Multi-objective mixture design and optimisation of steel fiber reinforced UHPC using machine learning algorithms and metaheuristics

Ultra-high-performance concrete (UHPC) is a recent class of concrete with improved durability, rheological and mechanical and durability properties compared to traditional concrete. The production cost of UHPC is considerably high due to a large amount of cement used, and also the high price of other required constituents such as quartz powder, silica fume, fibres and superplasticisers. To achieve specific requirements such as desired production cost, strength and flowability, the proportions of UHPC’s constituents must be well adjusted. The traditional mixture design of concrete requires cumbersome, costly and extensive experimental program. Therefore, mathematical optimisation, design of experiments (DOE) and statistical mixture design (SMD) methods have been used in recent years, particularly for meeting multiple objectives. In traditional methods, simple regression models such as multiple linear regression models are used as objective functions according to the requirements. Once the model is constructed, mathematical programming and simplex algorithms are usually used to find optimal solutions. However, a more flexible procedure enabling the use of high accuracy nonlinear models and defining different scenarios for multi-objective mixture design is required, particularly when it comes to data which are not well structured to fit simple regression models such as multiple linear regression. This paper aims to demonstrate a procedure integrating machine learning (ML) algorithms such as Artificial Neural Networks (ANNs) and Gaussian Process Regression (GPR) to develop high-accuracy models, and a metaheuristic optimisation algorithm called Particle Swarm Optimisation (PSO) algorithm for multi-objective mixture design and optimisation of UHPC reinforced with steel fibers. A reliable experimental dataset is used to develop the models and to justify the final results. The comparison of the obtained results with the experimental results validates the capability of the proposed procedure for multi-objective mixture design and optimisation of steel fiber reinforced UHPC. The proposed procedure not only reduces the efforts in the experimental design of UHPC but also leads to the optimal mixtures when the designer faces strength-flowability-cost paradoxes.