# Estimation at Completion Simulation Using the Potential of Soft Computing Models: Case Study of Construction Engineering Projects

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## Abstract

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## 1. Introduction

- A new intelligence model called extreme learning machine was introduced to the model EAC.
- The predictability of the ELM model in computing EAC was validated against the traditional artificial neural network.
- The predictive ELM model was improved by input attribute optimization approaches called global harmony search and brute force for the identification of the factors that significantly affect project cost.
- Overall, the research explored a new modeling strategy based on the coupled intelligence model which can assist project managers in making decisions.

## 2. Materials and Methods

#### 2.1. Extreme Learning Machine (ELM) Model

#### 2.2. Artificial Neural Network (ANN) Model

#### 2.3. Global Harmony Search (GHS) Optimization Algorithm

#### 2.4. Brute Force Input Optimization Method

#### 2.5. Modeling Procedure Phase

## 3. Results and Discussions

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The proposed global harmony search-extreme learning machine GHS -ELM model for the prediction of the estimation at completion (EAC).

**Figure 3.**The correlation variance between the classical ELM and ANN predictive models over the testing phase.

**Figure 4.**The correlation variance between the hybrid GHS-ELM and GHS-ANN predictive models over the testing phase for all the investigated input combinations.

**Figure 5.**The correlation variance between the hybrid BF-ELM and BF-ANN predictive models over the testing phase for all the investigated input combinations.

**Figure 6.**The Taylor diagram presentations of the proposed hybrid predictive models and the comparable ones.

**Table 1.**The surveyed literature of artificial intelligence models’ implementation on cost projects over the last decade.

References | Research Remark |
---|---|

[25] | The study was conducted on the usage of the Artificial Neural Network (ANN) model to simulate project cost with the aim to improve the earned value management (EVM) system. The finding evidenced the applicability of the intelligent model to minimize the project cost overruns. |

[26] | An integration of support vector machine with fast messy genetic algorithm (SVM-FMGA) was performed for construction management monitoring. The validation of the model approved the estimation of the building cost over the conceptual cost estimation. |

[27] | The study inspected a conceptual cost estimation using the evolutionary fuzzy hybrid neural network for industrial project construction. The research outcomes exhibited another optimistic finding for a precise cost estimation at the early stages. |

[28] | An independent intelligent based on the weighted support vector machine model and fuzzy logic set was studied for EAC prediction. The fuzzy model was applied to solve the associated uncertainty in the tie series data. |

[29] | A fuzzy neural network was used to determine the EAC. The modeling was piloted based on various factors (both qualitative and quantitative) that influence the EAC value. The results demonstrated good outcomes from the contractors and managers aspects. |

[30] | The authors investigated a relatively new model based on the Bayesian theory integrated with the EVM framework aiming to compute the EAC. The proposed model evidenced its applicability and effectiveness on modeling the estimation at completion. |

[10] | The scholars developed a new cost EAC methodology by integrating the Cost Estimate at Completion (CEAC) method and four growth models and concluded that the EAC formula based on the Gompertz model outperforms the other indexed formulas. |

[31] | The support vector regression model was analyzed to perform the EVM. The authors concluded that their model outperformed the available best performing EVM methods through the training of the identical data set. |

[32] | An automotive programming approach based on the ANN model was proposed for estimating the EAC element of a dam construction project. The results demonstrated a remarkable performance for the investigated case study. |

Project Name | Total Area (m^{2}) | Underground Floors | Ground Floors | Buildings | Start Date | Finish Date | Duration (Days) | Contract Amount ($) | Prediction Periods |
---|---|---|---|---|---|---|---|---|---|

A | 11,254 | 1 | 1 | 3 | 2 March 2008 | 24 April 2009 | 418 | 7,445,825 | 13 |

B | 9326 | 1 | 1 | 1 | 15 August 2008 | 28 July 2009 | 347 | 6,329,548 | 14 |

C | 12,548 | 1 | 1 | 2 | 23 April 2003 | 28 February 2004 | 311 | 9,518,465 | 12 |

D | 9482 | 0 | 1 | 1 | 10 October 2009 | 3 November 2010 | 389 | 7,458,124 | 11 |

E | 10,554 | 2 | 1 | 2 | 5 June 2005 | 2 July 2006 | 392 | 8,452,847 | 12 |

F | 8751 | 1 | 1 | 2 | 5 July 2011 | 30 April 2012 | 300 | 6,895,348 | 14 |

G | 9458 | 0 | 1 | 1 | 13 August 2005 | 25 July 2006 | 346 | 7,518,452 | 13 |

H | 13,758 | 1 | 1 | 3 | 20 September 2004 | 15 October 2005 | 390 | 9,548,249 | 16 |

I | 11,249 | 1 | 1 | 3 | 20 April 2007 | 18 April 2008 | 364 | 8,628,945 | 13 |

J | 7851 | 0 | 1 | 1 | 24 December 2011 | 19 January 2013 | 392 | 5,936,461 | 14 |

Total | 132 | ||||||||

Training | 99 | ||||||||

Testing | 33 |

**Table 3.**The numerical evaluation indicators for the ELM and ANN predictive models “Based-models versions” over the testing modeling phase.

Predictive Models | RMSE | MAE | MRE | NSE | SI | BIAS | R |
---|---|---|---|---|---|---|---|

ELM | 0.1492 | 0.0766 | −0.1219 | 0.5782 | 0.8750 | 0.0413 | 0.8167 |

ANN | 0.2085 | 0.1036 | 0.4548 | 0.1764 | 1.2227 | 0.0359 | 0.5031 |

**Table 4.**The input combination attributes used to determine the value of the EAC using the GHS-ELM model.

The Number of Inputs | Models | The Type of Input Variables | Output |
---|---|---|---|

2 inputs | Model 1 | Cost variance (CV), schedule performance index (SPI) | EAC |

3 inputs | Model 2 | CV, schedule variance (SV), SPI | EAC |

4 inputs | Model 3 | CV, SV, SPI, Change order index | EAC |

5 inputs | Model 4 | CV, SV, cost performance index (CPI), SPI, owner billed index | EAC |

6 inputs | Model 5 | CV, SV, CPI, SPI, owner billed index, change order index | EAC |

7 inputs | Model 6 | CV, SV, CPI, SPI, subcontractor billed index, change order index, climate effect index | EAC |

8 inputs | Model 7 | CV, SV, CPI, SPI, subcontractor billed index, owner billed index, change order index, climate effect index | EAC |

**Table 5.**The numerical evaluation indicators for the GHS-ELM predictive model over the testing modeling phase (Bold is the best input combination).

Method | RMSE | MAE | MRE | NSE | SI | BIAS | R |
---|---|---|---|---|---|---|---|

Model 1 | 0.0904 | 0.0536 | −0.0778 | 0.8453 | 0.5299 | 0.0159 | 0.9303 |

Model 2 | 0.0806 | 0.0467 | −0.2834 | 0.8769 | 0.4727 | 0.0370 | 0.9607 |

Model 3 | 0.0973 | 0.0471 | −0.1069 | 0.8207 | 0.5706 | 0.0254 | 0.9216 |

Model 4 | 0.1089 | 0.0530 | −0.3081 | 0.7751 | 0.6389 | 0.0266 | 0.8880 |

Model 5 | 0.1293 | 0.0570 | −0.0220 | 0.6831 | 0.7584 | 0.0157 | 0.8313 |

Model 6 | 0.1499 | 0.0770 | 0.1256 | 0.5741 | 0.8793 | 0.0006 | 0.7633 |

Model 7 | 0.1573 | 0.0828 | 0.1407 | 0.5308 | 0.9229 | 0.0075 | 0.7296 |

**Table 6.**The input combination attributes used to determine the value of the EAC using the BF-ELM model.

The Number of Inputs | Models | The Type of Input Variables | Output |
---|---|---|---|

2 inputs | Model 1 | CV, SV | EAC |

3 inputs | Model 2 | CV, SV, CPI | EAC |

4 inputs | Model 3 | CV, SV, CPI, SPI | EAC |

5 inputs | Model 4 | CV, SV, CPI, SPI, subcontractor billed index | EAC |

6 inputs | Model 5 | CV, SV, CPI, SPI, subcontractor billed index, owner billed index | EAC |

7 inputs | Model 6 | CV, SV, CPI, SPI, subcontractor billed index, owner billed index, Change order index | EAC |

8 inputs | Model 7 | CV, SV, CPI, SPI, subcontractor billed index, owner billed index, change order index, construction price fluctuation (CCI) | EAC |

**Table 7.**The numerical evaluation indicators for the BF-ELM predictive model over the testing modeling phase (Bold is the best input combination).

Models | RMSE | MAE | MRE | NSE | SI | BIAS | R |
---|---|---|---|---|---|---|---|

Model 1 | 0.0435 | 0.0305 | −0.2475 | 0.9642 | 0.2551 | 0.0218 | 0.9887 |

Model 2 | 0.0874 | 0.0482 | −0.2860 | 0.8554 | 0.5123 | 0.0378 | 0.9552 |

Model 3 | 0.0854 | 0.0448 | −0.1389 | 0.8617 | 0.5010 | 0.0304 | 0.9482 |

Model 4 | 0.1037 | 0.0502 | −0.0715 | 0.7963 | 0.6081 | 0.0163 | 0.9079 |

Model 5 | 0.1186 | 0.0683 | 0.0946 | 0.7333 | 0.6958 | 0.0103 | 0.8624 |

Model 6 | 0.1447 | 0.0776 | 0.2167 | 0.6034 | 0.8485 | 0.0075 | 0.7809 |

Model 7 | 0.1487 | 0.0714 | 0.4096 | 0.5812 | 0.8719 | −0.0093 | 0.7733 |

**Table 8.**The input combination attributes used to determine the value of the EAC using the GHS-ANN model.

The Number of Inputs | Models | The Type of Input Variables | Output |
---|---|---|---|

2 inputs | Model 1 | CPI, CCI | EAC |

3 inputs | Model 2 | CV, SPI, change order index | EAC |

4 inputs | Model 3 | CV, CPI, SPI, CCI | EAC |

5 inputs | Model 4 | CV, CPI, SPI, subcontractor billed index, CCI | EAC |

6 inputs | Model 5 | CV, SV, CPI, SPI, subcontractor billed index, climate effect index | EAC |

7 inputs | Model 6 | CV, SV, CPI, SPI, subcontractor billed index, owner billed index, climate effect index | EAC |

8 inputs | Model 7 | CV, SV, CPI, SPI, subcontractor billed index, owner billed index, change order index, CCI | EAC |

**Table 9.**The numerical evaluation indicators for the GHS-ANN predictive model over the testing modeling phase (Bold is the best input combination).

Method | RMSE | MAE | MRE | NSE | SI | BIAS | R |
---|---|---|---|---|---|---|---|

Model 1 | 0.1219 | 0.0472 | 0.0030 | 0.7183 | 0.7151 | 0.0154 | 0.8521 |

Model 2 | 0.1180 | 0.0465 | −0.0948 | 0.7361 | 0.6921 | 0.0270 | 0.8919 |

Model 3 | 0.1014 | 0.0359 | −0.0153 | 0.8052 | 0.5946 | 0.0143 | 0.9052 |

Model 4 | 0.1380 | 0.0601 | −0.3018 | 0.6392 | 0.8093 | 0.0462 | 0.8509 |

Model 5 | 0.1350 | 0.0711 | 0.3339 | 0.6548 | 0.7916 | 0.0030 | 0.8106 |

Model 6 | 0.1831 | 0.0843 | 0.3776 | 0.3645 | 1.0740 | 0.0293 | 0.6746 |

Model 7 | 0.1656 | 0.0994 | 0.6472 | 0.4803 | 0.9713 | −0.0237 | 0.7140 |

**Table 10.**The input combination attributes used to determine the value of the EAC using the BF-ANN model.

The Number of Inputs | Models | The Type of Input Variables | Output |
---|---|---|---|

2 inputs | Model 1 | SV, CV | EAC |

3 inputs | Model 2 | CV, SV, CPI | EAC |

4 inputs | Model 3 | CV, SV, CPI, SPI | EAC |

5 inputs | Model 4 | CV, SV, CPI, SPI | EAC |

6 inputs | Model 5 | CV, SV, CPI, SPI, subcontractor billed index, owner billed index | EAC |

7 inputs | Model 6 | CV, SV, CPI, SPI, subcontractor billed index, owner billed index, change order index | EAC |

8 inputs | Model 7 | CV, SV, CPI, SPI, subcontractor billed index, owner billed index, change order index, CCI | EAC |

**Table 11.**The numerical evaluation indicators for the BF-ANN predictive model over the testing modeling phase (Bold is the best input combination).

Method | RMSE | MAE | MRE | NSE | SI | BIAS | R |
---|---|---|---|---|---|---|---|

Model 1 | 0.1114 | 0.0353 | −0.0967 | 0.7646 | 0.6537 | 0.0291 | 0.9024 |

Model 2 | 0.0983 | 0.0318 | −0.0125 | 0.8171 | 0.5763 | 0.0206 | 0.9277 |

Model 3 | 0.1045 | 0.0468 | 0.0462 | 0.7931 | 0.6129 | −0.0042 | 0.8910 |

Model 4 | 0.1198 | 0.0610 | 0.0418 | 0.7279 | 0.7028 | −0.0029 | 0.8585 |

Model 5 | 0.1343 | 0.0711 | 0.3784 | 0.6583 | 0.7876 | −0.0201 | 0.8215 |

Model 6 | 0.1526 | 0.0888 | 0.7292 | 0.5589 | 0.8948 | −0.0265 | 0.7634 |

Model 7 | 0.1656 | 0.0994 | 0.6472 | 0.4803 | 0.9713 | −0.0237 | 0.7140 |

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**MDPI and ACS Style**

AlHares, E.F.T.; Budayan, C.
Estimation at Completion Simulation Using the Potential of Soft Computing Models: Case Study of Construction Engineering Projects. *Symmetry* **2019**, *11*, 190.
https://doi.org/10.3390/sym11020190

**AMA Style**

AlHares EFT, Budayan C.
Estimation at Completion Simulation Using the Potential of Soft Computing Models: Case Study of Construction Engineering Projects. *Symmetry*. 2019; 11(2):190.
https://doi.org/10.3390/sym11020190

**Chicago/Turabian Style**

AlHares, Enas Fathi Taher, and Cenk Budayan.
2019. "Estimation at Completion Simulation Using the Potential of Soft Computing Models: Case Study of Construction Engineering Projects" *Symmetry* 11, no. 2: 190.
https://doi.org/10.3390/sym11020190