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

Ping Qiao, Qi Zhang () and Yizhong Wu
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Ping Qiao: School of Mechanical Engineering, Suzhou University of Science and Technology, Suzhou 215009, China
Qi Zhang: School of Cyber Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Yizhong Wu: School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Mathematics, 2025, vol. 13, issue 4, 1-28

Abstract: 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.

Keywords: dynamic system; reliability-based dynamic optimization; random control variable; constraint function response shift scalar (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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