# Extracting Optimal Operation Rule Curves of Multi-Reservoir System Using Atom Search Optimization, Genetic Programming and Wind Driven Optimization

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Collection

#### 2.2. The Proposed Computational Approach

#### 2.3. Atom Search Optimization Algorithm for Finding Operation Rule Curves

#### 2.4. Genetic Programming for Finding Operation Rule Curves

#### 2.5. Wind-Driven Optimization for Finding Operation Rule Curves

_{1}, xi

_{2}, ..., xi

_{24}]. The application of WDO and reservoir simulation models for searching the rule curves is described in Figure 5 as a computational flowchart.

#### 2.6. Rule Curve Performance Assessment

- The performance of the proposed model was evaluated with historical inflow data for 2005–2020 and monthly synthetic inflow data across 1000 incident sets with the standard operating rule of release criteria.
- A comparison of the performance of the rule curve obtained by the ASO with the current rule curves, genetic programming (GP) and wind-driven optimization (WDO) using the least mean excess water content.
- The water situation when considering the amount of water discharged from the Upper Huai Sai-1 reservoir, the Upper Huai Sai-2 reservoir and the Upper Huai Sai-3 reservoir when combined flows are limited by the capacity of the Huai Sai Weir (that can drain the maximum 3.5 MCM/months) before flowing into the Huai Sai Kamin reservoir was evaluated.

## 3. Results

#### 3.1. The Multi-Reservoir Rule Curves Search

#### 3.2. Assessment of the Amount of Inflow into the Huai Sai Kamin Reservoir Obtained from the Newly Obtained Rule Curves

#### 3.3. Performance of Optimal Rule Curves in Monthly Historical and Synthetic Inflow Data across 1000 Incident Sets

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Optimal Reservoir Rule Curves of The Huai Sai Kamin Reservoir Obtained from ASO, GP, and WDO for Considerations (

**a**) a Single Reservoir Case and (

**b**) Multi-Reservoir System Case.

**Figure 7.**The Amount of Inflow into The Huai Sai Kamin Reservoir from Search Techniques with ASO, GP, and WDO between Single Reservoir Case and Multi-Reservoir System Case.

Characteristics | Huai Nam Bo | Upper Huai Sai-1 | Upper Huai Sai-2 | Upper Huai Sai-3 | Huai Sai Kamin |
---|---|---|---|---|---|

Type of dam | Earth dam | Earth dam | Earth dam | Earth dam | Earth dam |

First year of operation | 1964 | 1991 | 1986 | 1985 | 1956 |

Catchment area (km^{2}) | 9.87 | 6.63 | 5.6 | 0.6 | 29.00 |

Height from foundation (m) | 17 | 13.5 | 12.9 | 8 | 8.30 |

Crest length (m) | 950 | 575 | 690 | 450 | 1300 |

Normal storage capacity (MCM) | 2.2 | 2.1 | 2.1 | 0.21 | 3.18 |

Irrigation area (km^{2}) | 4.8 | 6.4 | 6.08 | 1.12 | 6.40 |

Spillway discharge capacity (m^{3}/s) | 15 | 25 | 21.3 | 1.9 | 85.50 |

Average annual inflow (MCM) | 9.04 | 2.38 | 1.54 | 0.40 | 45.77 |

Reservoir | Average Monthly Inflow (MCM/Month) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

January | February | March | April | May | June | July | August | September | October | November | December | |

Huai Nam Bo | 0.130 | 0.128 | 0.215 | 0.151 | 0.282 | 1.008 | 1.777 | 1.643 | 1.857 | 1.452 | 0.266 | 0.137 |

Upper Huaisai-1 | 0.044 | 0.047 | 0.052 | 0.047 | 0.147 | 0.250 | 0.360 | 0.425 | 0.479 | 0.408 | 0.074 | 0.051 |

Upper Huaisai-2 | 0.087 | 0.038 | 0.045 | 0.038 | 0.086 | 0.167 | 0.315 | 0.286 | 0.197 | 0.159 | 0.083 | 0.043 |

Upper Huaisai-3 | 0.002 | 0.002 | 0.004 | 0.006 | 0.075 | 0.124 | 0.055 | 0.070 | 0.060 | 0.182 | 0.008 | 0.005 |

Huai Sai Kamin | 0.878 | 0.683 | 0.779 | 0.374 | 0.555 | 2.415 | 8.161 | 11.654 | 12.053 | 6.321 | 1.401 | 0.499 |

**Table 3.**The Amount of Inflow into The Huai Sai Kamin Reservoir from Search Techniques with ASO, GP, and WDO between Single Reservoir Case and Multi-Reservoir System Case.

Rule Curves | Volume of Inflow through Huai Sai Weir (MCM/Month) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

January | February | March | April | May | June | July | August | September | October | November | December | ||

Single Reservoir | RC-Existing | 0.000 | 0.000 | 0.392 | 0.626 | 0.959 | 1.962 | 2.668 | 4.175 | 4.741 | 1.342 | 0.559 | 0.223 |

S-RC-ASO | 0.005 | 0.004 | 0.238 | 0.383 | 0.585 | 1.862 | 2.806 | 3.835 | 4.716 | 1.332 | 0.509 | 0.135 | |

S-RC-GP | 0.005 | 0.000 | 0.238 | 0.395 | 0.747 | 1.712 | 2.766 | 3.759 | 4.866 | 1.202 | 0.559 | 0.135 | |

S-RC-WDO | 0.005 | 0.004 | 0.238 | 0.380 | 0.590 | 1.860 | 2.786 | 3.840 | 4.816 | 1.232 | 0.539 | 0.135 | |

Multi Reservoir | M-RC-ASO | 0.005 | 0.000 | 0.238 | 0.383 | 0.581 | 1.192 | 2.026 | 3.409 | 4.726 | 1.572 | 0.619 | 0.135 |

M-RC-GP | 0.005 | 0.000 | 0.238 | 0.395 | 0.581 | 1.192 | 2.066 | 3.445 | 4.751 | 1.512 | 0.579 | 0.135 | |

M-RC-WDO | 0.005 | 0.000 | 0.238 | 0.385 | 0.581 | 1.162 | 2.03 | 3.412 | 4.732 | 1.552 | 0.609 | 0.135 |

**Table 4.**Situations of Excess Release of The Huai Sai Kamin Reservoir Considering Monthly Historical Data between Single Reservoir Case and Multi-Reservoir System Case.

Criteria for Consideration | Rule Curves | Frequency | Magnitude of Excess Release Water (MCM/Year) | Duration (Year) | ||
---|---|---|---|---|---|---|

(Times/Year) | Average | Maximum | Average | Maximum | ||

Single Reservoir | RC-existing | 1 | 45.788 | 90.945 | 16 | 16 |

S-RC-ASO | 1 | 45.602 | 90.550 | 16 | 16 | |

S-RC-GP | 1 | 45.562 | 90.408 | 16 | 16 | |

S-RC-WDO | 1 | 45.588 | 90.502 | 16 | 16 | |

Multi Reservoir | RC-existing | 1 | 45.788 | 90.945 | 16 | 16 |

M-RC-ASO | 1 | 43.828 | 88.345 | 16 | 16 | |

M-RC-GP | 1 | 43.722 | 88.794 | 16 | 16 | |

M-RC-WDO | 1 | 43.822 | 88.455 | 16 | 16 |

**Table 5.**Situations of Excess Release of The Huai Sai Kamin Reservoir Considering Monthly Synthetic Inflow between Single Reservoir Case and Multi-Reservoir System Case.

Criteria for Consideration | Rule Curves | Frequency | Magnitude of Excess Release Water (MCM/Year) | Duration (Year) | |||
---|---|---|---|---|---|---|---|

(Times/Year) | Average | Maximum | Average | Maximum | |||

Single Reservoir | RC-existing | µ | 1 | 45.639 | 75.388 | 16 | 16 |

σ | 0 | 3.769 | 10.006 | 0 | 0 | ||

S-RC-ASO | µ | 1 | 45.536 | 74.834 | 16 | 16 | |

σ | 0 | 3.869 | 9.569 | 0 | 0 | ||

S-RC-GP | µ | 1 | 45.495 | 74.793 | 16 | 16 | |

σ | 0 | 3.868 | 9.569 | 0 | 0 | ||

S-RC-WDO | µ | 1 | 45.533 | 74.828 | 16 | 16 | |

σ | 0 | 3.869 | 9.569 | 0 | 0 | ||

Multi Reservoir | RC-existing | µ | 1 | 45.639 | 75.388 | 16 | 16 |

σ | 0 | 3.769 | 10.006 | 0 | 0 | ||

M-RC-ASO | µ | 1 | 43.833 | 72.389 | 16 | 16 | |

σ | 0 | 3.697 | 9.286 | 0 | 0 | ||

M-RC-GP | µ | 1 | 43.673 | 72.893 | 16 | 16 | |

σ | 0 | 3.798 | 9.939 | 0 | 0 | ||

M-RC-WDO | µ | 1 | 43.734 | 72.445 | 16 | 16 | |

σ | 0 | 3.705 | 9.546 | 0 | 0 |

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**MDPI and ACS Style**

Kosasaeng, S.; Yamoat, N.; Ashrafi, S.M.; Kangrang, A.
Extracting Optimal Operation Rule Curves of Multi-Reservoir System Using Atom Search Optimization, Genetic Programming and Wind Driven Optimization. *Sustainability* **2022**, *14*, 16205.
https://doi.org/10.3390/su142316205

**AMA Style**

Kosasaeng S, Yamoat N, Ashrafi SM, Kangrang A.
Extracting Optimal Operation Rule Curves of Multi-Reservoir System Using Atom Search Optimization, Genetic Programming and Wind Driven Optimization. *Sustainability*. 2022; 14(23):16205.
https://doi.org/10.3390/su142316205

**Chicago/Turabian Style**

Kosasaeng, Suwapat, Nirat Yamoat, Seyed Mohammad Ashrafi, and Anongrit Kangrang.
2022. "Extracting Optimal Operation Rule Curves of Multi-Reservoir System Using Atom Search Optimization, Genetic Programming and Wind Driven Optimization" *Sustainability* 14, no. 23: 16205.
https://doi.org/10.3390/su142316205