# BIM-Based Resource Tradeoff in Project Scheduling Using Fire Hawk Optimizer (FHO)

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## Abstract

**:**

_{2}in the project under consideration, an optimization problem is created, and the FHO’s capability for solving it is assessed. The results show that the FHO algorithm is capable of producing competitive and exceptional outcomes when it comes to the trade-off of various resource options in projects.

## 1. Introduction

_{2}) than any other kind of industrial production [8]. Delivering a project in the intended time, at the desired cost, with the appropriate quality, and with the least amount of risk or uncertainty is an essential success factor for project assessment. However, environmental issues have received a lot of attention lately [9].

## 2. Literature Review

#### 2.1. Studies of Resource Trade-Offs

_{2}emission, and resource utilization. Ozcan-Deniz et al. [37] evaluated environmental effect by considering total greenhouse gas emissions connected with a project and used NSGA-II to tradeoff time, cost, and environmental impact. Tran et al. [38] created the opposition multiple objective symbiotic organisms search strategy, which could be useful way to address challenges including trade-offs between time, cost, quality, and task continuity. Luong et al. [39] solved the TCQT problem using the opposition-based multiple objective differential evolution (OMODE) algorithm, which uses an opposition-based learning method for early population onset and generational jump. However, scant research has been carried out concerning time-cost-quality-risk trade-off problems. Mohammadipour and Sadjadi [40] considered risk in the TCQ trade-off. The authors provided proper linear programming to minimize the total additional cost of the project, the overall risk of the project, as well as the overall quality reduction in the project. Amoozad Mahdiraji et al. [41] proposed a new technique for identifying the best implementation situation for each activity in a project by optimizing and balancing time, cost, quality, and risk. Tran and Long [3] proposed a multi-objective project scheduling optimization model using the DE method. By leveraging the existing data and resources, the authors stated that the suggested model could help project managers and decision-makers finish the project on schedule and with less risk. Sharma and Trivedi [42] presented a multimode resource-constrained time–cost–quality–safety trade-off optimization model using the NSGA-III algorithm. Keshavarz and Shoul [43] formulated a three-objective programming problem associated with the time–cost–quality trade-off problem using a fuzzy decision-making methodology.

#### 2.2. Applications of Building Information Modelling

_{2}tradeoff in construction projects.

_{2}trade-off (TCQRCT) issue in a real building project based on the Building Information Modeling (BIM) procedure. The required number of objective function evaluations, the mean, the worst, and the standard deviation are all determined statistically via the use of 30 separate optimization runs. Based on a maximum of 5000 objective function evaluations, a predetermined stopping condition is also taken into consideration. However, being parameter-free, fast convergence behaviour and the lowest possible objective function evaluation could be deemed the privileges of the FHO algorithm. On the other hand, the FHO method, like other metaheuristic algorithms, can only approximate problems; it cannot supply accurate answers.

Authors | Time | Cost | Quality | Risk | CO_{2} | Other Parameters | BIM |
---|---|---|---|---|---|---|---|

Hajiagha et al. [59] | $\times $ | $\times $ | $\times $ | ||||

Tran and Long [3] | $\times $ | $\times $ | $\times $ | ||||

Zheng [60] | $\times $ | $\times $ | $\times $ | $\times $ | |||

Al Haj and El-Sayegh [61] | $\times $ | $\times $ | |||||

Khalili-Damghani et al. [62] | $\times $ | $\times $ | $\times $ | ||||

Moghadam et al. [63] | $\times $ | $\times $ | $\times $ | ||||

Zahraie and Tavakolan [64] | $\times $ | $\times $ | $\times $ | ||||

Huynh et al. [65] | $\times $ | $\times $ | $\times $ | $\times $ | |||

Banihashemi and Khalilzadeh [66] | $\times $ | $\times $ | $\times $ | $\times $ | |||

Ghoddousi et al. [67] | $\times $ | $\times $ | $\times $ | ||||

Mahmoudi and Feylizadeh [68] | $\times $ | $\times $ | $\times $ | $\times $ | $\times $ | ||

Ebrahimnezhad et al. [69] | $\times $ | $\times $ | $\times $ | ||||

Mungle et al. [70] | $\times $ | $\times $ | $\times $ | ||||

Koo et al. [71] | $\times $ | $\times $ | |||||

Heravi and Moridi [72] | $\times $ | $\times $ | |||||

Mohammadipour and Sadjadi [40] | $\times $ | $\times $ | $\times $ | ||||

Jeunet and Bou Orm [73] | $\times $ | $\times $ | $\times $ | $\times $ | |||

Hamta et al. [74] | $\times $ | $\times $ | $\times $ | ||||

Kosztyán and Szalkai [75] | $\times $ | $\times $ | $\times $ | ||||

Current Study | $\times $ | $\times $ | $\times $ | $\times $ | $\times $ | $\times $ |

## 3. Framework for Resource Tradeoff

#### 3.1. Initialization and Decision Variables

_{i}), which is given by Equation (6) [78].

_{2}. CO

_{2}emissions can occur in two ways during the on-site construction process: directly from electricity consumption and fuel combustion, and indirectly from the manufacturing of building materials and their transportation. CO

_{2}emissions can be reduced by not only selecting environmentally friendly materials, but also by ensuring that materials are transported in the shortest possible manner. Thus, the objective function to minimize the total amount of CO

_{2}in the project can be calculated by Equation (9).

_{2}emission in the project; ${\mathrm{E}}_{\mathrm{dij}}$ and ${\mathrm{E}}_{\mathrm{inij}}$ are the direct and indirect CO

_{2}emissions in the project, respectively; ${\mathrm{Q}}_{\mathrm{ed}}$ shows an activity’s electricity consumption; ${\mathrm{Q}}_{\mathrm{dd}}$ elucidates an activity’s diesel consumption; ${\mathrm{Q}}_{\mathrm{ij}}\text{}$ shows the consumption of material k in an activity; ${\text{}\mathrm{Q}}_{\mathrm{ek}}$ indicates the electricity consumption for the transportation of material k for an activity; ${\mathrm{Q}}_{\mathrm{dk}}$ shows the diesel consumption for the transportation of material k for an activity; ${\mathrm{F}}_{\mathrm{e}}$, ${\mathrm{F}}_{\mathrm{d}}$, and ${\mathrm{F}}_{\mathrm{j}}$ are the carbon emission factor (CEF) per electricity unit, diesel unit consumption, and per unit production of material k, respectively. Concerning the project’s risk, the actual project risk is mostly determined by the project’s circumstances, delivery systems, and contract terms. A “risk value” is described as a function that combines the two components: (i) the project’s overall float, and (ii) resource volatility. When noncritical operations have a high degree of temporal uncertainty, the usage of float may result in increased project risk and schedule overruns. Thus, construction managers are required to execute schedule adjustments to minimize unplanned changes in resource use throughout the duration of the project’s execution. Allowing noncritical operations to float may result in more effective resource use [79,80,81]. Consequently, the fifth objective function for risk can be formulated as Equation (10):

_{i}represents the weights.

_{2}(All) trade-off, simultaneously, Equation (11) is used:

#### 3.2. BIM Module

^{2}that is used to validate the FHO algorithm with five objectives: time, cost, quality, risk, and CO

_{2}emissions. As shown in Table A1, all activity information is elicited by the BIM process, project data, and experts’ judgments in the planning and designing steps. In other words, in completing this table, the experiences of various elite people and experts in this field have been used. The time and cost of executive mode NO.1 are the actual time and cost of the project extracted from the final status of the construction, NO.3 are obtained from BIM, and NO.5 are the contractor’s initial offers. In addition, two other executive modes were considered based on expert opinions in this field. Admittedly, contractors’ initial offers are often illogical and dreamy to attract the attention of employers, which is why most projects fail. Because most contractors do not consider rework, clashes, non-payment by employers, severe weather conditions, etc.; however, each activity is randomly written with three types of quality indicators at distinct percentages. The final quality in each line is obtained from the percentage of the total effects of those three quality modes. Finally, for each activity, the risk percentage is randomly deemed based on the viewpoints of elite professors and experts in this field.

#### 3.3. Fire Hawk Optimizer (FHO)

#### 3.3.1. Inspiration

#### 3.3.2. Mathematical Model

## 4. Optimization Results

_{2}in the case study, thereby realizing environmentally friendly construction. In contrast, the PSO algorithm provided the highest value for CO

_{2}in this scenario, indicating its unfavorable performance in achieving the project with the lowest carbon footprint. However, the SOS algorithm gave the lowest computational time, registered at 1.38 (s), followed by TLBO. As a result, considering the average computational time, the FHO algorithm could be considered an appropriate alternative to optimize the amount of carbon dioxide in construction projects.

## 5. Discussion

_{2}.

_{2}and the All optimizations, the third mode is superior to the others. Meanwhile, it should be noted that the 4th and 5th modes were not preferred by any algorithms for any of the problems in the current case.

_{2}emission caused by the logistics and equipment at the project’s site. Furthermore, project managers and schedulers of all projects are able to analyze and propose the most feasible resource options, considering the organization’s goals and scopes, to the employers or owners by using the BIM process and an optimization process with metaheuristic algorithms, such as the FHO algorithm.

## 6. Conclusions

- Based on the outcomes of best optimization runs conducted by different methods in dealing with time optimization, the FHO algorithm could reach the lowest time for the case study, accounting for 258 days.
- The FHO can provide 116,783 ($) for the cost of the case study, which is the best among all approaches.
- Regarding quality optimization, the FHO is capable of providing reasonable quality value, but the SOS algorithm gave the best results.
- The FHO algorithm is able to provide the best results for both risk and CO
_{2}optimization in the case study, compared to other alternative algorithms. - Based on the best results of the TCQRCT problem, the FHO algorithm can provide a score of 0.74, which is much better than the other algorithms.

_{2}in a two-by-two manner.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

NO | Activity | Logical | Mode 1 | Mode 2 | Mode 3 | Mode 4 | Mode 5 | ||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Time | Cost $ | Quality % | Risk | CO_{2} | Time | Cost $ | Quality % | Risk | CO_{2} | Time | Cost $ | Quality % | Risk | CO_{2} | Time | Cost $ | Quality % | Risk | CO_{2} | Time | Cost $ | Quality % | Risk | CO_{2} | |||

1 | Foundation | - | 26 | 8100 | 90.65 | 14.96667 | 225.3313 | 24 | 7850 | 89.2 | 12 | 198.45 | 20 | 8120 | 92.1 | 12.5 | 187.52 | 15 | 8400 | 78.9 | 12.9 | 98.32 | 13 | 9408 | 74.955 | 16.31367 | 108.152 |

2 | Retaining wall | 1FS + 1 | 15 | 2252 | 94.905 | 13.21667 | 137.9707 | 13 | 2150 | 94.51 | 10.5 | 125.08 | 11 | 2220 | 95.3 | 11.3 | 111.04 | 9 | 2410 | 87.1 | 11.54 | 54.25 | 8 | 2699.2 | 82.745 | 14.40617 | 59.675 |

3 | Columns of ground | 2FS | 13 | 2015 | 91.155 | 10.33333 | 116.3133 | 10 | 1980 | 90.21 | 8 | 101.3 | 7 | 2042 | 92.1 | 9.4 | 98 | 6 | 2100 | 85.45 | 9.5 | 36.32 | 5 | 2352 | 81.1775 | 11.26333 | 39.952 |

4 | Beam and roof of ground | 3FS + 1 | 10 | 4325 | 91.98 | 11.95167 | 188.2833 | 8 | 3652 | 91.4 | 9.65 | 169.91 | 6 | 3920 | 92.56 | 9.8 | 152.36 | 4 | 4150 | 86.41 | 10.3 | 111.25 | 3 | 4648 | 82.0895 | 13.02732 | 122.375 |

5 | Columns of 1st floor | 4FS + 2 | 13 | 1550 | 93.605 | 5.58 | 190.8767 | 10 | 1200 | 92.65 | 4.2 | 178.35 | 7 | 1356 | 94.56 | 5.4 | 148 | 6 | 1420 | 89.36 | 6 | 128.6 | 5 | 1590.4 | 84.892 | 6.0822 | 141.46 |

6 | Beam and roof of 1st floor | 5FS + 1 | 10 | 3600 | 95.625 | 12.82 | 177.7653 | 8 | 3200 | 94.8 | 10.3 | 177.88 | 6 | 3410 | 96.45 | 10.65 | 125.36 | 4 | 3540 | 85.45 | 11.02 | 45.25 | 3 | 3964.8 | 81.1775 | 13.9738 | 49.775 |

7 | Columns of 2nd floor | 6FS + 2 | 13 | 1550 | 92.04 | 8.038 | 158.5137 | 10 | 1200 | 91.3 | 6.32 | 143.65 | 7 | 1356 | 92.78 | 7.05 | 127.63 | 6 | 1420 | 84.12 | 7.8 | 35.98 | 5 | 1590.4 | 79.914 | 8.76142 | 39.578 |

8 | Beam and roof of 2nd floor | 7FS + 1 | 10 | 3600 | 97.575 | 9.275 | 183.8583 | 8 | 3200 | 96.5 | 7.25 | 169.25 | 6 | 3410 | 98.65 | 8.25 | 145.25 | 4 | 3540 | 88.89 | 8.5 | 89.54 | 3 | 3964.8 | 84.4455 | 10.10975 | 98.494 |

9 | Columns of 3rd floor | 8FS + 2 | 13 | 1550 | 93.99 | 6.903333 | 150.1917 | 10 | 1200 | 93.4 | 5.3 | 145.25 | 7 | 1356 | 94.58 | 6.4 | 111.25 | 6 | 1420 | 78.45 | 6.45 | 74.63 | 5 | 1590.4 | 74.5275 | 7.524633 | 82.093 |

10 | Beam and roof of 3rd floor | 9FS + 1 | 10 | 3600 | 91.475 | 3.541667 | 167.4697 | 8 | 3200 | 90.5 | 2.65 | 151.72 | 6 | 3410 | 92.45 | 3.47 | 134.89 | 4 | 3540 | 82.1 | 3.9 | 125.25 | 3 | 3964.8 | 77.995 | 3.860417 | 137.775 |

11 | Columns of 4th floor | 10FS + 2 | 13 | 1550 | 92.825 | 6.316667 | 114.523 | 10 | 1200 | 91.4 | 4.5 | 106.58 | 7 | 1356 | 94.25 | 6.8 | 89.25 | 6 | 1420 | 86.45 | 7 | 65.32 | 5 | 1590.4 | 82.1275 | 6.885167 | 71.852 |

12 | Beam and roof of 4th floor | 11FS + 1 | 10 | 3600 | 96.375 | 15.29833 | 156.7313 | 8 | 3200 | 95.3 | 11.85 | 143.56 | 6 | 3410 | 97.45 | 13.9 | 124.58 | 4 | 3540 | 91.2 | 14.2 | 43.56 | 3 | 3964.8 | 86.64 | 16.67518 | 47.916 |

13 | Columns of 5th floor | 12FS + 2 | 13 | 1550 | 95.315 | 11.845 | 163.6473 | 10 | 1200 | 94.62 | 9.45 | 144.32 | 7 | 1356 | 96.01 | 10.02 | 135.98 | 6 | 1420 | 86.41 | 11.3 | 97.2 | 5 | 1590.4 | 82.0895 | 12.91105 | 106.92 |

14 | Beam and roof of 5th floor | 13FS + 1 | 10 | 3600 | 98.57 | 4.689 | 139.1107 | 8 | 3200 | 97.4 | 3.21 | 126.98 | 6 | 3410 | 99.74 | 5.4 | 111.04 | 4 | 3540 | 91.02 | 5.52 | 56.98 | 3 | 3964.8 | 86.469 | 5.11101 | 62.678 |

15 | Columns of ridge roof | 14FS + 1 | 5 | 420 | 91.815 | 5.851667 | 124.31 | 3 | 356 | 91.6 | 4.25 | 114.25 | 2 | 411 | 92.03 | 6.08 | 98.4 | 1 | 580 | 83.25 | 6.85 | 75.98 | 1 | 649.6 | 79.0875 | 6.378317 | 83.578 |

16 | Beam and roof of ridge floor | 15FS + 1 | 6 | 1110 | 92.96 | 3.342333 | 168.6317 | 4 | 980 | 92.45 | 2.51 | 156.32 | 3 | 995 | 93.47 | 3.25 | 132.07 | 2 | 1020 | 87.98 | 3.65 | 100.36 | 2 | 1142.4 | 83.581 | 3.643143 | 110.396 |

17 | Brickworks of ground | 4FS + 1 | 14 | 1620 | 94.035 | 1.658333 | 166.89 | 11 | 1480 | 93 | 1.05 | 157.45 | 9 | 1620 | 95.07 | 2.14 | 127.8 | 8 | 1740 | 79.99 | 2.45 | 98.65 | 7 | 1948.8 | 75.9905 | 1.807583 | 108.515 |

18 | Mechanical installations of ground | 17FS + 2 | 10 | 1300 | 95.355 | 8.316667 | 109.0827 | 8 | 1220 | 94.5 | 6.5 | 101.98 | 6 | 1352 | 96.21 | 7.4 | 84.52 | 4 | 1480 | 82.14 | 7.65 | 24.65 | 3 | 1657.6 | 78.033 | 9.065167 | 27.115 |

19 | Electrical installations of ground | 17FS + 2 | 15 | 1250 | 95.54 | 6.08 | 128.7647 | 13 | 1100 | 95.3 | 4.9 | 121.07 | 9 | 1260 | 95.78 | 5.01 | 99.04 | 6 | 1350 | 89.65 | 5.63 | 68.42 | 5 | 1512 | 85.1675 | 6.6272 | 75.262 |

20 | Brickworks of 1st floor | 6FS + 1 | 14 | 1800 | 92.21 | 5.149333 | 125.9527 | 11 | 1620 | 90.7 | 3.54 | 114.06 | 9 | 1870 | 93.72 | 5.89 | 101.5 | 8 | 1942 | 80.45 | 6 | 45.65 | 7 | 2175.04 | 76.4275 | 5.612773 | 50.215 |

21 | Mechanical installations of 1st floor | 20FS + 2 | 10 | 1600 | 97.525 | 5.934667 | 130.917 | 8 | 1520 | 97 | 4.22 | 125.97 | 6 | 1710 | 98.05 | 6.41 | 97.65 | 4 | 1780 | 91.45 | 6.54 | 82.63 | 3 | 1993.6 | 86.8775 | 6.468787 | 90.893 |

22 | Electrical installations of 1st floor | 20FS + 2 | 9 | 1420 | 97.65 | 3.786333 | 167.2277 | 7 | 1350 | 96.4 | 2.87 | 151.26 | 5 | 1420 | 98.9 | 3.61 | 134.95 | 4 | 1500 | 87.26 | 3.75 | 111.52 | 3 | 1680 | 82.897 | 4.127103 | 122.672 |

23 | Brickworks of 2nd floor | 8FS + 1 | 14 | 1800 | 93.495 | 5.546667 | 193.3917 | 11 | 1620 | 92.3 | 4.2 | 178.32 | 9 | 1870 | 94.69 | 5.3 | 152.47 | 8 | 1942 | 83.45 | 5.5 | 97.52 | 7 | 2175.04 | 79.2775 | 6.045867 | 107.272 |

24 | Mechanical installations of 2nd floor | 23FS + 2 | 10 | 1680 | 94.93 | 12.066 | 138.6687 | 8 | 1532 | 94.15 | 9.34 | 126.47 | 6 | 1750 | 95.71 | 10.98 | 110.8 | 4 | 1780 | 88.98 | 11.36 | 64.52 | 3 | 1993.6 | 84.531 | 13.15194 | 70.972 |

25 | Electrical installations of 2nd floor | 23FS + 2 | 9 | 1420 | 92.55 | 10.74167 | 181.7427 | 7 | 1350 | 90.47 | 8.45 | 175.65 | 5 | 1420 | 94.63 | 9.41 | 134.74 | 4 | 1500 | 78.32 | 9.5 | 86.52 | 3 | 1680 | 74.404 | 11.70842 | 95.172 |

26 | Brickworks of 3rd floor | 10FS + 1 | 14 | 1800 | 94.16 | 2.455 | 165.5457 | 11 | 1620 | 93.32 | 1.65 | 149.08 | 9 | 1870 | 95 | 2.91 | 134.29 | 8 | 1942 | 85.65 | 3.2 | 98.42 | 7 | 2175.04 | 81.3675 | 2.67595 | 108.262 |

27 | Mechanical installations of 3rd floor | 26FS + 2 | 10 | 1680 | 91.82 | 2.866 | 178.6877 | 8 | 1530 | 91.24 | 2.04 | 170.36 | 6 | 1740 | 92.4 | 3.09 | 134.95 | 4 | 1780 | 86.97 | 5.2 | 74.77 | 3 | 1993.6 | 82.6215 | 3.12394 | 82.247 |

28 | Electrical installations of 3rd floor | 26FS + 2 | 9 | 1420 | 90.435 | 8.185 | 159.032 | 7 | 1350 | 90 | 6.45 | 156.65 | 1420 | 90.87 | 7.14 | 114.78 | 4 | 1500 | 82.42 | 7.65 | 64.52 | 3 | 1680 | 78.299 | 8.92165 | 70.972 | |

29 | Brickworks of 4th floor | 12FS + 1 | 14 | 1800 | 96.155 | 12.95467 | 159.094 | 11 | 1620 | 94.98 | 10.32 | 142.36 | 9 | 1870 | 97.33 | 11 | 130.02 | 8 | 1942 | 86.41 | 11.4 | 111.78 | 7 | 2175.04 | 82.0895 | 14.12059 | 122.958 |

30 | Mechanical installations of 4th floor | 29FS + 2 | 10 | 1695 | 93.375 | 8.26 | 163.8757 | 8 | 1570 | 92.63 | 6.4 | 153.21 | 6 | 1760 | 94.12 | 7.5 | 126.97 | 4 | 1780 | 86.35 | 7.7 | 42.63 | 3 | 1993.6 | 82.0325 | 9.0034 | 46.893 |

31 | Electrical installations of 4th floor | 29FS + 2 | 9 | 1420 | 94.63 | 6.648667 | 158.8867 | 7 | 1350 | 94.17 | 4.98 | 147.36 | 5 | 1420 | 95.09 | 6.5 | 124.36 | 4 | 1500 | 87.42 | 6.52 | 35.59 | 3 | 1680 | 83.049 | 7.247047 | 39.149 |

32 | Brickworks of 5th floor | 14FS + 1 | 14 | 1800 | 93.02 | 4.885 | 128.853 | 11 | 1620 | 92.83 | 3.45 | 120.32 | 9 | 1870 | 93.21 | 5.34 | 99.99 | 8 | 1942 | 88.2 | 5.98 | 65.42 | 7 | 2175.04 | 83.79 | 5.32465 | 71.962 |

33 | Mechanical installations of 5th floor | 32FS + 2 | 10 | 1680 | 94.025 | 3.137667 | 124.2857 | 8 | 1530 | 93.4 | 2.09 | 111.14 | 6 | 1740 | 94.65 | 3.77 | 101.65 | 4 | 1780 | 85.72 | 3.89 | 85.41 | 3 | 1993.6 | 81.434 | 3.420057 | 93.951 |

34 | Electrical installations of 5th floor | 32FS + 2 | 9 | 1420 | 95.065 | 2.351333 | 213.33 | 7 | 1350 | 94.42 | 1.52 | 199.32 | 5 | 1420 | 95.71 | 2.95 | 165.42 | 4 | 1500 | 90.45 | 3.02 | 123.65 | 3 | 1680 | 85.9275 | 2.562953 | 136.015 |

35 | Rooftop | 34FS | 15 | 935 | 93.62 | 8.639667 | 188.6087 | 10 | 870 | 92.41 | 6.47 | 178.65 | 7 | 890 | 94.83 | 8.45 | 143.68 | 5 | 920 | 80.65 | 9.2 | 99.98 | 4 | 1030.4 | 76.6175 | 9.417237 | 109.978 |

36 | Elevator | 34FS + 2 | 17 | 2400 | 90.805 | 7.126 | 105.351 | 15 | 2150 | 90.56 | 5.24 | 100.36 | 11 | 2350 | 91.05 | 7.23 | 79.65 | 8 | 2680 | 82.42 | 7.77 | 24.63 | 7 | 3001.6 | 78.299 | 7.76734 | 27.093 |

37 | Facade | 34FS + 5 | 55 | 5320 | 91.575 | 4.351333 | 194.41 | 52 | 4580 | 91.15 | 3.12 | 189.32 | 37 | 5120 | 92 | 4.63 | 142.62 | 29 | 5980 | 79 | 4.97 | 75.63 | 25 | 6697.6 | 75.05 | 4.742953 | 83.193 |

38 | Outdoors | 35FS + 1 | 37 | 2420 | 92.63 | 11.958 | 143.945 | 32 | 2100 | 91.78 | 9.12 | 134.65 | 25 | 2850 | 93.48 | 11.25 | 111.45 | 19 | 3412 | 84.53 | 11.32 | 80.25 | 16 | 3821.44 | 80.3035 | 13.03422 | 88.275 |

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**Figure 4.**Convergence history of 30 independent optimization runs of FHO and alternative algorithms.

FA | MVO | PSO | SOS | TLBO | FHO (Current Study) | |
---|---|---|---|---|---|---|

Time | 261 | 258 | 321 | 258 | 281 | 258 |

Cost | 118,230 | 117,056 | 119,564.8 | 117,104.6 | 117,512 | 116,783 |

Quality | 94.35 | 94.16 | 93.82 | 94.41 | 93.89 | 87.81 |

Risk | 5.78 | 5.94 | 6.53 | 5.78 | 5.93 | 5.78 |

CO_{2} | 76.35 | 76.74 | 103.35 | 76.35 | 79.60 | 76.35 |

All | 0.74 | 0.76 | 0.99 | 0.74 | 0.77 | 0.74 |

FA | MVO | PSO | SOS | TLBO | FHO (Current Study) | |
---|---|---|---|---|---|---|

Time | ||||||

Best | 261 | 258 | 321 | 258 | 281 | 258 |

Mean | 261 | 258.9 | 392.7 | 260.76 | 300.6 | 258.03 |

Worst | 261 | 261 | 453 | 266 | 316 | 259 |

Std | 0 | 1.21 | 35.07 | 1.71 | 9.04 | 0.18 |

Computational time (s) | 2.19 | 1.61 | 2.35 | 1.40 | 1.44 | 8.66 |

Cost | ||||||

Best | 118,230 | 117,056 | 119,564.8 | 117,104.6 | 117,512 | 116,783 |

Mean | 118,558.6 | 117,511.9 | 135,480.6 | 117,498.3 | 118,322.9 | 116,839.7 |

Worst | 118,780 | 118,284.6 | 155,151.7 | 117,920 | 119,070 | 117,011 |

Std | 148.09 | 271.58 | 9952.33 | 222.75 | 397.19 | 59.57 |

Computational time (s) | 2.16 | 1.57 | 2.13 | 1.39 | 1.44 | 9.66 |

Quality | ||||||

Best | 94.35 | 94.16 | 93.82 | 94.41 | 93.89 | 87.81 |

Mean | 94.46 | 94.24 | 93.89 | 94.54 | 94.01 | 89.63 |

Worst | 94.56 | 94.40 | 94.12 | 94.62 | 94.27 | 91.46 |

Std | 0.04 | 0.05 | 0.06 | 0.04 | 0.08 | 0.78 |

Computational time (s) | 9.05 | 1.44 | 2.11 | 1.40 | 1.44 | 2.03 |

Risk | ||||||

Best | 5.78 | 5.94 | 6.53 | 5.78 | 5.93 | 5.78 |

Mean | 5.78 | 6.07 | 7.13 | 5.79 | 6.03 | 5.78 |

Worst | 5.78 | 6.28 | 7.46 | 5.82 | 6.20 | 5.78 |

Std | 9.03 × 10^{−16} | 8.45 × 10^{−02} | 2.47 × 10^{−1} | 0.01 | 6.99 × 10^{−2} | 9.03 × 10^{−16} |

Computational time (s) | 2.27 | 1.56 | 2.05 | 1.39 | 1.43 | 8.67 |

CO_{2} | ||||||

Best | 76.35 | 76.44 | 103.35 | 76.35 | 79.60 | 76.35 |

Mean | 76.35 | 77.87 | 116.23 | 76.68 | 88.24 | 76.40 |

Worst | 76.35 | 80.41 | 129.54 | 77.20 | 94.47 | 76.59 |

Std | 1.45 × 10^{−14} | 0.92 | 6.20 | 0.24 | 4.19 | 0.06 |

Computational time (s) | 1.93 | 1.59 | 2.29 | 1.38 | 1.42 | 12.52 |

All | ||||||

Best | 0.74 | 0.76 | 0.99 | 0.74 | 0.77 | 0.74 |

Mean | 0.74 | 0.84 | 1.42 | 0.75 | 0.86 | 0.74 |

Worst | 0.74 | 0.95 | 1.67 | 0.78 | 0.94 | 0.74 |

Std | 2.26 × 10^{−16} | 0.04 | 0.21 | 0.01 | 0.04 | 2.26 × 10^{−16} |

Computational time (s) | 1.98 | 1.70 | 2.42 | 1.38 | 1.43 | 10.96 |

Number | Objective | Mode of Activities |
---|---|---|

1 | Time | FA:55555555555555555555555555555555555555 |

MVO:55555555555555555555555555535555555555 | ||

PSO:54435325555255525554445513453113245445 | ||

SOS:55555555555555555555555555535555555555 | ||

TLBO:55555555451455444555452455535554533555 | ||

FHO:55555555555555555555555555535555555555 | ||

2 | Cost | FA:43334343343242333433343332332343434342 |

MVO:44423244423333243443442432432432444332 | ||

PSO:23323225253434543344542434433424342234 | ||

SOS:43423432334442343442432533432432434332 | ||

TLBO:43444442424243244342432443234444244332 | ||

FHO:43424442444242343442432442432442434332 | ||

3 | Quality | FA:33331133333111131131333333331331133311 |

MVO:13331131311313331331131111333133113311 | ||

PSO:11111111111111111111111111111111111111 | ||

SOS:13113333131333313313113333313313313133 | ||

TLBO:11311111111111111111111113311111111111 | ||

FHO:15344214411545354222554535254442254422 | ||

4 | Risk | FA:22222222222222222222222222222222222222 |

MVO:22222222222225525232222222222222252222 | ||

PSO:22334322222225253225425431323232412424 | ||

SOS:22222222222222222222222222222222222222 | ||

TLBO:23222322322222222232231222222322222222 | ||

FHO:22222222222222222222222222222222222222 | ||

5 | CO_{2} | FA:44444444444444444444444444444444444444 |

MVO:15544232142225444342331444434454444444 | ||

PSO:15544232142225444342331444434454444444 | ||

SOS:44444444444444444444444444444444444444 | ||

TLBO:54443454444543444544444445445444544444 | ||

FHO:44444444444444444444444444444444444444 | ||

6 | All | FA:33333333333333333333333333333333333333 |

MVO:33333333333333323333333333333333333353 | ||

PSO:33323343223244133333535234333222333333 | ||

SOS:33333333333333333333333333333333333333 | ||

TLBO:33333333333333333333333332333333332333 | ||

FHO:33333333333333333333333333333333333333 |

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**MDPI and ACS Style**

Shishehgarkhaneh, M.B.; Azizi, M.; Basiri, M.; Moehler, R.C. BIM-Based Resource Tradeoff in Project Scheduling Using Fire Hawk Optimizer (FHO). *Buildings* **2022**, *12*, 1472.
https://doi.org/10.3390/buildings12091472

**AMA Style**

Shishehgarkhaneh MB, Azizi M, Basiri M, Moehler RC. BIM-Based Resource Tradeoff in Project Scheduling Using Fire Hawk Optimizer (FHO). *Buildings*. 2022; 12(9):1472.
https://doi.org/10.3390/buildings12091472

**Chicago/Turabian Style**

Shishehgarkhaneh, Milad Baghalzadeh, Mahdi Azizi, Mahla Basiri, and Robert C. Moehler. 2022. "BIM-Based Resource Tradeoff in Project Scheduling Using Fire Hawk Optimizer (FHO)" *Buildings* 12, no. 9: 1472.
https://doi.org/10.3390/buildings12091472