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The Constraint Function Response Shifting Scalar-Based Optimization Method for the Reliability-Based Dynamic Optimization Problem.

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Název: The Constraint Function Response Shifting Scalar-Based Optimization Method for the Reliability-Based Dynamic Optimization Problem.
Autoři: Qiao, Ping, Zhang, Qi, Wu, Yizhong
Zdroj: Mathematics (2227-7390); Feb2025, Vol. 13 Issue 4, p567, 25p
Témata: PROBABILITY density function, DYNAMICAL systems, RANDOM variables, FUNCTION spaces, ORBITS (Astronomy)
Abstrakt: This work aims to improve the reliability of dynamic systems by eliminating the effect of random control variables. At first, the reliability-based dynamic optimization problem (RB-DOP) is introduced and defined to account for dynamic systems with uncertainty associated with random control variables. Whereafter, in order to solve RB-DOP efficiently, the constraint function response shift scalar (CFRSS)-based RB-DOP optimization method is proposed, in which the nested RB-DOP is decoupled into an equivalent deterministic DOP and a CFRSS search problem, and the two problems are addressed iteratively until the control law converges. Specifically, the shift scalar CFRSS is calculated by the probability density function of the constraint function response and deducted for probabilistic constraints in the constraint function response space to move the violated constraints toward the reliable region, avoiding solving large-scale optimization problems in the control variable space. Finally, two numerical examples and a low-thrust orbit transfer problem are investigated to demonstrate the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]
Copyright of Mathematics (2227-7390) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Label: Title
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  Data: The Constraint Function Response Shifting Scalar-Based Optimization Method for the Reliability-Based Dynamic Optimization Problem.
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  Data: <searchLink fieldCode="AR" term="%22Qiao%2C+Ping%22">Qiao, Ping</searchLink><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Qi%22">Zhang, Qi</searchLink><br /><searchLink fieldCode="AR" term="%22Wu%2C+Yizhong%22">Wu, Yizhong</searchLink>
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  Data: Mathematics (2227-7390); Feb2025, Vol. 13 Issue 4, p567, 25p
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  Data: <searchLink fieldCode="DE" term="%22PROBABILITY+density+function%22">PROBABILITY density function</searchLink><br /><searchLink fieldCode="DE" term="%22DYNAMICAL+systems%22">DYNAMICAL systems</searchLink><br /><searchLink fieldCode="DE" term="%22RANDOM+variables%22">RANDOM variables</searchLink><br /><searchLink fieldCode="DE" term="%22FUNCTION+spaces%22">FUNCTION spaces</searchLink><br /><searchLink fieldCode="DE" term="%22ORBITS+%28Astronomy%29%22">ORBITS (Astronomy)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This work aims to improve the reliability of dynamic systems by eliminating the effect of random control variables. At first, the reliability-based dynamic optimization problem (RB-DOP) is introduced and defined to account for dynamic systems with uncertainty associated with random control variables. Whereafter, in order to solve RB-DOP efficiently, the constraint function response shift scalar (CFRSS)-based RB-DOP optimization method is proposed, in which the nested RB-DOP is decoupled into an equivalent deterministic DOP and a CFRSS search problem, and the two problems are addressed iteratively until the control law converges. Specifically, the shift scalar CFRSS is calculated by the probability density function of the constraint function response and deducted for probabilistic constraints in the constraint function response space to move the violated constraints toward the reliable region, avoiding solving large-scale optimization problems in the control variable space. Finally, two numerical examples and a low-thrust orbit transfer problem are investigated to demonstrate the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Mathematics (2227-7390) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.3390/math13040567
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        Text: English
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    Subjects:
      – SubjectFull: PROBABILITY density function
        Type: general
      – SubjectFull: DYNAMICAL systems
        Type: general
      – SubjectFull: RANDOM variables
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      – SubjectFull: FUNCTION spaces
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      – SubjectFull: ORBITS (Astronomy)
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              Text: Feb2025
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