An efficient reliability-based design optimization approach based on probability quantile estimation and structural constraint integration

Yuwei Shi

doi:10.1016/j.cie.2026.112102

An efficient reliability-based design optimization approach based on probability quantile estimation and structural constraint integration

2026-05-05

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DOI：10.1016/j.cie.2026.112102

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To efficiently address reliability-based design optimization (RBDO) problems with multiple local optima, strong nonlinearity and expensive black-box evaluations, this work proposes a novel RBDO framework that integrates reliability constraints through quantile models and incorporates Bayesian optimization algorithm. The core contribution lies in introducing a quantile-based constrained expected improvement (QCEI) criterion, which simultaneously accounts for objective improvement and reliability satisfaction. In practice, the QCEI criterion facilitates the global optimization within the reliability design space, while the U function is employed to enhance the model accuracy of the active constraint in the random space. In addition, a hybrid stopping criterion ensures the identification of the potential optimum region, and a subsequent local optimization is applied to refine the solution. Finally, several numerical and engineering examples are presented to validate the effectiveness of the proposed method. The experimental results demonstrate that the proposed criterion is more suitable for RBDO problems with multiple local optima than existing acquisition strategies and exhibits superior performance compared with most state-of-the-art methods.

Keywords:

Reliability-based design optimization

Quantile estimation

Bayesian optimization

Expected improvement

Structural constraint integration

An efficient reliability-based design optimization approach based on probability quantile estimation and structural constraint integration

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