Detecting resilient structures in stochastic networks: A two‐stage stochastic optimization approach

Rysz, Maciej; Krokhmal, Pavlo A.; Pasiliao, Eduardo L.

doi:10.1002/net.21727

Cited by 7 publications

(4 citation statements)

References 31 publications

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“…Rysz et al [180] consider a general class of problems which seeks to detect a “structure” (e.g., a clique) in a network with a certain property prior to the perturbation so that the structure can be repaired quickly after the perturbation to maintain this property. In other words, they seek to identify a portion of the network so that the property is quickly re‐established after any perturbation.…”

Section: Optimization Models and Network Robustnessmentioning

confidence: 99%

In search of network resilience: An optimization‐based view

et al. 2020

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Fifty years of research in Networks coincides with 50 years of advances in resilience theory and applications. The purpose of this review is to identify how these two technical communities influenced each other in the past and can bolster each other in the future. Advances in resilience theory show that there are at least four ways networks demonstrate resilience: robustness, rebound, extensibility, and adaptability. Research published in Networks and by the broader network optimization community has focused primarily on technical methods for robustness and rebound. We review this literature to organize seminal problems and papers on the ability of networks to manage increasing stressors and return to normal activities after a stressful event. In contrast, the Networks community has made less progress addressing issues for network extensibility and adaptability. Extensibility refers to the ability to stretch current operations to surprising situations and adaptability refers to the ability to sustain operations into the future. We discuss ways to harness existing network optimization methods to study these forms of resilience and outline their limitations. We conclude by providing a research agenda that ensures the Networks community remains central to future advances in resilience while being pragmatic about the limitations of network optimization for achieving this task.

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Section: Optimization Models and Network Robustnessmentioning

confidence: 99%

In search of network resilience: An optimization‐based view

et al. 2020

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“…Applications to transportation networks [176,196], VLSI [178], and facility location [220,225] employ such reliability and performance methods. Algorithms to address repairability are discussed in [185]. In [64], component states with memory are considered in evaluating s,T-connectedness.…”

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confidence: 99%

Network reliability: Heading out on the highway

et al. 2020

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A variety of probabilistic notions of network reliability of graphs and digraphs have been proposed and studied since the early 1950s. Although grounded in the engineering and logistics of network design and analysis, the research also spans pure and applied mathematics, with connections to areas as diverse as combinatorics and graph theory, combinatorial enumeration, optimization, probability theory, real and complex analysis, algebraic topology, commutative algebra, the design and analysis of algorithms, and computational complexity. In this paper we describe the landscape of various notions of network reliability, the roads well traveled, and some that appear likely to lead to meaningful and important journeys.

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“…We use a two-stage stochastic programming framework as our model. This modeling framework is well-studied in the literature, and we follow the structure presented in [75]. Let G = (N, A) represent an undirected graph with node set N and arc set A.…”

Section: A General Modeling Frameworkmentioning

confidence: 99%

“…A general two-stage stochastic programming framework may be represented explicitly as follows [75]: We can represent the same general two-stage stochastic program in its implicit, or recourse, form as follows:…”

Section: A General Modeling Frameworkmentioning

confidence: 99%

On stochastic network design

Richmond¹

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Network design problems have been prevalent and popular in the operations research community for decades, because of their practical and theoretical significance. Due to the relentless progression of technology and the creative development of intelligent, efficient algorithms, today we are able to efficiently solve or give excellent heuristic solutions to many network design problem instances. The purpose of this work is to thoroughly examine and tackle two classes of highly complex network design problems which find themselves at the cutting edge of modern research. First we examine the stochastic incremental network design problem. This problem differs from traditional network design problems through the addition of both temporal and stochastic elements. We present a modeling framework for this class of problems, conduct a thorough theoretical analysis of the solution structure, and give insights into solution methods. Next we introduce the robust network design problem with decision-dependent uncertainties. Traditional stochastic optimization approaches shy away from randomness which is directly influenced by a user's decisions, due to the computational challenges that arise. We present a two-stage stochastic programming framework, noting that the complexity of this class of problems is derived from a highly nonlinear term in the first-stage objective function. This term is due to the decision-dependent nature of the uncertainty. We perform a rigorous computational study in which we implement various solution algorithms which are both exact and heuristic, as well as iv both well-studied and original. For each of the two classes of problems examined in our work, we give suggestions for future study and offer insights into effective ways of tackling these problems

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Detecting resilient structures in stochastic networks: A two‐stage stochastic optimization approach

Cited by 7 publications

References 31 publications

In search of network resilience: An optimization‐based view

In search of network resilience: An optimization‐based view

Network reliability: Heading out on the highway

On stochastic network design

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