With the continuous promotion of the "carbon neutrality" and "carbon peak" strategies, reducing carbon emissions from cement production is urgent. Replacing cement with a combination of one or multiple mineral materials can not only improve the physical properties of cement products, but also reduce the use of cement clinker, thereby reducing carbon emissions in cement production and saving resources. However, due to the complex properties and multiple interrelated properties of cement matrix composites, the optimization design of these materials in cement matrix composites faces challenges. Therefore, it is necessary to find more efficient and accurate methods for optimizing the design of cement matrix composites.

Response surface experiments were conducted by using Shangfeng cement clinker that meets the Chinese national standard GB 21372-2008, standard sand that meets the European standard EN 196-1∶2005, multiple mineral materials (grade II fly ash, S95 mineral powder, limestone powder, and tuff powder), and external gypsum (natural gypsum, desulfurization gypsum). The response surface experiment was conducted using Design Expert 13.0 software for Box Behnken response surface design. The response surface design consists of four factors and three levels. Four factors were selected: fly ash content (A), limestone powder content(B), tuff powder content(C), and slag content(D). The response values were cement 3 d compressive strength, 28 d compressive strength, and the cumulative hydration heat release of cement within 3 d, and 29 experimental points were designed.

Firstly, use Monte Carlo sampling method to analyze the reliability of each response quantity. Select process factors as noise, randomly select 8 000 samples points to analyze the contribution of each random input variable to the response, and confirm its distribution characteristics including mean value, standard deviation, and Sigma level. Next, Further construct optimization objectives that meet the minimum 3 d compressive strength value (Y₁), maximum 28 d compressive strength value (Y₂), and minimum the cumulative hydration heat release value of cement within 3 d (Y₃), as well as the maximum content of multiple mineral materials (Y₄). The deterministic constraint range for Y₁ is 17.0-27.0 MPa, and the deterministic constraint range for Y₂ is 42.5-52.5 MPa. Y₃ is set to be no higher than the mean value of reliability analysis and not lower than 170.0 J/g; Y₄ is set to not less than 30% of the total material quantity. And the reliability of each performance response and design variable should be not less than 6-Sigma. A multi-objective optimization design for multi mineral materials, based on the mathematical model obtained from response surface experiments and the multi-objective optimization design of multivariate mineral materials, the non-dominated sorting genetic algorithm (NSGA-II) is used for multi-objective optimization. When optimizing, set the initial population size of NSGA-II to 200, genetic algebra to 20, cross distribution index to 10, and mutation operator to 20.

Based on the response surface experimental matrix, the experimental results were obtained. After removing the insignificant items (p-value>0.05) from the response surface experimental results, the mathematical model was obtained as follows:

Y₁=12.148+0.748A+0.690B-0.392C+2.089D-0.078A×D-0.066B²-0.065D²

Y₂=49.595-1.179A+0.893B+0.654C+0.381D+0.042A×C+0.073B×C-0.048C×D+0.048A²-0.155B²-0.094C²

Y₃=368.801-12.309A+0.369B-12.273C-7.958D-0.192A×B+0.258A×C+0.757A×D+0.569C×D

A 6-Sigma reliability analysis was conducted on the response surface mathematical model, and the sigma level values for Y₁ and Y₂ were 1.144 and 1.497, respectively, with reliability values of 74.76% and 86.55%, both lower than 90%. However, the sigma level value for Y₃ was 3.953, with reliability values of 93.83%. After multi-objective optimization of the mathematical model, the obtained Pareto solutions were sorted to get the optimal process parameters: A of 2.72%, B of 7.14%, C of 9.95%, and D of 19.93%. The optimized Y₁ of cement is 23.43 MPa, and the Y₂ is 46.82 MPa, the Y₃ is 214.36 J/g, and the total content of cement multi mineral materials is 39.74%. Five repeated experiments were conducted to verify the optimal process parameters, and the experimental values were close to the optimized values. The maximum relative error is 3.71%, which is within an acceptable error range (>90% confidence level).

According to the mathematical model obtained from the response surface, it is found that there is a good correlation between the multi mineral material system and the mechanical properties of cement. There is an excellent linear correlation between the multi mineral material system and the hydration heat of cement. Based on mathematical models, a multi-objective optimization method based on NSGA-II can be used to solve the optimal formula. In addition, by using the 6sigma robust multi-objective optimization method, the reliable multi-objective optimization results can be obtained. When the content of fly ash is 2.72%, the content of limestone powder is 7.14%, the content of tuff powder is 9.95%, and the content of slag is 19.93%, the three-dimensional compressive strength value of cement is 23.43 MPa, the 28 d compressive strength value is 46.82 MPa, and the Y₃ is 214.36 J/g. This study validated the robustness and feasibility of composite design methods (including response surface design and multi-objective optimization based on NSGA-II) in multi-component mineral systems.