Multi-Objective Optimal Design of Steel Beams Based on Genetic Algorithm–Response Surface Methodology

Aiming at the complex nonlinear solution of optimizing the design parameters for the static load-carrying capacity of steel beams, this study proposes a multi-parameter optimal design approach for the structure based on the response surface methodology (RSM) surrogate model and the genetic algorithm (GA). First, a finite element model for static calculation of a steel beam is established. Meanwhile, parameter sensitivity is analyzed based on the Plackett–Burman (PB) test design to reduce the dimensionality of the optimization model. Subsequently, utilising the Box–Behnken design (BBD) test method, response surface models for the ultimate load-carrying capacity and the structure mass are fitted to establish the correlation between design variables and response respectively. Then, the optimal solution for RSM and GA-RSM are carried out on the multi-objective optimization of load-carrying capacity and structure mass, respectively. Ultimately, the optimization results are compared and analyzed. The results indicate that the PB test effectively reduces the variable space and computational volume of the response surface model. The prediction accuracy of the models after applying RSM and GA-RSM reaches more than 90% and 99%, respectively. Notably, optimization using GA-RSM yields a reduction of structure mass by 4.5% and an increase of load-carrying capacity by 10.9%, thus verifying its role of serving as a reliable guide for enhancing performance of steel beams. In conclusion, GA-RSM is validated as an effective approach to guide the optimal design of steel beams.