Multi-Objective Optimization Design of Hybrid Fiber-Reinforced ECC Based on Box–Behnken and NSGA-II

To enhance the effectiveness and precision of design and to produce more low-carbon and high-performance Engineered Cementitious Composites (ECCs), novel hybrid fiber-reinforced high-ductility cementitious composites developed by incorporating a combination of ultra-high-molecular-weight polyethylene fibers (UHMWPE) and basalt fibers (BFs) into the cementitious matrix. Building upon the Box-Behnken design model from Response Surface Methodology (RSM), this study investigates the effects of different water-to-binder ratios and fiber contents on the mechanical properties of hybrid fiber-reinforced ECC. Analysis of variance (ANOVA) was used to validate the regression models. Furthermore, multi-objective optimization of the ECC mix proportion was achieved by employing the NSGA-II algorithm in conjunction with the TOPSIS comprehensive evaluation method. The results indicate that UHMWPE and BFs exhibited a significant positive hybrid effect. The order of factor significance was as follows: The content of ultra-high-molecular-weight polyethylene is greater than that of basalt fiber, and the content of basalt fiber is greater than that of the water-binder ratio. The results of variance analysis show that the regression model has high fitting accuracy. Furthermore, the algorithmic optimization yielded an optimal mix proportion: a water-to-binder ratio of 0.21, UHMWPE fiber content of 1.51%, and BF content of 0.85%. This study provides a valuable reference for the multi-objective optimization design of ECC mix proportions targeting diverse strength and toughness requirements.