Integrating Environmental and Economic Considerations in Charging Station Planning: An Improved Quantum Genetic Algorithm
Abstract
:1. Introduction
- IQGA introduces a dynamic quantum rotation angle that adapts based on the number of iterations. By adjusting the rotation angle, the algorithm can strike a balance between exploration and exploitation, enabling faster convergence towards optimal solutions. This dynamic adjustment mechanism ensures efficient exploration of the search space, leading to improved solution quality.
- IQGA incorporates the concept of simulated annealing into the population updating process. Simulated annealing helps the algorithm escape local optima by allowing occasional acceptance of solutions that are worse than the current best. This mechanism prevents premature convergence and promotes exploration of the solution space, enhancing the algorithm’s ability to discover high-quality solutions.
2. Location and Sizing Model of the CSs
2.1. Model Objectives
2.1.1. Construction Cost
2.1.2. Operating Cost
2.1.3. User Charging Cost
2.1.4. Carbon Emissions Cost
2.2. Constraints
3. Algorithms
3.1. IQGA
- (1)
- Dynamic changes in the quantum rotation angle: the size of the quantum rotation angle is adjusted from a fixed value to a dynamic value. The original parameter value () is modified using the following formula to determine the value of :
- (2)
- Simulated annealing strategy: SAA uses the probabilistic jump property to explore the solution space and avoid local optima. By introducing controlled randomness and allowing occasional acceptance of worse solutions, SAA enables the algorithm to make exploratory moves and potentially discover better solutions that may lie outside the immediate vicinity of the current solution.
Algorithm 1 IQGA |
|
3.2. Function Testing
4. Case Study
5. Conclusions
6. Future Research
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Category | Description |
---|---|
Sets | |
J | Set of candidate CS |
I | Set of demand points |
Parameters | |
Fixed investment cost for constructing CS j | |
Unit price of chargers | |
S | The area required by a single charger |
The unit land price of CS j | |
The coefficient that converts the construction cost into the annual operating cost | |
Discount rate | |
Expected operating life of the CS | |
Coefficient converting construction cost to annual operating cost | |
Average daily number of EVs to be charged at demand point i | |
Road curvature coefficient | |
Euclidean distance from demand point i to CS j | |
P | Unit cost of EV charging (yuan/kWh) |
E | Power consumption of an EV per kilometer traveled (kWh/km) |
Average waiting time of an EV at CS j | |
Coefficient converting unit waiting cost to unit cost of EV charging | |
Average charging rate of one charger | |
Average daily number of EVs arriving at CS j | |
Utilization factor of chargers at CS j | |
Probability that CS j is idle | |
c | Carbon emission factor (gCO2/km) |
Transmission efficiency of the distribution power network | |
The carbon emission factor of power grid | |
Carbon emission price from the national carbon trading market | |
Decision Variables | |
Binary variable indicating whether CS j is selected | |
Binary variable indicating whether EVs from demand point i go to CS j for charging | |
Number of chargers to be installed in CS j |
Function | Function Expression | Interval | Global Minimum Value | Dimension D |
---|---|---|---|---|
(−32.768, 32.768) | 0 | 30 | ||
(−5.12, 5.12) | 0 | 30 | ||
(−600, 600) | 0 | 30 | ||
0 | 300 | |||
−959.6407 | 300 | |||
0 | 300 |
Functions | |||||||
---|---|---|---|---|---|---|---|
Algorithms | |||||||
IQGA | Optimum value | 8.88 × | 0 | 0 | 0.02 | −895.09 | 0 |
Average value | 8.88 × | 0 | 0 | 0.05 | −888.63 | 5.17 × | |
Average gap | 8.88 × | 0 | 0 | 0.05 | 71.05 | 5.17 × | |
Running time (s) | 7.62 | 8.17 | 6.07 | 47.31 | 35.44 | 34.15 | |
FWA | Optimum value | 2.93 × | 0 | 0.01 | 0.04 | −857.10 | 0.50 |
Average value | 3.34 × | 3.84 × | 0.03 | 3.95 | −850.03 | 0.50 | |
Average gap | 3.34 × | 3.84 × | 0.03 | 3.95 | 109.61 | 0.50 | |
Running time (s) | 5.43 | 4.96 | 5.94 | 46.38 | 40.27 | 49.98 | |
WOA | Optimum value | 4.44 × | 0 | 0 | 0.05 | −793.60 | 0 |
Average value | 1.90 × | 0.53 | 4.60 × | 0.05 | −740.69 | 0.33 | |
Average gap | 1.90 × | 0.53 | 4.60 × | 0.05 | 218.95 | 0.33 | |
Running time (s) | 5.113 | 4.933 | 16.50 | 10.16 | 10.92 | 11.04 | |
IWO | Optimum value | 2.06 × | 1.82 × | 0.40 | 3.6 × | −701.07 | 0.50 |
Average value | 7.41 | 0.40 | 8.34 | 0.34 | −523.87 | 0.50 | |
Average gap | 7.41 | 0.40 | 8.34 | 0.34 | 435.77 | 0.50 | |
Running time (s) | 2.51 | 3.31 | 7.23 | 31.48 | 30.74 | 52.35 | |
GWO | Optimum value | 4.44 × | 0 | 0 | 0.90 | −880.87 | 0 |
Average value | 2.25 × | 1.30 × | 9.49 × | 2.72 | −869.42 | 0.14 | |
Average gap | 2.25 × | 1.30 × | 9.49 × | 2.72 | 90.22 | 0.14 | |
Running time (s) | 3.43 | 2.73 | 5.52 | 34.57 | 43.08 | 24.25 | |
QGA | Optimum value | 4.11 × | 1.81 × | 1.35 × | 0.08 | −875.08 | 1.09 × |
Average value | 1.34 × | 3.82 × | 7.60 × | 0.30 | −835.09 | 2.44 × | |
Average gap | 1.34 × | 3.82 × | 7.60 × | 0.30 | 124.55 | 2.44 × | |
Running time (s) | 5.53 | 9.52 | 6.13 | 40.12 | 28.64 | 33.16 |
Optimization Solution (Number of CSs/Number of Chargers) | Total Cost | |||||
---|---|---|---|---|---|---|
1 | 210/23,200 | 247.3 | 219.9 | 47 | 23.09 | 536.29 |
2 | 95/15,500 | 144.9 | 123.7 | 53.01 | 31.81 | 353.42 |
3 | 65/12,600 | 161 | 149 | 58.34 | 37.7 | 406.04 |
4 | 45/9340 | 173.5 | 155.2 | 71.65 | 51.42 | 451.77 |
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Hu, D.; Li, X.; Liu, C.; Liu, Z.-W. Integrating Environmental and Economic Considerations in Charging Station Planning: An Improved Quantum Genetic Algorithm. Sustainability 2024, 16, 1158. https://doi.org/10.3390/su16031158
Hu D, Li X, Liu C, Liu Z-W. Integrating Environmental and Economic Considerations in Charging Station Planning: An Improved Quantum Genetic Algorithm. Sustainability. 2024; 16(3):1158. https://doi.org/10.3390/su16031158
Chicago/Turabian StyleHu, Dandan, Xiongkai Li, Chen Liu, and Zhi-Wei Liu. 2024. "Integrating Environmental and Economic Considerations in Charging Station Planning: An Improved Quantum Genetic Algorithm" Sustainability 16, no. 3: 1158. https://doi.org/10.3390/su16031158