Reliability-based design optimization. Robust multiobjetive optimization. Reinforced concrete frames. Computational efficiency. FEM. Python.

Traditionally, concrete structure designs employ semi-probabilistic methods that apply safety factors to compensate for uncertainties, increasing loads and reducing resistances. While this ensures safety and reliability, probabilistic methods offer a more comprehensive approach by quantifying the probability of failure for a structure. This study applied Reliability-Based Design Optimization (RBDO) and Robust Reliability-Based Multi-objective Design Optimization (RBRMDO) to a reinforced concrete linear plane frame. The study compared efficiency among procedures, considering accuracy, processing time, iterations, number of function evaluations, and Pareto point distribution quality. The main contribution lies in investigating various algorithm combinations to identify the most efficient and robust procedure for multi-objective optimization under uncertainties in concrete structure designs. The numerical methods Reliability Index Approach (RIA), Performance Measure Approach (PMA), Single-Loop Approach (SLA), and Sequential Optimization and Reliability Assessment (SORA) were coupled with Weighted Sum (WS) and Normal-Boundary Intersection (NBI) methods to build the Pareto frontier. The optimization used the Sequential Quadratic Programming (SQP) through the Scipy library. The structural analysis employed the Finite Element Method (FEM) through the CasPy package. The reliability analysis employed the First-Order Reliability Method (FORM) for RIA and PMA through the Pystra package. SLA and SORA used a FORM routine we implemented. HL-RF algorithm assessed the Most Probable Point (MPP), and the finite differences method calculated numerical derivatives. Four examples were tested before the main application. SLA and SORA showed excellent results, with SLA being the most efficient algorithm. RIA and PMA underperformed in processing time and the number of limit state function evaluations. NBI outperformed in the Pareto point distribution quality compared to WS.