# A Charging Guidance Optimization Model for Electric Vehicle Travel by Considering Multi-Dimensional Preferences of Users

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. User Preference Analysis

#### 3.1. Collaborative Filtering Algorithm

#### 3.2. Modeling of User Preferences for Charging Stations

- Similarity calculation

- 2.
- Feature extraction

- 3.
- Model Design

## 4. Optimization Model for EV Charging Guidance

#### 4.1. Basic Assumptions

**Assumption**

**1.**

**Assumption**

**2.**

**Assumption**

**3.**

**Assumption**

**4.**

**Assumption**

**5.**

#### 4.2. Notations

#### 4.3. Objective Functions

#### 4.3.1. Energy Consumption Cost

#### 4.3.2. Time Cost

#### 4.3.3. Fee Costs

#### 4.3.4. Penalty Costs

#### 4.4. Constraints

#### 4.4.1. Charging Station Capacity Constraint

#### 4.4.2. Remaining Mileage Constraint

- $R$—User i selects the travel path to the charging station j;
- $k$—Nodes on the path;
- ${D}_{ijk}$—Remaining mileage at the node on the path.

## 5. Numerical Simulation

#### 5.1. Example Scenario Description

Start Node | End Node | Section Length | Start Node Latitude and Longitude | End Node Latitude and Longitude | Travel Time |
---|---|---|---|---|---|

3634 | 19983 | 165.3992 | 116.3379, 39.91324 | 116.3359, 39.91314 | 29.77185 |

26 | 13103 | 35.15128 | 116.3281,39.9133 | 116.3282, 39.91359 | 5.061784 |

13103 | 23963 | 364.2321 | 116.3282,39.91359 | 116.3283, 39.91685 | 52.44942 |

17374 | 350 | 216.9624 | 116.2817, 39.93521 | 116.2816, 39.93715 | 11.00091 |

350 | 22529 | 224.9431 | 116.2816, 39.93715 | 116.2813, 39.93917 | 11.40557 |

730 | 3731 | 35.16322 | 116.3506, 39.99189 | 116.351, 39.99192 | 1.947502 |

3731 | 17628 | 378.7178 | 116.351, 39.99192 | 116.3554, 39.99212 | 20.97514 |

17628 | 16729 | 161.4882 | 116.3554, 39.99212 | 116.3573, 39.99221 | 8.943964 |

16729 | 16730 | 54.82072 | 116.3573, 39.99221 | 116.358, 39.99225 | 3.036225 |

2200 | 359 | 268.0961 | 116.3596, 39.97348 | 116.3564, 39.97342 | 16.08577 |

359 | 22176 | 115.0853 | 116.3564, 39.97342 | 116.3551, 39.97339 | 6.905119 |

17460 | 21939 | 119.731 | 116.3164, 39.95222 | 116.3164, 39.95115 | 7.18386 |

36 | 9542 | 371.0652 | 116.3621, 39.94738 | 116.3629, 39.95062 | 21.89893 |

#### 5.2. Optimal Results and Analysis

#### 5.3. Analysis of Algorithm Parameters and Convergence

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Notations | Explanation |
---|---|

${R}_{u,i}$ | User u’s rating value for charging station i |

${R}_{u,j}$ | User u’s rating value for charging station j |

$U$ | Collection of users |

$\overline{{R}_{i}}$ | Average rating of charging station i |

$\overline{{R}_{j}}$ | Average rating of charging station j |

${R}_{x,i}$ | User x’s rating value for charging station i |

${R}_{y,i}$ | User y’s rating value for charging station j |

$I$ | Collection of charging stations |

$\overline{{R}_{x}}$ | Average rating of charging stations by user x |

$\overline{{R}_{y}}$ | Average rating of charging stations by user y |

$sim(u,n)$ | Similarity of user u to user n |

$sim(i,j)$ | Similarity of charging station u to charging station n |

${e}_{ij}^{os}$ | The maximum energy consumption in kWh from the starting point to the charging station when user i selects charging station j |

${e}_{ij}^{sd}$ | The maximum energy consumption in kWh from the charging station j to the end point when user i selects charging station j |

${F}_{ij}^{o}$ | Energy consumption for user i to travel from the starting point to charging station j in kWh |

${R}_{ij}^{o}$ | Set of optional paths for user i from the starting point to charging station j |

${R}_{ij}^{d}$ | Set of optional paths for user i from charging station j to destination |

$U$ | Collection of users |

$S$ | Collection of charging stations |

${e}_{r}$ | The driving energy consumption of road section r, which is related to the driving speed and the length of the road section in kWh |

${t}_{ij}^{r}$ | The total travel time consumed by user i throughout the trip in hours (h) |

${t}_{ij}^{w}$ | Queuing time for user i at the charging station in hours (h) |

${t}_{ij}^{c}$ | Charging time of the user at the charging station in hours (h) |

${R}_{ij1}^{*}$ | Robust optimal path of user i from the starting point to charging station j |

${R}_{ij2}^{*}$ | Robust optimal path of user i from charging station j to the end point |

${d}_{r}$ | The length of the road segment r in meters (m) |

${P}_{j}^{s}$ | Charging station j slow charging power in watts (W) |

${P}_{j}^{f}$ | Charging station j fast charging power in watts (W) |

$SO{C}_{ij}^{c}$ | The current SOC value of the vehicle of user i when the vehicle is charged at charging station j (SOC is the power-to-battery capacity ratio) |

$\u25b3e$ | Average user charge at charging stations in CNY/kWh |

${N}_{ij}$ | Total number of vehicles in the charging station when user i arrives at charging station j |

${C}_{j}$ | Number of charging posts in charging station j |

${V}_{j}$ | Number of vehicles allowed in charging station j |

${a}_{j}$ | Vehicle arrival rate for charging station j in vehicles/min |

${c}_{ij}^{s}$ | Service charge for user i at charging station j in CNY |

${c}_{ij}^{c}$ | Charging fee for user i at charging station j in CNY |

${c}_{ij}^{p}$ | Parking fee for user i at charging station j in CNY |

${\rho}_{j}^{s}$ | The unit service charge for charging station j in CNY/kWh |

${\rho}_{j}^{c}$ | The unit charging fee for charging station j in CNY/kWh |

${\rho}_{j}^{p}$ | The unit parking fee for charging station j in CNY/h |

${p}_{ij}$ | The penalty cost for user i to select charging station j in CNY |

${T}_{i}^{e}$ | User i expects to start charging at the earliest possible moment |

${T}_{i}^{d}$ | User i expects to start charging at the latest possible moment |

${\lambda}_{e}$ | User i’s penalty factor for early charging in CNY/min |

${\lambda}_{d}$ | Penalty factor for delayed charging by user i in CNY/min |

${E}_{i}^{o}$ | The initial power of user i at the starting point in kWh |

${E}_{e}$ | Electric vehicle battery capacity in kWh |

$w$ | User preference vector with dimensionality depending on the objective function dimension |

${e}_{ij}^{os}$ | The maximum energy consumption in kWh from the starting point to the charging station when user i selects charging station j |

${e}_{ij}^{sd}$ | The maximum energy consumption in kWh from the charging station j to the end point when user i selects the charging station j |

${F}_{ij}^{o}$ | Energy consumption for user i to travel from the starting point to charging station j in kWh |

${R}_{ij}^{o}$ | Set of optional paths for user i from the starting point to charging station j |

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Users | Charging Station 1 | Charging Station 2 | Charging Station 3 |
---|---|---|---|

1 | ${R}_{1,1}$ | ${R}_{1,2}$ | ${R}_{1,3}$ |

2 | ${R}_{2,1}$ | ${R}_{2,2}$ | ${R}_{2,3}$ |

3 | ${R}_{3,1}$ | ${R}_{3,2}$ | ${R}_{3,3}$ |

Charging Station Number | Node Number |
---|---|

1 | 48654 |

2 | 19984 |

3 | 19 |

4 | 24093 |

5 | 29 |

6 | 24098 |

7 | 33830 |

8 | 33831 |

9 | 3640 |

10 | 12349 |

11 | 12367 |

12 | 48742 |

13 | 20600 |

14 | 38011 |

15 | 12418 |

16 | 48262 |

17 | 20615 |

18 | 20616 |

Charging Station | 50 | 41 | 47 | 1 | 2 | 33 | 3 | 11 | |
---|---|---|---|---|---|---|---|---|---|

Charging Station | |||||||||

50 | 1 | −0.356 | 0.979 | −0.400 | −0.133 | 0.509 | −0.356 | −0.400 | |

41 | −0.356 | 1 | −0.250 | 0.612 | −0.250 | 0.612 | −0.250 | −0.408 | |

47 | 0.979 | −0.250 | 1 | −0.408 | −0.250 | 0.612 | −0.250 | −0.408 | |

1 | −0.400 | 0.612 | −0.408 | 1 | −0.408 | 0.166 | −0.408 | 0.166 | |

2 | −0.133 | −0.250 | −0.250 | −0.408 | 1 | −0.408 | −0.250 | −0.408 | |

33 | 0.509 | 0.612 | 0.612 | 0.166 | −0.408 | 1 | −0.408 | −0.666 | |

3 | −0.356 | −0.250 | −0.250 | −0.408 | −0.250 | −0.408 | 1 | 0.612 | |

11 | −0.400 | −0.408 | −0.408 | 0.166 | −0.408 | −0.666 | 0.612 | 1 |

Users | Departure Nodes | Destination Nodes | Initial Charge (kWh) | Earliest Time to Start Charging | Latest Time to Start Charging |
---|---|---|---|---|---|

U1 | 6528 | 7512 | 10 | 8:00 | 9:00 |

U2 | 29857 | 48484 | 15 | 8:00 | 9:00 |

U3 | 29603 | 48603 | 10 | 10:00 | 12:00 |

U4 | 21385 | 20842 | 12 | 12:00 | 14:00 |

U5 | 17358 | 48408 | 9 | 17:00 | 19:00 |

id | ${\mathsf{\rho}}_{\mathit{j}}^{\mathit{s}}$ | ${\mathsf{\rho}}_{\mathit{j}}^{\mathit{c}}$ | ${\mathsf{\rho}}_{\mathit{j}}^{\mathit{p}}$ | ${\mathit{a}}_{\mathit{j}}$ | ${\mathit{C}}_{\mathit{j}}$ | ${\mathit{V}}_{\mathit{j}}$ | ${\mathit{N}}_{\mathbf{0}}$ |
---|---|---|---|---|---|---|---|

1 | 0.8 | 1.6 | 10 | 0.12 | 7 | 19 | 3 |

2 | 0.6 | 1.7 | 8 | 0.07 | 6 | 16 | 3 |

3 | 1 | 2.5 | 5 | 0.05 | 3 | 16 | 6 |

4 | 1.2 | 1.6 | 2 | 0.12 | 3 | 20 | 2 |

5 | 0.8 | 1.7 | 10 | 0.04 | 10 | 18 | 3 |

6 | 0.8 | 2.5 | 5 | 0.14 | 10 | 17 | 4 |

7 | 1 | 1.6 | 2 | 0.05 | 8 | 15 | 5 |

8 | 1 | 1.7 | 2 | 0.07 | 4 | 15 | 1 |

9 | 1 | 2.5 | 2 | 0.14 | 9 | 20 | 6 |

10 | 1 | 2.3 | 5 | 0.06 | 7 | 16 | 8 |

11 | 1 | 2.2 | 5 | 0.07 | 10 | 17 | 7 |

12 | 0.6 | 2.3 | 10 | 0.14 | 4 | 18 | 2 |

13 | 0.6 | 2.5 | 10 | 0.12 | 6 | 15 | 1 |

14 | 0.6 | 1.6 | 10 | 0.09 | 3 | 17 | 2 |

15 | 0.6 | 1.6 | 10 | 0.03 | 8 | 15 | 2 |

16 | 0.6 | 1.6 | 10 | 0.06 | 5 | 19 | 7 |

17 | 0.6 | 1.6 | 8 | 0.12 | 8 | 19 | 6 |

18 | 0.6 | 1.6 | 8 | 0.09 | 9 | 19 | 2 |

19 | 0.6 | 1.6 | 8 | 0.03 | 8 | 17 | 3 |

20 | 0.8 | 1.6 | 8 | 0.06 | 5 | 15 | 3 |

Algorithm Parameters | Description | Value |
---|---|---|

generation | Number of iterations | 100 |

popSize | Population size | 50 |

${p}_{c}$ | Crossover probability | 0.9 |

${p}_{m}$ | Mutation probability | 1 |

User 1 | User 2 | User 3 | User 4 | User 5 | |||||
---|---|---|---|---|---|---|---|---|---|

Charging Station | Departure Time | Charging Station | Departure Time | Charging Station | Departure Time | Charging Station | Departure Time | Charging Station | Departure Time |

20 | 502 | 14 | 490 | 17 | 660 | 17 | 773 | 18 | 1025 |

18 | 454 | 19 | 487 | 17 | 660 | 17 | 772 | 18 | 1004 |

20 | 454 | 14 | 462 | 17 | 662 | 17 | 717 | 20 | 1062 |

18 | 472 | 19 | 460 | 17 | 668 | 17 | 778 | 18 | 1057 |

20 | 454 | 19 | 492 | 17 | 668 | 13 | 773 | 20 | 1038 |

18 | 454 | 19 | 459 | 17 | 668 | 17 | 779 | 18 | 1077 |

18 | 472 | 19 | 458 | 17 | 668 | 17 | 779 | 18 | 1000 |

20 | 454 | 19 | 462 | 17 | 668 | 17 | 773 | 20 | 1027 |

20 | 454 | 19 | 460 | 17 | 668 | 17 | 773 | 20 | 1056 |

18 | 454 | 19 | 458 | 17 | 668 | 17 | 780 | 18 | 1027 |

20 | 454 | 19 | 462 | 17 | 668 | 13 | 773 | 20 | 999 |

20 | 454 | 19 | 459 | 17 | 667 | 13 | 780 | 20 | 999 |

20 | 454 | 19 | 458 | 17 | 669 | 17 | 780 | 18 | 1012 |

20 | 458 | 19 | 459 | 17 | 632 | 17 | 733 | 18 | 1029 |

18 | 471 | 19 | 458 | 17 | 668 | 17 | 779 | 18 | 1000 |

20 | 454 | 19 | 459 | 17 | 658 | 17 | 771 | 17 | 1000 |

18 | 473 | 19 | 463 | 17 | 659 | 17 | 771 | 17 | 1017 |

20 | 468 | 19 | 460 | 17 | 613 | 17 | 772 | 18 | 1004 |

20 | 454 | 19 | 462 | 17 | 663 | 17 | 774 | 18 | 1025 |

20 | 454 | 14 | 462 | 17 | 662 | 17 | 717 | 20 | 1062 |

18 | 471 | 19 | 489 | 17 | 662 | 17 | 773 | 17 | 1001 |

20 | 454 | 19 | 492 | 17 | 668 | 17 | 773 | 20 | 1038 |

18 | 454 | 19 | 461 | 17 | 660 | 17 | 779 | 18 | 1026 |

18 | 453 | 19 | 462 | 17 | 658 | 17 | 780 | 17 | 999 |

20 | 457 | 19 | 462 | 17 | 663 | 17 | 779 | 17 | 1017 |

18 | 454 | 19 | 489 | 17 | 658 | 17 | 780 | 17 | 999 |

20 | 468 | 19 | 488 | 17 | 613 | 17 | 772 | 18 | 1004 |

20 | 454 | 19 | 487 | 17 | 667 | 13 | 752 | 20 | 999 |

20 | 454 | 19 | 458 | 17 | 669 | 17 | 780 | 18 | 1012 |

20 | 454 | 19 | 462 | 17 | 668 | 17 | 718 | 20 | 1027 |

18 | 472 | 19 | 458 | 17 | 695 | 17 | 774 | 18 | 1000 |

18 | 471 | 19 | 458 | 17 | 668 | 17 | 779 | 18 | 1000 |

20 | 455 | 19 | 490 | 17 | 659 | 17 | 773 | 17 | 1001 |

18 | 453 | 19 | 460 | 17 | 668 | 17 | 778 | 18 | 1057 |

20 | 454 | 19 | 458 | 17 | 669 | 17 | 780 | 18 | 1038 |

Energy Consumption Cost (kWh) | Time Cost (h) | Fee Cost (CNY) | Penalty Cost (CNY) |
---|---|---|---|

12.953 | 2.960 | 155.658 | 4.701 |

13.094 | 3.011 | 152.349 | 0 |

12.734 | 2.919 | 158.346 | 0 |

13.094 | 3.011 | 152.349 | 0 |

12.524 | 2.923 | 169.293 | 0 |

13.094 | 3.011 | 152.349 | 0 |

13.094 | 3.011 | 152.349 | 0 |

12.660 | 2.929 | 157.500 | 0 |

12.660 | 2.929 | 157.500 | 0 |

13.094 | 3.011 | 152.349 | 0 |

12.524 | 2.923 | 169.293 | 0 |

12.524 | 2.923 | 169.293 | 0 |

12.879 | 2.970 | 154.813 | 0 |

12.879 | 2.970 | 154.813 | 0 |

13.094 | 3.011 | 152.349 | 0 |

13.045 | 2.997 | 154.441 | 0 |

13.260 | 3.037 | 151.977 | 0 |

12.879 | 2.970 | 154.813 | 0 |

12.879 | 2.970 | 154.813 | 0 |

12.734 | 2.919 | 158.346 | 0 |

13.260 | 3.037 | 151.977 | 0 |

12.660 | 2.929 | 157.500 | 0 |

13.094 | 3.011 | 152.349 | 0 |

13.260 | 3.037 | 151.977 | 0 |

13.045 | 2.997 | 154.441 | 0 |

13.260 | 3.037 | 151.977 | 0 |

12.879 | 2.970 | 154.813 | 0 |

12.524 | 2.923 | 169.293 | 0 |

12.879 | 2.970 | 154.813 | 0 |

12.660 | 2.929 | 157.500 | 0 |

13.094 | 3.011 | 152.349 | 0 |

13.094 | 3.011 | 152.349 | 0 |

13.045 | 2.997 | 154.441 | 0 |

13.094 | 3.011 | 152.349 | 0 |

12.879 | 2.970 | 154.813 | 0 |

Users | Charging Station Preference Weights |
---|---|

1 | (18, 1.0), (20, 0.3) |

2 | (14, 0.7), (19, 0.8) |

3 | (17, 1.0) |

4 | (13, 1.0), (17, 0.5) |

5 | (17, 1.0), (18, 0.3), (20, 0.7) |

User | O-D Nodes | Departure Time | Charging Station | Road Network Nodes Where Charging Stations Are Located |
---|---|---|---|---|

1 | 6528→7512 | 7:34 | 20 | 20618 |

2 | 29857→48484 | 8:12 | 19 | 48263 |

3 | 29603→48603 | 11:08 | 17 | 20615 |

4 | 21385→20842 | 12:53 | 13 | 20600 |

5 | 17358→48408 | 17:18 | 20 | 20618 |

User | O-D Nodes | Departure Time | Charging Station | Road Network Nodes Where Charging Stations Are Located |
---|---|---|---|---|

1 | 6528→7512 | 7:34 | 18 | 20616 |

2 | 29857→48484 | 8:07 | 19 | 48263 |

3 | 29603→48603 | 11:00 | 17 | 20615 |

4 | 21385→20842 | 12:52 | 17 | 20615 |

5 | 17358→48408 | 16:44 | 18 | 20616 |

User | O-D Nodes | Departure Time | Charging Station | Road Network Nodes Where Charging Stations Are Located |
---|---|---|---|---|

1 | 6528→7512 | 8:22 | 20 | 20618 |

2 | 29857→48484 | 8:10 | 14 | 38011 |

3 | 29603→48603 | 11:00 | 17 | 20615 |

4 | 21385→20842 | 12:53 | 17 | 20615 |

5 | 17358→48408 | 17:05 | 18 | 20618 |

**Table 14.**The value of each objective function corresponding to the three different types of user preferences.

Value of the Objective Function | ${\mathit{Z}}_{\mathit{e}}$ | ${\mathit{Z}}_{\mathit{t}}$ | ${\mathit{Z}}_{\mathit{c}}$ | |
---|---|---|---|---|

Weight | ||||

${w}^{1}$ | 12.524 | 2.923 | 169.292 | |

${w}^{2}$ | 13.094 | 3.011 | 152.348 | |

${w}^{3}$ | 12.524 | 2.923 | 169.292 |

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## Share and Cite

**MDPI and ACS Style**

Zuo, X.; Bi, J.; Wang, Y.; Du, Y.
A Charging Guidance Optimization Model for Electric Vehicle Travel by Considering Multi-Dimensional Preferences of Users. *World Electr. Veh. J.* **2023**, *14*, 171.
https://doi.org/10.3390/wevj14070171

**AMA Style**

Zuo X, Bi J, Wang Y, Du Y.
A Charging Guidance Optimization Model for Electric Vehicle Travel by Considering Multi-Dimensional Preferences of Users. *World Electric Vehicle Journal*. 2023; 14(7):171.
https://doi.org/10.3390/wevj14070171

**Chicago/Turabian Style**

Zuo, Xiaolong, Jun Bi, Yongxing Wang, and Yujia Du.
2023. "A Charging Guidance Optimization Model for Electric Vehicle Travel by Considering Multi-Dimensional Preferences of Users" *World Electric Vehicle Journal* 14, no. 7: 171.
https://doi.org/10.3390/wevj14070171