3D UAV Route Optimization in Complex Environments Using an Enhanced Artificial Lemming Algorithm
Abstract
1. Introduction
- (1)
- A multi-environment UAV logistics delivery route planning model was constructed. This model is capable of simulating the logistics delivery environments in mountainous and urban areas.
- (2)
- In an urban environment, the environment is only rasterized in a two-dimensional space and the restriction that candidate points can only be at the grid centers is removed, allowing the UAV to select route points more freely and, thus, conforming it to the actual delivery environments.
- (3)
- Aiming at the problem that the artificial lemming algorithm (ALA) is prone to falling into local optimal solutions, three improvement strategies were applied to the original ALA algorithm, thus forming a new multi-strategy improved artificial lemming algorithm (MsIALA).
- (4)
- The improved algorithm was perfectly integrated with the proposed model, demonstrating the effectiveness and high efficiency of the algorithm and providing a certain reference for the 3D route planning of UAV logistics delivery.
2. Multi-Environment Logistics Delivery Route Planning Model Based on UAV
2.1. Environmental Model
- (a)
- Mountainous environments
- (b)
- Urban environments
2.2. UAV Dynamics Model
2.3. Route Generation and Smoothing
2.3.1. Encoding and Decoding
- (a)
- The x-coordinates of all points are sequentially placed in the first positions.
- (b)
- The y-coordinates are placed in the middle positions.
- (c)
- The z-coordinates occupy the last positions.
2.3.2. Cubic Spline Interpolation
- (a)
- ;
- (b)
- (c)
- On each sub-interval , is a cubic polynomial.
2.4. UAV Logistics Delivery 3D Route Planning Model
2.4.1. Cost Function Design
- (a)
- Route length
- (b)
- Flight fluctuation
2.4.2. Constraints
- (a)
- Flight length
- (b)
- Goods weight
- (c)
- Yaw angle constraint
- (d)
- Pitch angle constraint
- (e)
- Obstacle constraint
3. Multi-Strategy Improved Artificial Lemming Algorithm
3.1. Principle of Artificial Lemming Algorithm
- (a)
- Long-distance migration
- (b)
- Digging holes
- (c)
- Foraging
- (d)
- Evading predators
3.2. Improvement Strategies
3.2.1. Cubic Chaotic Map Initialization
3.2.2. Double Adaptive T-Distribution Perturbation
3.2.3. Population Dynamic Optimization
3.3. Algorithm Flow and Computational Complexity
Algorithm 1. Multi-strategy improved artificial lemming algorithm. |
Input: The maximum iterations ; the size of the population ; the dimension size . |
Output: The optimal position ; the optimal fitness value .
|
|
3.4. Data Experiment
4. Simulation Experiment and Result Analysis
4.1. Experimental Environment and Parameter Settings
4.2. Experimental Results
4.3. Stability Analysis
5. Summary and Outlook
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Function | Dimension | Variable Interval | Theoretical Best |
---|---|---|---|
30 | [−100, 100] | 0 | |
30 | [−10, 10] | 0 | |
30 | [−100, 100] | 0 | |
30 | [−100, 100] | 0 | |
30 | [−100, 100] | 0 | |
30 | [−1.28, 1.28] | 0 | |
30 | [−5.12, 5.12] | 0 | |
30 | [−32, 32] | 0 | |
30 | [−600, 600] | 0 | |
4 | [0, 10] | −10 |
Function | Index | PSO [21] | LO [22] | WOA [23] | DBO [24] | ALA [19] | MsIALA |
---|---|---|---|---|---|---|---|
F1 | min | 3.3242 × 10−7 | 2.4920 × 10−9 | 2.6029 × 10−191 | 0 | 1.0525 × 10−13 | 0 |
avg | 6.9896 × 10−6 | 9.9626 × 10−9 | 8.7434 × 10−173 | 4.4799 × 10−242 | 4.2962 × 10−12 | 0 | |
std | 6.0767 × 10−6 | 6.7974 × 10−9 | 0 | 0 | 6.4890 × 10−12 | 0 | |
rank | 6 | 5 | 3 | 2 | 4 | 1 | |
F2 | min | 1.0305 × 10−5 | 1.2161 × 10−8 | 4.7842 × 10−118 | 3.4470 × 10−164 | 4.3032 × 10−8 | 0 |
avg | 9.5755 × 10−5 | 3.6532 × 10−8 | 3.6048 × 10−108 | 7.7406 × 10−116 | 7.4625 × 10−7 | 0 | |
std | 7.7301 × 10−5 | 2.1566 × 10−8 | 1.5532 × 10−107 | 4.2394 × 10−115 | 1.0019 × 10−6 | 0 | |
rank | 6 | 4 | 3 | 2 | 5 | 1 | |
F3 | min | 1.0758 × 102 | 3.6240 × 103 | 9.0110 × 101 | 1.6612 × 10−302 | 5.2294 × 10−7 | 0 |
avg | 2.9602 × 102 | 6.8778 × 103 | 1.1289 × 104 | 1.0380 × 10−81 | 8.5696 × 10−6 | 0 | |
std | 1.5206 × 102 | 2.3929 × 103 | 7.9584 × 103 | 5.6854 × 10−81 | 5.9557 × 10−6 | 0 | |
rank | 4 | 5 | 6 | 2 | 3 | 1 | |
F4 | min | 1.6186 | 1.3287 × 101 | 3.8734 × 10−2 | 2.9150 × 10−159 | 1.2411 × 10−3 | 0 |
avg | 3.2801 | 2.5391 × 101 | 2.4754 × 101 | 9.9028 × 10−111 | 2.0928 × 10−3 | 0 | |
std | 9.3955 × 10−1 | 5.9376 | 2.5915 × 101 | 5.4240 × 10−110 | 5.1219 × 10−4 | 0 | |
rank | 4 | 6 | 5 | 2 | 3 | 1 | |
F5 | min | 9.0341 × 10−8 | 7.9580 × 10−10 | 9.9785 × 10−4 | 4.3750 × 10−20 | 1.8851 × 10−17 | 1.5155 × 10−19 |
avg | 1.5058 × 10−5 | 1.5998 × 10−8 | 1.0662 × 10−2 | 1.1032 × 10−17 | 6.4047 × 10−15 | 7.8822 × 10−18 | |
std | 4.8925 × 10−5 | 1.8316 × 10−8 | 3.6293 × 10−2 | 2.0447 × 10−17 | 2.8089 × 10−14 | 1.1270 × 10−17 | |
rank | 5 | 4 | 6 | 2 | 3 | 1 | |
F6 | min | 9.0231 × 10−3 | 1.3055 × 10−2 | 1.6601 × 10−5 | 9.3644 × 10−5 | 4.1837 × 10−5 | 6.3925 × 10−7 |
avg | 1.9319 × 10−2 | 3.5652 × 10−2 | 1.1118 × 10−3 | 9.7710 × 10−4 | 8.4487 × 10−4 | 3.8916 × 10−5 | |
std | 5.6102 × 10−3 | 1.2317 × 10−2 | 1.1345 × 10−3 | 8.8982 × 10−4 | 6.7041 × 10−4 | 3.4013 × 10−5 | |
rank | 5 | 6 | 4 | 3 | 2 | 1 | |
F7 | min | 2.0036 × 101 | 1.5477 × 101 | 0 | 0 | 2.6205 × 10−11 | 0 |
avg | 3.7507 × 101 | 3.0337 × 101 | 0 | 1.2409 × 101 | 2.3216 × 10−1 | 0 | |
std | 1.0367 × 101 | 8.3687 | 0 | 3.8427 × 101 | 5.0147 × 10−1 | 0 | |
rank | 5 | 4 | 1 | 3 | 2 | 1 | |
F8 | min | 1.3568 × 10−4 | 8.9129 × 10−6 | 4.4409 × 10−16 | 4.4409 × 10−16 | 3.6721 × 10−7 | 4.4409 × 10−16 |
avg | 8.5912 × 10−4 | 3.2615 × 10−5 | 3.0494 × 10−15 | 5.6251 × 10−16 | 6.8409 × 10−6 | 4.4409 × 10−16 | |
std | 7.3137 × 10−4 | 1.3461 × 10−5 | 2.0723 × 10−15 | 6.4863 × 10−16 | 9.8553 × 10−6 | 0 | |
rank | 6 | 5 | 2 | 3 | 4 | 1 | |
F9 | min | 1.1316 × 10−6 | 1.2785 × 10−8 | 0 | 0 | 2.1755 × 10−12 | 0 |
avg | 1.8485 × 10−2 | 4.7617 × 10−3 | 1.2419 × 10−3 | 3.3561 × 10−3 | 5.8549 × 10−11 | 0 | |
std | 2.4299 × 10−2 | 7.6158 × 10−3 | 6.8020 × 10−3 | 1.2966 × 10−2 | 8.0085 × 10−11 | 0 | |
rank | 6 | 5 | 3 | 4 | 2 | 1 | |
F10 | min | −1.0403 × 101 | −1.0403 × 101 | −1.0403 × 101 | −1.0403 × 101 | −1.0403 × 101 | −1.0403 × 101 |
avg | −7.9169 | −1.0403 × 101 | −9.7937 | −7.6334 | −9.6488 | −1.0403 × 101 | |
std | 3.4054 | 4.5308 × 10−12 | 1.8909 | 2.8565 | 1.9678 | 9.8958 × 10−16 | |
rank | 4 | 1 | 2 | 5 | 3 | 1 |
Parameter | Value | Parameter | Value |
---|---|---|---|
/km | 5 | π/2 | |
/kg | 10 | α1 | 0.6 |
π/2 | α2 | 0.4 |
Environment | Algorithm | PSO | WOA | DBO | ALA | MsIALA | |
---|---|---|---|---|---|---|---|
Index | |||||||
Mountainous 1 | min | 156.87 | 231.39 | 141.58 | 143.65 | 143.71 | |
avg | 199.96 | 294.18 | 193.72 | 168.17 | 160.44 | ||
std | 46.99 | 60.76 | 36.74 | 22.51 | 11.78 | ||
failure rate | 26.67% | 36.67% | 0 | 0 | 0 | ||
Mountainous 2 | min | 155.75 | 150.68 | 140.54 | 141.96 | 140.42 | |
avg | 247.42 | 261.66 | 203.13 | 195.92 | 167.42 | ||
std | 64.60 | 71.50 | 50.46 | 37.66 | 17.61 | ||
failure rate | 56.67% | 53.33% | 6.67% | 10.00% | 0 | ||
Urban 1 | min | 293.18 | 293.35 | 286.11 | 286.06 | 285.44 | |
avg | 302.68 | 322.07 | 297.61 | 299.52 | 290.34 | ||
std | 6.41 | 13.87 | 11.75 | 12.05 | 5.85 | ||
failure rate | 0 | 0 | 0 | 0 | 0 | ||
Urban 2 | min | 301.67 | 299.01 | 296.25 | 295.73 | 294.34 | |
avg | 315.88 | 347.65 | 320.47 | 323.74 | 301.98 | ||
std | 12.96 | 30.93 | 43.42 | 23.39 | 7.61 | ||
failure rate | 23.33% | 43.33% | 0 | 3.33% | 0 |
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Xie, Y.; Sun, Z.; Yuan, K.; Sun, Z. 3D UAV Route Optimization in Complex Environments Using an Enhanced Artificial Lemming Algorithm. Symmetry 2025, 17, 946. https://doi.org/10.3390/sym17060946
Xie Y, Sun Z, Yuan K, Sun Z. 3D UAV Route Optimization in Complex Environments Using an Enhanced Artificial Lemming Algorithm. Symmetry. 2025; 17(6):946. https://doi.org/10.3390/sym17060946
Chicago/Turabian StyleXie, Yuxuan, Zhe Sun, Kai Yuan, and Zhixin Sun. 2025. "3D UAV Route Optimization in Complex Environments Using an Enhanced Artificial Lemming Algorithm" Symmetry 17, no. 6: 946. https://doi.org/10.3390/sym17060946
APA StyleXie, Y., Sun, Z., Yuan, K., & Sun, Z. (2025). 3D UAV Route Optimization in Complex Environments Using an Enhanced Artificial Lemming Algorithm. Symmetry, 17(6), 946. https://doi.org/10.3390/sym17060946