Efficient optimization-based method for simultaneous calibration of load and resistance factors considering multiple target reliability indices

This study introduces an innovative optimization process for calibrating probabilistic load and resistance factors (LRFs) in limit state designs, effectively accommodating multiple target reliability indices. Given the impracticality of direct Monte Carlo simulations (MCS) for this task, a response surface method (RSM) is proposed to approximate load and resistance components separately rather than fitting conventional safety factors. This approach eliminates the need for additional implicit evaluations, thereby improving the efficiency of LRF calibration across multiple targets. The process is further enhanced by an adaptive boundary algorithm that updates search domains in real-time, streamlining the optimization. Validation through three examples—including one explicit and two implicit performance functions (a structural and a geotechnical example)—demonstrates that the method achieves accurate results with fewer iterations by dynamically narrowing search domains. Specifically, the accuracy of the proposed method is confirmed by comparing results with those from the literature for the explicit example and with basic MCS results applied to the initial implicit problems. Performance on the illustrative examples shows that the structural example achieves calibration for three targets within ten iterations. Additionally, this method eliminates the need for approximately ten thousand implicit evaluations when calculating limit state points for the geotechnical example.