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This paper presents a new multigene genetic programming (MGGP) approach for estimation of elastic modulus of concrete. The MGGP technique models the elastic modulus behavior by integrating the capabilities of standard genetic programming and classical regression. The main aim is to derive precise relationships between the tangent elastic moduli of normal and high strength concrete and the corresponding compressive strength values. Another important contribution of this study is to develop a generalized prediction model for the elastic moduli of both normal and high strength concrete. Numerous concrete compressive strength test results are obtained from the literature to develop the models. A comprehensive comparative study is conducted to verify the performance of the models. The proposed models perform superior to the existing traditional models, as well as those derived using other powerful soft computing tools.

The importance of elastic modulus of concrete in structural and material engineering is well understood. This parameter has been widely used for the analysis of structure deformations, concrete creep, shrinkage, crack control, and so forth [

This study proposes a new multigene genetic programming (MGGP) approach to derive prediction models for the elastic modulus of concrete. MGGP combines the modeling capabilities of both GP and statistical regression methods. Despite remarkable prediction capabilities of the MGGP approach [

GP creates computer programs to solve a problem by simulating the biological evolution of living organisms [

A typical program evolved by MGGP.

In order to obtain the linear coefficients, an ordinary least squares analysis is performed on the training data. Besides, it is possible to embed multigene approach within a partial least squares method [

The modulus of elasticity is frequently formulated as a function of the compressive strength of concrete. Most of the national and international codes use this way to express the modulus of elasticity of concrete (e.g., American Concrete Code (ACI-318-95) [

Parameter settings for the MGGP algorithm.

Parameter | Settings |
---|---|

Population size | 200, 500, 1000 |

Number of generations | 200, 500, 1000 |

Maximum number of genes allowed in an individual | 1, 3, 6 |

Maximum tree depth | 4, 6 |

Tournament size | 12 |

Elitism | 0.01% of population |

Crossover events | 0.1, 0.85 |

High level crossover | 0.2 |

Low level crossover | 0.8 |

Mutation events | 0.1, 0.85 |

Subtree mutation | 0.9 |

Function set | +, −, ×, /, |

The best MGGP models are chosen on the basis of providing the best fitness value on the training data as well as the simplicity of the models [

An experimental database of the previously published test results [

The optimal formulation of the

Predicted versus experimental

Variation of the best and mean fitness with the number of generations for MGGP I.

Statistical properties of the evolved MGGP I model (on training data).

The optimal formulation of the

Predicted versus experimental

Variation of the best and mean fitness with the number of generations for MGGP II.

Statistical properties of the evolved MGGP II model (on training data).

The best prediction model for the

Predicted versus experimental

Variation of the best and mean fitness with the number of generations for MGGP III.

Statistical properties of the evolved MGGP III model (on training data).

Figures

A comparison of the ratio between the predicted and experimental

A comparison of the ratio between the predicted and experimental

A comparison of the ratio between the predicted and experimental

For further verification of the MGGP models, a parametric analysis is performed in this study. The parametric analysis investigates the response of the predicted

Parametric analysis of the

In this paper, a promising extension of the classical GP, namely, MGGP, is employed for the analysis of the tangent

The authors declare that there is no conflict of interests regarding the publication of this paper.

_{2}-oil minimum miscibility pressure model based on multi-gene genetic programming