A decomposition algorithm applied to planning the interdiction of stochastic networks

Held, Harald; Hemmecke, Raymond; Woodruff, David L.

doi:10.1002/nav.20079

Cited by 41 publications

(23 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Examples have been reported in the literature for some time, and include server location [28], batch sizing [21], electricity generation unit commitment [37], supply chain design [34], network interdiction [6,15,17], and many others [38]. The general combinatorial, NP-hard nature of integer and mixed-integer problems makes them difficult to solve even when all the data are known, but special structure may allow for easier solution.…”

Section: Introductionmentioning

confidence: 99%

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

et al. 2016

Self Cite

View full text Add to dashboard Cite

We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. We report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds. Abstract We present a method for computing lower bounds in the Progressive Hedging Algorithm (PHA) for two-stage and multi-stage stochastic mixedinteger programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. We report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.

show abstract

Section: Introductionmentioning

confidence: 99%

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

et al. 2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…The algorithmic treatment of stochastic two-stage problems with the excess probability objective leads to linear programs with (additional) binary variables, which indicate for each scenario whether the cost threshold η has been exceeded or not. This is for example discussed in [72,93], and has been applied in [53]. In principle, the ideas from the finite dimensional linear case could be transferred to the infinite dimensional setting of the shape optimization problem with excess probability.…”

Section: Risk Measuresmentioning

confidence: 99%

Shape Optimization under Uncertainty from a Stochastic Programming Point of View

Held¹

2009

Self Cite

View full text Add to dashboard Cite

“…They formulate the problem of identifying locations for installing smuggled nuclear material detectors as a two-stage stochastic mixed-integer program with recourse, and showed that the problem is NP-Hard. In Held, Hemmecke, Woodruff [12], the stochastic network interdiction problem is shown to be solved effectively by applying a decomposition-based method. Our approach to solving the problem is akin to that proposed by Cormican in her master's thesis [3], where she proposes using Bender's decomposition to solve a deterministic version of the problem.…”

Section: Introductionmentioning

confidence: 99%

Reformulation and sampling to solve a stochastic network interdiction problem

Janjarassuk

Linderoth

2008

Networks

View full text Add to dashboard Cite

The Network Interdiction Problem involves interrupting an adversary's ability to maximize flow through a capacitated network by destroying portions of the network. A budget constraint limits the amount of the network that can be destroyed. In this paper, we study a stochastic version of the network interdiction problem in which the successful destruction of an arc of the network is a Bernoulli random variable, and the objective is to minimize the maximum expected flow of the adversary. Using duality and linearization techniques, an equivalent deterministic mixed integer program is formulated. The structure of the reformulation allows for the application of decomposition techniques for its solution. Using a parallel algorithm designed to run on a distributed computing platform known as a computational grid, we give computational results showing the efficacy of a sampling-based approach to solving the problem.

show abstract

A decomposition algorithm applied to planning the interdiction of stochastic networks

Cited by 41 publications

References 9 publications

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

Shape Optimization under Uncertainty from a Stochastic Programming Point of View

Reformulation and sampling to solve a stochastic network interdiction problem

Contact Info

Product

Resources

About