An RF and LSSVM–NSGA-II method for the multi-objective optimization of high-performance concrete durability

Abstract

The development of cost-effective high-performance concrete (HPC) has long been a focus of concrete research. Multiple objectives are required for the design of the HPC mix proportion. This paper develops a hybrid intelligent framework based on the random forest (RF) algorithm, the least-squares support vector machine (LSSVM) algorithm and the nondominated sorting genetic algorithm with an elite strategy (NSGA-II) to realize the efficient optimization of concrete mixture. The developed framework can identify the key influencing factors in terms of the concrete mix proportion, predict concrete performance, and obtain a series of optimized solutions through multi-objective optimization. The optimal solution is then determined according to the engineer's preference as the recommended mix proportion. An actual engineering case is studied to verify the feasibility of the developed framework, in which the material proportions in the concrete composition are taken as decision variables and the frost resistance, impermeability and cost of the concrete are taken as objectives. The results are as follows: (1) In the RF-based importance ranking, the water–binder ratio, cement content, fly ash content, fine aggregate content, coarse aggregate content and compound superplasticizer content are found to be key factors influencing concrete durability, indicating that predictions based on these factors will yield more accurate results. (2) LSSVM models show excellent predictive fitting capabilities, with the goodness of fit for predicting the frost resistance and impermeability of concrete reaching 0.94084 and 0.9443, respectively. The obtained surrogate model can be used to establish the fitness function for the optimization algorithm to improve efficiency. (3) The LSSVM–NSGA-II algorithm can determine the optimal mix proportion for concrete considering durability and cost. Compared with the average performance of the original mixture, the permeability and frost resistance of the obtained mixture are increased by 30.71% and 3.17%, respectively, and the cost is lower by 1.84%. In practice, the proposed approach can provide guidance for realizing multi-objective optimization of concrete and improve the efficiency of concrete mix proportion design. Notably, the current algorithm needs to be trained on a large amount of data to obtain accurate results; in the future, either a large amount of data should be collected or the algorithm should be improved to enhance its universality.