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Multi-Objective Optimization of Drainage Networks for Flood Control in Urban Area Due to Climate Change^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

- The design storm is considered static for the entire network.
- The mathematical simulation model SWMM [15] is used as a network analysis tool. Dynamic wave analysis using the complete Saint-Venant equations is used.
- The mathematical model of the network must be calibrated and simplified without this decreasing the reliability in the results.
- The actions that will be taken are the renewal of pipes with others of greater diameter, the installation of STs and the installation of hydraulic controls. Changes in the morphology of the network are out of this work.
- The STs are considered installed on-line. The invert elevation is also considered the same of the existing manhole.
- The optimization problem is analyzed in terms of costs. The cost function must be established based on the hydraulic variables and includes the cost of pipe renewal, the cost of installation of ST and the cost of damage caused by flooding.
- The flood damage cost function does not consider intangible damage.

#### 2.1. Decision Variables

_{S}, B

_{S}and C

_{S}are adjustment coefficients of the tank section and z is the maximum water level of the node. For tanks of constant section, the coefficient A represents the cross section while the coefficients B and C are null.

_{d}is a dimensionaless orifice discharge coefficient and D

_{o}is the orifice diameter. The proposed optimization model locates pipes that require hydraulic control to retain water and prevent flooding. This objective is achieved when the ST and the hydraulic control work together so that the location of the latter will be in the outlet pipe of certain STs. These DVs can take values from 0 (no hydraulic control is required) to a previously defined maximum value.

#### 2.2. Objective Function

_{i}in case it is required to prioritize or minimize a term with respect to the others.

#### 2.2.1. Pipe Replacement Cost Functions

#### 2.2.2. Storm Tank Installation Cost Functions

#### 2.2.3. Flood Damage Cost functions

## 3. Case Study

## 4. Results

## 5. Conclusions

- The combined use of replacement pipes, the installation of pipes and hydraulic controls is an appropriate methodology for optimizing drainage networks that require rehabilitation. The use of multi-objective evolutionary algorithms proves to be valid for this type of analysis.
- The main conclusion of this work is that the use of CH significantly decreases the cost of the intervention in the drainage network because it retains the water upstream using the volume of the network to momentarily store the water, making the system more efficient and avoiding accumulation downstream, avoiding flooding.

## Author Contributions

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

DOAJ | Directory of open access journals |

AR5 | Fifth Assessment Report |

ICCP | Intergovernmental Panel on Climate Change |

ST | Storm Tank |

DV | Decision variable |

HC | Hydraulic control |

IDF | Intensity, Duration, Frequency |

NSGA | Non-dominated sorting genetic algorithm |

SWMM | Storm Water Management Model |

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**Figure 3.**Representation of STs and HC installed and pipes to replace according to results of the optimization model.

**Figure 4.**Pareto front representation of previous results and results with the inclusion of hydraulic controls.

Node | Flood Volume (m^{3}) | Flood Area (m^{2}) | ymax (m) | Cost (€) |
---|---|---|---|---|

N02 | 123.56 | 1240 | 0.1 | 135,857.00 € |

N04 | 132.56 | 930 | 0.413 | 181,375.00 € |

N06 | 501.79 | 1890 | 0.265 | 875,502.00 € |

N07 | 23.95 | 1250 | 0.019 | 6644.00 € |

N09 | 1.82 | 1130 | 0.002 | 45.00 € |

N10 | 385.12 | 700 | 0.55 | 646,838.00 € |

N11 | 25.83 | 820 | 0.032 | 11,288.00 € |

N23 | 949.54 | 450 | 2.11 | 569,922.00 € |

N32 | 36.65 | 1500 | 0.024 | 12,727.00 € |

N33 | 469.82 | 3030 | 0.155 | 671,908.00 € |

N34 | 1181.87 | 3270 | 0.361 | 2,131,929.00 € |

TOTAL | 5,244,035.00 € |

Scenario | Objective Function | Term in Objetive Function | N_{O} Elementos in the Solution | ||||
---|---|---|---|---|---|---|---|

Floods | STs | Pipes | STs | Pipes | HC | ||

[12] | 213,981.00 € | 12,701.00 € | 186,353.00 € | 14,927.00 € | 3 | 3 | 0 |

Proposed | 209,150.40 € | 9061.91 € | 188,957.79 € | 11,130.70 € | 3 | 2 | 2 |

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**MDPI and ACS Style**

Bayas-Jiménez, L.; Iglesias-Rey, P.L.; Martínez-Solano, F.J.
Multi-Objective Optimization of Drainage Networks for Flood Control in Urban Area Due to Climate Change. *Proceedings* **2020**, *48*, 27.
https://doi.org/10.3390/ECWS-4-06451

**AMA Style**

Bayas-Jiménez L, Iglesias-Rey PL, Martínez-Solano FJ.
Multi-Objective Optimization of Drainage Networks for Flood Control in Urban Area Due to Climate Change. *Proceedings*. 2020; 48(1):27.
https://doi.org/10.3390/ECWS-4-06451

**Chicago/Turabian Style**

Bayas-Jiménez, Leonardo, Pedro L. Iglesias-Rey, and F. Javier Martínez-Solano.
2020. "Multi-Objective Optimization of Drainage Networks for Flood Control in Urban Area Due to Climate Change" *Proceedings* 48, no. 1: 27.
https://doi.org/10.3390/ECWS-4-06451