Two-Stage Submodular Maximization Problem Beyond Non-negative and Monotone

Liu, Zhicheng; Chang, Hong; Ma, Ran; Du, Donglei; Zhang, Xiaoyan

doi:10.1007/978-3-030-59267-7_13

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…Furthermore, some studies extend TSSO model. [31] relaxes TSSO to the problems that are neither non-negative nor monotone. [32] integrates TSSO with the curvature index.…”

Section: B Two-stage Submodular Optimizationmentioning

confidence: 99%

“…Unlike the typical modular function settings in [31][32][44], the modular function c i (T i ) in this work is separate as…”

Section: A Solving Algorithm Designmentioning

confidence: 99%

“…After that, [29] specializes the TSSO application in the contents of unknown distribution. And TSSO is also applied to streaming scenario [30], difference type [31] and so on.…”

Section: Introductionmentioning

confidence: 99%

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Submodular Optimization of Dynamic Thermal Rating for Cascading Failure Risk Mitigation Considering Braess Paradox

Long

Liu

et al. 2022

IEEE Trans. Power Syst.

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Cascading failure causes a major risk to society currently. To effectively mitigate the risk, dynamic thermal rating (DTR) technique can be applied as a cost-effective strategy to exploit potential transmission capability. From the perspectives of service life and Braess paradox, it is important and challenging to jointly optimize the DTR placement and operation schedule for changing system state, which is a two-stage combinatorial problem with only discrete variables, suffering from no approximation guarantee and dimension curse only based on traditional models. Thus, the present work proposes a novel two-stage submodular optimization (TSSO) of DTR for risk mitigation considering placement and operation schedule. Specifically, it optimizes DTR placement with proper redundancy in first stage, and then determines the corresponding DTR operation for each system state in second stage. Under the condition of the Markov and submodular features in sub-function of risk mitigation, the submodularity of total objective function of TSSO can be proven for the first time. Based on this, a state-of-the-art efficient solving algorithm is developed that can provide a better approximation guarantee than previous studies by coordinating the separate curvature and error form. The performance of the proposed algorithms is verified by case results.

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“…Furthermore, some studies extend TSSO model. [31] relaxes TSSO to the problems that are neither non-negative nor monotone. [32] integrates TSSO with the curvature index.…”

Section: B Two-stage Submodular Optimizationmentioning

confidence: 99%

“…Unlike the typical modular function settings in [31][32][44], the modular function c i (T i ) in this work is separate as…”

Section: A Solving Algorithm Designmentioning

confidence: 99%

See 1 more Smart Citation

Submodular Optimization of Dynamic Thermal Rating for Cascading Failure Risk Mitigation Considering Braess Paradox

Long

Liu

et al. 2022

IEEE Trans. Power Syst.

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Two-stage submodular maximization problem beyond nonnegative and monotone

Liu

Chang

et al. 2021

Math. Struct. Comp. Sci.

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We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximation algorithms for this problem. The first is a deterministic $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right),1} \right)$ -approximation algorithm, and the second is a randomized $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}}}} \right) - \varepsilon ,1} \right)$ -approximation algorithm with improved time efficiency.

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