# Determining the Optimal Restricted Driving Zone Using Genetic Algorithm in a Smart City

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## Abstract

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## 1. Introduction

- An innovative technique called Optimal Restricted Driving Zone (ORDZ) is introduced that intelligently determines restricted driving zones using a machine learning technique. RDZ reduces traffic load and air pollution, and increase citizens satisfaction who wish to travel by their own vehicle. All the aforementioned objectives are formulated into a single multi-objective function that constitute an evolutionary algorithm called genetic algorithm. While the previous works [8,9] determine restrict zone empirically, ORDZ generates a possible solution iteratively until it reaches the optimal solution (with each episode creating a viable solution). This approach has a significant advantage in dynamic traffic conditions as shown in the following sections.
- In our simulation, ORDZ is compared against the other well-known methods including: the Restricted Traffic Zone (RTZ) [8], the Odd-Even Zone (OEZ) [8] and the optimal cordon-based network congestion based on pricing (OCP) [14]. We compare our work against the other well-known empirical approaches. The performance of each method is evaluated with two metrics, traffic load and citizen satisfaction rate. The results show that ORDZ has 23.81% less traffic load than OCP. Also, ORDZ has 22.35% increase in citizen satisfaction than RTZ. We also compare both metrics together as a trade-off and a complete solution. The results show that ORDZ performs 30.6% better than the random modeling, empirical methods, RTZ, OEZ and OCP in terms of traffic load and citizen satisfaction rates.

## 2. Related Work

#### 2.1. Public Transportation

#### 2.2. Smart Traffic Lights Mmethods

#### 2.3. Modern Technology Method

#### 2.4. Restricted Driving Zone Methods

#### 2.5. Discussion

## 3. System Description

#### Problem Definition

**Scenario 1**: Assume that the traffic zone is determined but air pollution index is not decreased. This case indicates that the zone was not significant enough and did not have effect on the reduction of air pollution. Therefore, a more extended zone is required to effectively reduce air pollution. The determination of optimal limited traffic zone has a significant impact on reducing air pollution.

**Scenario 2**: Assume that an extensive traffic limited zone is selected, and the traffic and air pollution indexes are reduced; however, at the cost of increased dissatisfaction of the citizens. Therefore, finding an optimal traffic zone is a challenge that leads to citizen satisfaction and reduced traffic and air pollution.

## 4. Proposed Method: Optimal Restricted Driving Zone (ORDZ)

#### 4.1. Initial Plan

#### 4.2. Chromosome Formulation

#### 4.3. Constraints Satisfaction

**First state:**If the result of the determinant $\left(R\right)$ is positive, it means that the third cell is located on top of the line. For example, considering cells ${c}_{21},{c}_{44}$ with coordinates $\left(\right)$ and $\left(\right)open="("\; close=")">4,4$ on a grid cell with $m=5\phantom{\rule{0.277778em}{0ex}}$ in Figure 4. According to Equation (1), ${c}_{21},{c}_{44}$ are mapped to numbers 2 and 19. These two cells are connected by a line. Then, by calculating the determinants, the position of the third cell ${c}_{24}$ with the coordinates $\left(\right)$ which is mapped to 17, and it is determined as follows:

**Second state:**If the result of determinants $\left(R\right)$ is negative, the third cell’s location is placed on the bottom of the line. For example, in Figure 6, considering cells ${c}_{22},{c}_{45}$ have coordinates $\left(\right)$ and $\left(\right)$ in a grid cell with $m=5$. According to Equation (1), ${c}_{22},{c}_{45}$ are mapped to numbers 7 and 24. These two cells are connected by a line. Then, by calculating the determinants, the position of the third cell ${c}_{42}$ with the coordinates $\left(\right)$ which is mapped to 9, and it is determined as follows:

**Third state**: If the result of the determinant $\left(R\right)$ is zero, the third cell is placed on the line. So, it does not form a zone. For example, in Figure 8, considering cells ${c}_{21},{c}_{54}$ have coordinates $\left(\right)$ and $\left(\right)$ in a grid cell with $m=5$. According to Equation (1), ${c}_{21},{c}_{54}$ are mapped to numbers 2 and 20. These two cells are connected by a line. Then, by calculating the determinants, the position of the third cell ${c}_{32}$ with the coordinates $\left(\right)$ which is mapped to 8, and it is determined as follows:

#### 4.4. Initial Population

#### 4.5. Parent Selection

#### 4.6. Crossover

#### 4.7. Mutation

#### 4.8. Fitness Function

#### 4.8.1. Traffic Load

#### 4.8.2. Citizen Satisfaction

#### 4.8.3. Data Normalization

## 5. Experiments

#### 5.1. First Scenario

#### 5.2. Second Scenario

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 16.**Comparison of different techniques based on: (

**a**) impact of traffic load; (

**b**) impact of citizen satisfaction; (

**c**) fitness function for all methods.

**Figure 17.**Comparison of different techniques based on: (

**a**) impact of traffic load; (

**b**) impact of citizen satisfaction; (

**c**) compare fitness function for all methods.

Methods | Advantages | Disadvantages |
---|---|---|

Classic methods | • Reduce traffic volume • Reduce air pollution • Low cost | • Low quality • Low satisfaction • High travel time |

Smart traffic lights methods | • Reduce delay time • Reduce traffic volume • Reduce air pollution | • High maintenance cost |

Limited traffic zone methods | • Reduce traffic volume • Reduce air pollution • Low travel time | • Low satisfaction • Pay toll |

Modern Technology Methods | • Reduce air pollution • Reduce Traffic volume • Environment friendly | • High maintenance cost |

Notation | Description |
---|---|

$m\times m$ | Total number of grid cells |

$\left(\right)open="("\; close="\}">{c}_{11},\cdots ,{c}_{ij},\cdots ,{c}_{mm}$ | Grid cells |

$U=\left(\right)open="("\; close="\}">{u}_{1},\cdots ,{u}_{i},\cdots ,{u}_{r}$ | Vehicles |

${MP}_{{u}_{i}}$ | i -th vehicle movement pattern |

$t=\left(\right)open="("\; close="\}">1,2,3,\cdots ,T$ | Discrete time |

$\left(\right)$ | Couple-time vehicle movement pattern |

R | Determinant of matrix |

$\phantom{\rule{0.277778em}{0ex}}P\left(c1\phantom{\rule{0.277778em}{0ex}}\right)$ | Probability of selection each chromosome |

$\phantom{\rule{0.277778em}{0ex}}Q\left(c1\right)$ | Superiority of each chromosome |

$\mu $ | Initial population |

$\eta $ | Traffic load |

$\phi $ | citizen satisfaction rate |

$\phantom{\rule{0.277778em}{0ex}}F(\eta \phantom{\rule{0.277778em}{0ex}},\phantom{\rule{0.277778em}{0ex}}\phi )$ | Fitness function |

${N}_{ij}\phantom{\rule{0.277778em}{0ex}}\left(t\right)$ | Total number of vehicles entering a cell |

${\tau}_{ij}$ | Average traffic |

Z | Data normalization |

$\sigma $ | Standard deviation |

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**MDPI and ACS Style**

Jan, T.; Azami, P.; Iranmanesh, S.; Ameri Sianaki, O.; Hajiebrahimi, S.
Determining the Optimal Restricted Driving Zone Using Genetic Algorithm in a Smart City. *Sensors* **2020**, *20*, 2276.
https://doi.org/10.3390/s20082276

**AMA Style**

Jan T, Azami P, Iranmanesh S, Ameri Sianaki O, Hajiebrahimi S.
Determining the Optimal Restricted Driving Zone Using Genetic Algorithm in a Smart City. *Sensors*. 2020; 20(8):2276.
https://doi.org/10.3390/s20082276

**Chicago/Turabian Style**

Jan, Tony, Pegah Azami, Saeid Iranmanesh, Omid Ameri Sianaki, and Shiva Hajiebrahimi.
2020. "Determining the Optimal Restricted Driving Zone Using Genetic Algorithm in a Smart City" *Sensors* 20, no. 8: 2276.
https://doi.org/10.3390/s20082276