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Submodularity issues in value-of-information-based sensor placement

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  • Malings, C.
  • Pozzi, M.

Abstract

The value of information represents a rational metric for guiding the optimization of sensing efforts to support infrastructure system management under uncertainty. Unfortunately, this metric lacks the property of submodularity. Submodularity can be intuitively understood as a diminishing returns property, whereby the incremental benefit of a specific measurement is higher when the set of other available measures is smaller. Metrics which exhibit this property can be optimized using efficient greedy approaches, with certain guarantees on the near-optimality of the results. In this paper, we examine the issue of submodularity related to the optimization of sensor monitoring schemes using the value of information metric. We illustrate how greedy optimization approaches using value of information can lead to sub-optimal solutions for sensing in certain situations. We also examine how one potential heuristic approach involving a submodular surrogate metric (e.g. the conditional entropy) might be used to avoid some of these shortcomings.

Suggested Citation

  • Malings, C. & Pozzi, M., 2019. "Submodularity issues in value-of-information-based sensor placement," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 93-103.
    • Handle: RePEc:eee:reensy:v:183:y:2019:i:c:p:93-103
    DOI: 10.1016/j.ress.2018.11.010
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    References listed on IDEAS

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    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Nicky J. Welton & Howard H. Z. Thom, 2015. "Value of Information," Medical Decision Making, , vol. 35(5), pages 564-566, July.
    3. Malings, Carl & Pozzi, Matteo, 2016. "Value of information for spatially distributed systems: Application to sensor placement," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 219-233.
    4. Malings, C. & Pozzi, M., 2018. "Value-of-information in spatio-temporal systems: Sensor placement and scheduling," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 45-57.
    5. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Memarzadeh, Milad & Pozzi, Matteo, 2016. "Value of information in sequential decision making: Component inspection, permanent monitoring and system-level scheduling," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 137-151.
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    Cited by:

    1. Yang, Chen & Xia, Yuanqing, 2024. "Interval Pareto front-based multi-objective robust optimization for sensor placement in structural modal identification," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    2. Song, Chaolin & Zhang, Chi & Shafieezadeh, Abdollah & Xiao, Rucheng, 2022. "Value of information analysis in non-stationary stochastic decision environments: A reliability-assisted POMDP approach," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    3. Zou, Guang & Kolios, Athanasios, 2022. "Quantifying the value of negative inspection outcomes in fatigue maintenance planning: Cost reduction, risk mitigation and reliability growth," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    4. Jiachen Ju & Xiao Wang & Dachuan Xu, 2024. "Online non-monotone diminishing return submodular maximization in the bandit setting," Journal of Global Optimization, Springer, vol. 90(3), pages 619-649, November.
    5. Suning Gong & Qingqin Nong & Jiazhu Fang & Ding-Zhu Du, 2024. "Algorithms for Cardinality-Constrained Monotone DR-Submodular Maximization with Low Adaptivity and Query Complexity," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 194-214, January.
    6. Lin, Chaochao & Song, Junho & Pozzi, Matteo, 2022. "Optimal inspection of binary systems via Value of Information analysis," Reliability Engineering and System Safety, Elsevier, vol. 217(C).

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