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

## TL;DR

This paper presents a new method to optimize the design of high-performance cement composites using hybrid fibers and advanced algorithms.

## Contribution

The study introduces a novel multi-objective optimization approach combining Box–Behnken and NSGA-II for hybrid fiber-reinforced ECC design.

## Key findings

- UHMWPE and basalt fibers show a significant hybrid effect in improving ECC performance.
- Optimal mix proportion includes a 0.21 water-to-binder ratio, 1.51% UHMWPE, and 0.85% basalt fiber.
- Regression models validated by ANOVA demonstrate high fitting accuracy for ECC properties.

## Abstract

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.