, and the lower level is formed by access ring networks that connect the non‐hub nodes to the hub nodes. There is a fixed cost for each type of link, and a facility opening cost associated to each hub. The number of nodes in each access ring is bounded, and the number of access rings connected to a hub is limited to italicκ , thus resulting in a ring/ italicκ ‐rings topology. The aim is to decide the hubs to open and to design the backbone and access rings to minimize the installation cost. We propose a mathematical model, give valid inequalities, and describe a branch‐and‐cut algorithm to solve the problem. Computational results show the algorithm is able to find optimal solutions on instances involving up to 40 nodes within a reasonable time. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(2), 130–140 2016

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Connectivity Upgrade Models for Survivable Network Design

Cited by 6 publications

References 22 publications

Network Design with Service Requirements: Scaling-up the Size of Solvable Problems

Network Design with Service Requirements: Scaling-up the Size of Solvable Problems

A branch-and-cut algorithm for two-level survivable network design problems

The ring/κ‐rings network design problem: Model and branch‐and‐cut algorithm

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