# Novel Evolutionary-Optimized Neural Network for Predicting Fresh Concrete Slump

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## Abstract

**:**

## 1. Introduction

## 2. Data and Modeling Methodology

#### 2.1. Data Provision

#### 2.2. Methodology

#### 2.2.1. Shuffled Complex Evolution

- I.
- Initialize: three parameters of q, α, and β are selected where m ≥ q ≥ 2, β ≥ 1, and α ≥ 1.
- II.
- Weight assignment: a triangular probability distribution is assigned to the complex, as expressed in Equation (1):$${P}_{i}=\frac{2\left(m+1-i\right)}{m\left(m+1\right)}\text{\hspace{1em}\hspace{1em}\hspace{1em}}i=1,2,\dots ,m$$
- III.
- Selecting parents: based on the above equation, q different points (i.e., u
_{1}, u_{2}, …, u_{q}) are chosen from the proposed complex. They are then stored in an array, as expressed in Equation (2).B = {u_{j}, F_{j}, i = 1, 2, …, q} - IV.
- Generating the offspring: based on the function values, the points are sorted and the centroid c is calculated as follows:$$c=\frac{1}{q-1}{{\displaystyle \sum}}_{j=1}^{q-1}{u}_{j}$$

_{r}= 2c − u

_{q}. There are two possibilities for the next step:

- (a)
- If the new point is within the existing space, the FV is calculated and the number of evaluations (NFEs) is changed to NFEs + 1.
- (b)
- Otherwise, the smallest hypercube H (which contains the proposed complex) is computed. The point u
_{z}is randomly produced within H. The NFEs is changed to NFEs + 1, and in the mutation stage, u_{r}and F_{r}will equate u_{z}and F_{z}.

_{q}is replaced by u

_{r}, if F

_{r}< F

_{q}. Otherwise, u

_{ic}= (c + u

_{q})/2 and its FV (i.e., F

_{ic}) is calculated and NFEs is changed to NFEs + 1. Similarly, u

_{q}is replaced by u

_{ic}, if F

_{ic}< F

_{q}. Otherwise, u

_{z}is randomly generated within H and F

_{z}is computed, NFEs is changed to NFEs + 1, and u

_{q}is replaced by u

_{z}. This process continues for α times.

- V.
- In the last step, the parents are replaced by offspring and the complex is sorted regarding the obtained FVs.
- VI.
- Steps a to e are repeated β times [52].

#### 2.2.2. Benchmark Optimization Models

## 3. Results and Discussion

#### 3.1. Accuracy Indices

_{i predicted}and Z

_{i observed}stand for the forecasted and expected slumps, respectively.

#### 3.2. Improving ANN Using VSA, MVO, and SCE

#### 3.3. Efficiency Assessment

#### 3.4. Slump Predictive Model

_{SCE-MLP}= 0.5471 × U + 0.9176 × V + 0.7795 × W + 0.9107 × X + 0.7422 × Y + 0.4345 × Z − 0.2611

#### 3.5. Importance Analysis

#### 3.6. Further Comparison

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Correlation matrix of the dataset (points are data and purple lines show their trend and column charts are histogram).

**Figure 5.**Training errors obtained for (

**a**) LM-MLP, (

**b**) VSA-MLP, (

**c**) MVO-MLP, and (

**d**) SCE-MLP, respectively.

**Figure 6.**Results obtained for the testing samples by (

**a**,

**b**) LM-MLP, (

**c**,

**d**) VSA-MLP, (

**e**,

**f**) MVO-MLP, and (

**g**,

**h**) SCE-MLP.

Slump (cm) | Cement (kg/m^{3}) | Slag (kg/m^{3}) | Water (kg/m^{3}) | Fly Ash (kg/m^{3}) | SP (kg/m^{3}) | FA (kg/m^{3}) | CA (kg/m^{3}) | |
---|---|---|---|---|---|---|---|---|

Minimum | 0.0 | 137.0 | 0.0 | 160.0 | 0.0 | 4.4 | 640.6 | 708.0 |

Maximum | 29.0 | 374.0 | 260.0 | 240.0 | 193.0 | 19.0 | 902.0 | 1049.9 |

Mean | 18.0 | 229.9 | 149.0 | 197.2 | 78.0 | 8.5 | 739.6 | 884.0 |

Standard deviation | 8.7 | 78.9 | 85.4 | 20.2 | 60.5 | 2.8 | 63.3 | 88.4 |

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**MDPI and ACS Style**

Safayenikoo, H.; Khajehzadeh, M.; Nehdi, M.L.
Novel Evolutionary-Optimized Neural Network for Predicting Fresh Concrete Slump. *Sustainability* **2022**, *14*, 4934.
https://doi.org/10.3390/su14094934

**AMA Style**

Safayenikoo H, Khajehzadeh M, Nehdi ML.
Novel Evolutionary-Optimized Neural Network for Predicting Fresh Concrete Slump. *Sustainability*. 2022; 14(9):4934.
https://doi.org/10.3390/su14094934

**Chicago/Turabian Style**

Safayenikoo, Hamed, Mohammad Khajehzadeh, and Moncef L. Nehdi.
2022. "Novel Evolutionary-Optimized Neural Network for Predicting Fresh Concrete Slump" *Sustainability* 14, no. 9: 4934.
https://doi.org/10.3390/su14094934