## 1 Introduction
[PERSON] [23] adopted artificial neural networks (ANN) to predict the compressive strength of high-performance concrete, concluding that the ANN model was more accurate than a model based on regression analysis and it was easy to use ANN models for numerical experiments to review the effects of the proportions of each variable on the concrete mix. [PERSON] [24], [PERSON] [25] and [PERSON] [26] also applied the neural network for predicting the properties of conventional concrete and high-performance concretes. [PERSON] [27] proposed a method to predict the 28-day compressive strength of concrete by using multilayer feed-forward neural networks. [PERSON] [28] developed a fuzzy model to predict normal and high-strength concrete. And the main advantage of the fuzzy model was its ability to describe knowledge in a descriptive human-like manner in the form of simple rules using linguistic variables only [29]. [PERSON] [30] derived an equation from experimental results to estimate the compressive strength development in concrete which contained fly ash. [PERSON] [31] applied an artificial neural network to predict the compressive strength of ground granulated blast furnace slag concrete by using concrete ingredients as input parameters. [PERSON], [PERSON] et al. [4] used two different data-driven models, multiple linear regression and artificial neural network, in a MATLAB software environment to estimate the compressive strength of concrete. However, artificial intelligence models require a large training data set due to its \"black-box\" techniques [32]. Although there is a lot of literature about predicting the compressive strength of concrete, only a few of researchers could express the long-term compressive strength development in a certain kind of concrete. Meanwhile, the measurement and prediction of the compressive strength of concrete using non-destructive techniques is of interest to engineers worldwide. Such methods are easy to carry out because they require little or no sample preparation. Unlike artificial intelligence models that use \"black-box\" techniques and need a lot of data, the concrete compressive strength development over time (CCSDOT) model proposed in this study generates explicit formulas, which provide important advantages in practical applications. Meanwhile, adding optimization algorithms makes this model more adaptable to new data than conventional models. Moreover, the model can predict the compressive strength development over time in concrete which incorporated with up to three kinds of mineral admixtures by using concrete mix proportions. Since the existing research can either only predict the compressive strength of a certain concrete or predict the compressive strength of concrete at a certain age, it is necessary to carry out the research about a model to predict the compressive strength of all kinds of concrete development over time. The main objective of this research is to construct a CCSDOT model to predict the compressive strength development over time of all kinds of concretes. These concretes are incorporated with different mineral admixtures. The model requires a few trial tests, the concrete's ingredients, and the concrete's age. For this purpose, a computer program of sequence quadratic programming was developed in FORTRAN. Furthermore, the results obtained from the CCSDOT model were compared with the results of the experiments and backpropagation (BP) neural network. By adopting this predicting model, considerable costs and time could be saved. The outline of the rest of the study is as follows: Section 2 describes the model derivation and discusses the sequential quadratic programming method. Applications in green concrete are presented in Section 3, including the cross-validation and fitting analysis. In Section 4, the sensitivity analysis is presented, and the optimal performance of the model is compared with the optimal performance of the BP neural network. Section 5 is the conclusions of this study.