IHSSAO: An Improved Hybrid Salp Swarm Algorithm and Aquila Optimizer for UAV Path Planning in Complex Terrain
Abstract
:1. Introduction
- We integrate the leader mechanism of SSA into the position update formulation of the AO, which enables the search individuals to fully utilize the information of the optimal solution and enhances the global search capability of the proposed algorithm.
- Tent chaotic map helps the IHSSAO to increase the original population diversity.
- PIOBL helps the proposed algorithm to increase the original population diversity and the capability to escape from local optima.
- To verify the performance of the proposed IHSSAO, we tested it against the SSA, AO, and five other advanced meta-heuristic algorithms by 23 classical benchmark functions and 17 IEEE CEC2017 test functions.
- Eventually, we applied the IHSSAO, SSA, and AO to the UAV path planning problem. The experimental results verify that the proposed IHSSAO is superior to the basic SSA and AO in solving the path planning problem for UAVs in complex terrain.
2. Preliminary Knowledge
2.1. Salp Swarm Algorithm
2.2. Aquila Optimizer
2.2.1. Expanded Exploration ()
2.2.2. Narrowed Exploration ()
2.2.3. Expanded Exploitation ()
2.2.4. Narrowed Exploitation ()
2.3. Tent Chaotic Map
- Step 1:
- Randomly generate between the intervals (avoiding in small periods , , .
- Step 2:
- Iterate through Equation (21) to obtain a sequence of , .
- Step 3:
- If the maximum number of iterations is reached, then turn to Step 4. Otherwise, if or , change the initial value of the iteration by the equation where is a random number, . Otherwise return Step 2.
- Step 4:
- The operation is halted and the sequence is retained.
2.4. Pinhole Imaging Opposition-Based Learning
3. The Proposed Algorithm
Algorithm 1 Pseudo-code of the proposed IHSSAO algorithm |
1. Input the population , and the generation number |
2. Initialize the positions of each individual by tent chaotic map //tent chaotic map |
3. While |
4. Check if the position goes beyond the search space boundary and then adjust it |
5. Evaluate the fitness values of all search agents |
6. Update the global optimum |
7. using Equation (3) //SSA |
8. For to |
9. If t ≤ T then //AO |
10. If then |
11. Update the position using Equation (6) |
12. Else |
13. Update the position using Equation (8) |
14. End if |
15. Else |
16. If then |
17. Update the position using Equation (15) |
18. Else |
19. Update the position using Equation (16) |
20. End if |
21. End if |
22. End For |
23. Generate the opposite position of using Equation (24) and save the one with better fitness //PIOBL |
24. |
25. End While |
26. Return |
4. Experimental Results and Discussion of IHSSAO Performance Verification
4.1. Experiment I: Classical Benchmark Function
4.1.1. Parameter Setting
4.1.2. Assessment Standards of Performance
4.1.3. Comparison with IHSSAO and Other Algorithms
4.1.4. Scalability Test
4.2. Experiment II: IEEE CEC2017 Test Functions
5. IHSSAO for Solving UAV Path Planning in Complex Terrain
5.1. UAV Mission Environment Modeling
5.1.1. Terrain Constraints
5.1.2. Threat Constraints
5.2. UAV Path Planning Modeling
5.3. Simulation Results and Analysis of UAV Path Planning in Complex Terrain
5.3.1. Parameter Settings
5.3.2. Simulation Results and Analysis
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Function | Name | Dim | Range | Fmin |
---|---|---|---|---|
Sphere | 30 | [−100, 100] | 0 | |
Schwefel 2.22 | 30 | [−10, 10] | 0 | |
Schwefel 1.2 | 30 | [−100, 100] | 0 | |
Schwefel 2.21 | 30 | [−100, 100] | 0 | |
Rosenbrock | 30 | [−30, 30] | 0 | |
Step | 30 | [−100, 100] | 0 | |
Quartic | 30 | [−1.28, 1.28] | 0 |
Function | Name | Dim | Range | Fmin |
---|---|---|---|---|
Schwefel 2.26 | 30 | [−500, 500] | −418.9829 × Dim | |
Rastrigin | 30 | [−5.12, 5.12] | 0 | |
Ackley | 30 | [−32, 32] | 0 | |
Griewank | 30 | [−600, 600] | 0 | |
Penalized | 30 | [−50, 50] | 0 | |
Penalized2 | 30 | [−50, 50] | 0 |
Function | Name | Dim | Range | Fmin |
---|---|---|---|---|
Foxholes | 2 | [−65, 65] | 0.998 | |
Kowalik | 4 | [−5, 5] | 0.00030 | |
Six-hump Camel Back | 2 | [−5, 5] | −1.0316 | |
Branin | 2 | [−5, 5] | 0.398 | |
Goldstein Price | 2 | [−2, 2] | 3 | |
Hartman 3 | 3 | [−1, 2] | −3.8628 | |
Hartman 6 | 6 | [0, 1] | −3.32 | |
Langermann 5 | 4 | [0, 10] | −10.1532 | |
Langermann 7 | 4 | [0, 10] | −10.4028 | |
Langermann 10 | 4 | [0, 10] | −10.5363 |
Algorithm | Parameters |
---|---|
WOA [13] | |
HHO [14] | |
SSA [16] | |
MVO [34] | |
STOA [35] | |
TSA [36] | |
AO [23] |
Metric | WOA | HHO | SSA | MVO | STOA | TSA | AO | IHSSAO | |
---|---|---|---|---|---|---|---|---|---|
Avg | 3.07 × 10−72 | 3.72 × 10−94 | 1.53 × 10−7 | 1.17 × 100 | 8.28 × 10−7 | 2.46 × 10−21 | 1.56 × 10−104 | 0.00 × 100 | |
Std | 1.37 × 10−71 | 1.84 × 10−93 | 1.29 × 10−7 | 3.35 × 10−1 | 1.41 × 10−6 | 5.54 × 10−21 | 8.52 × 10−104 | 0.00 × 100 | |
Avg | 2.06 × 10−51 | 3.17 × 10−50 | 2.32 × 100 | 9.27 × 10−1 | 7.97 × 10−6 | 1.06 × 10−13 | 8.53 × 10−57 | 0.00 × 100 | |
Std | 8.00 × 10−51 | 9.82 × 10−50 | 1.95 × 100 | 4.70 × 10−1 | 6.96 × 10−6 | 1.29 × 10−13 | 3.76 × 10−56 | 0.00 × 100 | |
Avg | 4.24 × 104 | 1.07 × 10−76 | 1.72 × 103 | 1.92 × 102 | 8.82 × 10−2 | 8.91 × 10−5 | 1.58 × 10−101 | 0.00 × 100 | |
Std | 1.51 × 104 | 5.82 × 10−76 | 9.89 × 102 | 6.60 × 101 | 1.57 × 10−1 | 2.42 × 10−4 | 8.63 × 10−101 | 0.00 × 100 | |
Avg | 4.89 × 101 | 3.43 × 10−47 | 1.15 × 101 | 1.81 × 100 | 6.38 × 10−2 | 2.70 × 10−1 | 9.68 × 10−54 | 0.00 × 100 | |
Std | 2.95 × 101 | 1.87 × 10−46 | 2.81 × 100 | 6.14 × 10−1 | 8.84 × 10−2 | 2.29 × 10−1 | 3.16 × 10−53 | 0.00 × 100 | |
Avg | 2.80 × 101 | 1.02 × 10−2 | 2.76 × 102 | 6.11 × 102 | 2.84 × 101 | 2.81 × 101 | 5.80 × 10−3 | 2.49 × 10−5 | |
Std | 5.37 × 10−1 | 1.14 × 10−2 | 4.50 × 102 | 8.88 × 102 | 4.74 × 10−1 | 7.85 × 10−1 | 1.05 × 10−2 | 1.11 × 10−4 | |
Avg | 4.42 × 10−1 | 7.32 × 10−5 | 4.68 × 10−7 | 1.22 × 100 | 2.65 × 100 | 3.74 × 100 | 7.58 × 10−4 | 2.45 × 10−5 | |
Std | 2.25 × 10−1 | 8.16 × 10−5 | 1.41 × 10−6 | 4.04 × 10−1 | 6.06 × 10−1 | 7.28 × 10−1 | 1.69 × 10−3 | 3.68 × 10−5 | |
Avg | 2.53 × 10−3 | 1.59 × 10−4 | 1.89 × 10−1 | 3.02 × 10−2 | 5.66 × 10−3 | 1.20 × 10−2 | 1.08 × 10−4 | 4.30 × 10−5 | |
Std | 3.51 × 10−3 | 1.20 × 10−4 | 7.17 × 10−2 | 1.29 × 10−2 | 3.24 × 10−3 | 4.71 × 10−3 | 1.14 × 10−4 | 3.86 × 10−5 | |
Avg | −10,228.40 | −12,542.39 | −43,759.37 | −7419.26 | −5252.57 | −5819.64 | −9949.91 | −12,569.42 | |
Std | 1.86 × 103 | 1.11 × 102 | 7.84 × 103 | 6.31 × 102 | 6.62 × 102 | 6.81 × 102 | 3.65 × 103 | 1.30 × 10−1 | |
Avg | 3.79 × 10−15 | 0.00 × 100 | 5.29 × 101 | 1.12 × 102 | 9.92 × 100 | 1.81 × 102 | 0.00 × 100 | 0.00 × 100 | |
Std | 1.44 × 10−14 | 0.00 × 100 | 1.81 × 101 | 2.56 × 101 | 1.38 × 101 | 4.76 × 101 | 0.00 × 100 | 0.00 × 100 | |
Avg | 4.20 × 10−15 | 8.88 × 10−16 | 2.63 × 100 | 1.96 × 100 | 2.00 × 101 | 1.66 × 100 | 8.88 × 10−16 | 8.88 × 10−16 | |
Std | 2.46 × 10−15 | 0.00 × 100 | 9.37 × 10−1 | 6.16 × 10−1 | 1.41 × 10−3 | 1.73 × 100 | 0.00 × 100 | 0.00 × 100 | |
Avg | 0.00 × 100 | 0.00 × 100 | 2.21 × 10−2 | 8.73 × 10−1 | 3.64 × 10−2 | 7.19 × 10−3 | 0.00 × 100 | 0.00 × 100 | |
Std | 0.00 × 100 | 0.00 × 100 | 1.61 × 10−2 | 7.88 × 10−2 | 5.36 × 10−2 | 8.13 × 10−3 | 0.00 × 100 | 0.00 × 100 | |
Avg | 2.14 × 10−2 | 6.25 × 10−6 | 7.20 × 100 | 2.24 × 100 | 2.34 × 10−1 | 8.07 × 100 | 2.95 × 10−6 | 3.76 × 10−7 | |
Std | 1.34 × 10−2 | 9.13 × 10−6 | 3.23 × 100 | 1.34 × 100 | 7.20 × 10−2 | 5.44 × 100 | 5.55 × 10−6 | 9.21 × 10−7 | |
Avg | 5.03 × 10−1 | 9.14 × 10−5 | 1.61 × 101 | 2.17 × 10−1 | 1.91 × 100 | 3.13 × 100 | 1.50 × 10−5 | 2.17 × 10−6 | |
Std | 2.76 × 10−1 | 1.61 × 10−4 | 1.52 × 101 | 1.40 × 10−1 | 2.03 × 10−1 | 5.68 × 10−1 | 2.45 × 10−5 | 1.00 × 10−5 | |
Avg | 2.96 × 100 | 1.10 × 100 | 1.30 × 100 | 9.98 × 10−1 | 1.46 × 100 | 7.93 × 100 | 2.89 × 100 | 1.09 × 100 | |
Std | 3.23 × 100 | 3.03 × 10−1 | 5.92 × 10−1 | 3.66 × 10−11 | 8.54 × 10−1 | 4.75 × 100 | 3.60 × 100 | 3.99 × 10−1 | |
Avg | 6.23 × 10−4 | 3.79 × 10−4 | 1.21 × 10−3 | 1.11 × 10−2 | 1.65 × 10−3 | 7.66 × 10−3 | 4.89 × 10−4 | 2.78 × 10−4 | |
Std | 2.69 × 10−4 | 1.69 × 10−4 | 8.83 × 10−4 | 1.82 × 10−2 | 3.55 × 10−3 | 1.29 × 10−2 | 7.91 × 10−5 | 3.89 × 10−5 | |
Avg | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0316 | −1.0295 | −1.0311 | −1.0316 | |
Std | 3.16 × 10−9 | 1.55 × 10−9 | 2.89 × 10−14 | 4.02 × 10−7 | 2.57 × 10−6 | 8.02 × 10−3 | 5.78 × 10−4 | 5.32 × 10−15 | |
Avg | 0.39789 | 0.39790 | 0.39789 | 0.39789 | 0.39808 | 0.39789 | 0.39841 | 0.39795 | |
Std | 7.07 × 10−6 | 2.86 × 10−5 | 1.55 × 10−14 | 5.72 × 10−7 | 2.31 × 10−4 | 7.35 × 10−5 | 1.14 × 10−3 | 7.61 × 10−15 | |
Avg | 3.0001 | 3.0000 | 3.0000 | 3.0000 | 3.0001 | 19.2000 | 3.0417 | 3.0000 | |
Std | 1.21 × 10−4 | 3.62 × 10−7 | 1.79 × 10−13 | 2.46 × 10−6 | 8.29 × 10−5 | 3.04 × 101 | 4.91 × 10−4 | 2.12 × 10−10 | |
Avg | −3.8536 | −3.8583 | −3.8628 | −3.8628 | −3.8551 | −3.8624 | −3.8547 | −3.8628 | |
Std | 1.94 × 10−2 | 7.12 × 10−3 | 9.15 × 10−6 | 4.94 × 10−6 | 1.49 × 10−3 | 1.36 × 10−3 | 6.47 × 10−3 | 4.65 × 10−5 | |
Avg | −3.1361 | −3.1408 | −3.2078 | −3.2737 | −2.8436 | −3.2517 | −3.1270 | −3.1515 | |
Std | 2.28 × 10−1 | 9.11 × 10−2 | 1.44 × 10−1 | 6.02 × 10−2 | 5.71 × 10−1 | 6.74 × 10−2 | 1.34 × 10−1 | 1.06 × 10−1 | |
Avg | −8.1795 | −5.3744 | −7.3534 | −6.6234 | −2.8881 | −6.1994 | −10.1360 | −10.1500 | |
Std | 2.63 × 100 | 1.23 × 100 | 2.70 × 100 | 3.07 × 100 | 3.58 × 100 | 3.20 × 100 | 3.63 × 10−2 | 9.98 × 10−3 | |
Avg | −7.4821 | −5.0033 | −7.3910 | −8.6779 | −6.4799 | −7.1649 | −10.3930 | −10.4012 | |
Std | 2.99 × 100 | 4.30 × 10−1 | 2.68 × 100 | 2.97 × 100 | 4.10 × 100 | 3.54 × 100 | 1.86 × 10−2 | 3.49 × 10−3 | |
Avg | −7.5302 | −5.2127 | −7.5969 | −9.2142 | −8.0707 | −7.6860 | −10.5180 | −10.5343 | |
Std | 3.19 × 100 | 1.11 × 100 | 3.32 × 100 | 2.75 × 100 | 3.78 × 100 | 3.65 × 100 | 3.49 × 10−2 | 5.42 × 10−3 |
Fn | IHSSAO vs. WOA | IHSSAO vs. HHO | IHSSAO vs. SSA | IHSSAO vs. MVO | IHSSAO vs. STOA | IHSSAO vs. TSA | IHSSAO vs. AO |
---|---|---|---|---|---|---|---|
1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | |
1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | |
1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | |
1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | |
3.02 × 10−11 | 2.87 × 10−10 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 1.17 × 10−9 | |
3.02 × 10−11 | 1.86 × 10−6 | 3.26 × 10−1 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 9.51 × 10−6 | |
8.10 × 10−10 | 1.34 × 10−5 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 2.32 × 10−2 | |
2.72 × 10−11 | 6.92 × 10−5 | 2.72 × 10−11 | 2.72 × 10−11 | 2.72 × 10−11 | 2.72 × 10−11 | 2.72 × 10−11 | |
1.61 × 10−5 | NaN | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | NaN | |
1.09 × 10−8 | NaN | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | NaN | |
NaN | NaN | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.27 × 10−5 | NaN | |
3.02 × 10−11 | 3.09 × 10−6 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 1.87 × 10−5 | |
3.02 × 10−11 | 4.44 × 10−7 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 4.94 × 10−5 | |
2.38 × 10−3 | 6.97 × 10−3 | 4.67 × 10−8 | 2.83 × 10−8 | 9.79 × 10−5 | 2.15 × 10−10 | 8.56 × 10−4 | |
1.03 × 10−3 | 3.96 × 10−8 | 1.10 × 10−8 | 5.46 × 10−9 | 1.03 × 10−6 | 1.37 × 10−6 | 3.11 × 10−3 | |
1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 7.47 × 10−10 | 7.47 × 10−10 | |
1.21 × 10−12 | 7.47 × 10−10 | 1.16 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | 1.21 × 10−12 | |
4.57 × 10−9 | 3.34 × 10−11 | 3.02 × 10−11 | 4.20 × 10−10 | 3.65 × 10−8 | 7.73 × 10−6 | 1.91 × 10−1 | |
1.89 × 10−2 | 3.50 × 10−1 | 1.72 × 10−12 | 1.72 × 10−12 | 1.72 × 10−12 | 4.56 × 10−11 | 1.67 × 10−8 | |
5.59 × 10−5 | 3.71 × 10−3 | 3.03 × 10−2 | 3.16 × 10−5 | 5.97 × 10−5 | 1.44 × 10−3 | 4.29 × 10−3 | |
8.15 × 10−11 | 2.72 × 10−11 | 6.62 × 10−10 | 3.39 × 10−8 | 2.72 × 10−11 | 2.72 × 10−11 | 1.57 × 10−8 | |
2.37 × 10−10 | 3.02 × 10−11 | 3.79 × 10−10 | 1.81 × 10−8 | 3.69 × 10−11 | 3.02 × 10−11 | 1.78 × 10−4 | |
2.92 × 10−9 | 3.02 × 10−11 | 6.63 × 10−10 | 1.62 × 10−1 | 3.02 × 10−11 | 3.02 × 10−11 | 6.74 × 10−6 | |
+ | 22 | 19 | 22 | 22 | 23 | 23 | 19 |
= | 1 | 3 | 0 | 0 | 0 | 0 | 3 |
− | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
50 | 100 | 500 | |||||||
---|---|---|---|---|---|---|---|---|---|
SSA | AO | IHSSAO | SSA | AO | IHSSAO | SSA | AO | IHSSAO | |
7.81 × 10−1 | 3.02 × 10−103 | 0.00 × 100 | 1.44 × 103 | 5.05 × 10−100 | 0.00 × 100 | 9.75 × 104 | 1.52 × 10−100 | 0.00 × 100 | |
8.85 × 100 | 2.18 × 10−52 | 0.00 × 100 | 4.79 × 101 | 1.61 × 10−61 | 0.00 × 100 | 5.38 × 102 | 3.90 × 10−53 | 0.00 × 100 | |
1.00 × 104 | 3.56 × 10−103 | 0.00 × 100 | 5.46 × 104 | 6.3974 × 10−103 | 0.00 × 100 | 1.42 × 106 | 4.36 × 10−94 | 0.00 × 100 | |
1.93 × 101 | 5.45 × 10−60 | 0.00 × 100 | 2.84 × 101 | 2.37 × 10−58 | 0.00 × 100 | 4.06 × 101 | 4.93 × 10−53 | 0.00 × 100 | |
1.94 × 103 | 6.82 × 10−3 | 1.96 × 10−5 | 1.87 × 105 | 1.02 × 10−2 | 1.28 × 10−3 | 3.66 × 107 | 9.30 × 10−2 | 2.71 × 10−3 | |
9.78 × 10−1 | 8.21 × 10−4 | 4.21 × 10−5 | 1.47 × 103 | 2.41 × 10−4 | 5.14 × 10−5 | 9.44 × 104 | 5.29 × 10−4 | 9.14 × 10−5 | |
6.31 × 10−1 | 8.95 × 10−3 | 8.57 × 10−5 | 2.71 × 100 | 1.00 × 10−4 | 6.02 × 10−5 | 2.97 × 102 | 1.32 × 10−4 | 6.47 × 10−5 | |
−66,521.07 | −9938.43 | −20,948.97 | −136,320.92 | −10,996.51 | −41,897.78 | −375,776.05 | −8215.47 | −209,486.77 | |
8.88 × 101 | 0.00 × 100 | 0.00 × 100 | 2.48 × 102 | 0.00 × 100 | 0.00 × 100 | 3.17 × 103 | 0.00 × 100 | 0.00 × 100 | |
4.63 × 100 | 8.88 × 10−16 | 8.88 × 10−16 | 1.02 × 101 | 8.88 × 10−16 | 8.88 × 10−16 | 1.43 × 101 | 8.88 × 10−16 | 8.88 × 10−16 | |
4.94 × 10−1 | 0.00 × 100 | 0.00 × 100 | 1.46 × 101 | 0.00 × 100 | 0.00 × 100 | 8.52 × 102 | 0.00 × 100 | 0.00 × 100 | |
1.43 × 101 | 4.86 × 10−6 | 1.65 × 10−7 | 3.50 × 101 | 2.18 × 10−6 | 3.64 × 10−7 | 1.61 × 106 | 7.83 × 10−6 | 5.47 × 10−7 | |
7.59 × 101 | 3.76 × 10−5 | 1.77 × 10−5 | 7.61 × 103 | 4.84 × 10−5 | 7.71 × 10−6 | 3.47 × 107 | 3.46 × 10−4 | 8.40 × 10−6 |
Function | Name | Dim | Range | Fmin |
---|---|---|---|---|
Simple multimodal functions | ||||
F24 | Shifted and Rotated Rosenbrock’s Function | 10 | [−100, 100] | 400 |
F25 | Shifted and Rotated Rastrigin’s Function | 10 | [−100, 100] | 500 |
F26 | Shifted and Rotated Expanded Scaffer’s F6 Function | 10 | [−100, 100] | 600 |
F27 | Shifted and Rotated Non-Continuous Rastrigin’s Function | 10 | [−100, 100] | 800 |
Hybrid functions | ||||
F28 | Hybrid Function 1 (N = 3) | 10 | [−100, 100] | 1100 |
F29 | Hybrid Function 3 (N = 3) | 10 | [−100, 100] | 1300 |
F30 | Hybrid Function 4 (N = 4) | 10 | [−100, 100] | 1400 |
F31 | Hybrid Function 5 (N = 4) | 10 | [−100, 100] | 1500 |
F32 | Hybrid Function 6 (N = 5) | 10 | [−100, 100] | 1700 |
F33 | Hybrid Function 6 (N = 6) | 10 | [−100, 100] | 2000 |
Composite Functions | ||||
F34 | Composition Function 2 (N = 3) | 10 | [−100, 100] | 2200 |
F35 | Composition Function 3 (N = 4) | 10 | [−100, 100] | 2300 |
F36 | Composition Function 4 (N = 4) | 10 | [−100, 100] | 2400 |
F37 | Composition Function 5 (N = 5) | 10 | [−100, 100] | 2500 |
F38 | Composition Function 6 (N = 5) | 10 | [−100, 100] | 2600 |
F39 | Composition Function 7 (N = 6) | 10 | [−100, 100] | 2700 |
F40 | Composition Function 9 (N = 3) | 10 | [−100, 100] | 2900 |
Fn | Metric | WOA | HHO | SSA | MVO | STOA | TSA | AO | IHSSAO |
---|---|---|---|---|---|---|---|---|---|
F24 | Mean | 4.50 × 102 | 4.37 × 102 | 4.19 × 102 | 4.22 × 102 | 4.44 × 102 | 5.37 × 102 | 4.29 × 102 | 4.18 × 102 |
Std | 5.10 × 101 | 3.92 × 101 | 2.55 × 101 | 1.73 × 101 | 2.86 × 101 | 1.49 × 102 | 3.49 × 101 | 2.44 × 101 | |
F25 | Mean | 5.54 × 102 | 5.60 × 102 | 5.37 × 102 | 5.22 × 102 | 5.31 × 102 | 5.60 × 102 | 5.35 × 102 | 5.29 × 102 |
Std | 2.04 × 101 | 1.52 × 101 | 1.42 × 101 | 1.41 × 101 | 1.08 × 101 | 2.15 × 101 | 1.34 × 101 | 1.12 × 101 | |
F26 | Mean | 6.43 × 102 | 6.42 × 102 | 6.21 × 102 | 6.12 × 102 | 6.15 × 102 | 6.37 × 102 | 6.20 × 102 | 6.19 × 102 |
Std | 1.16 × 101 | 8.50 × 100 | 1.42 × 101 | 4.67 × 100 | 6.75 × 100 | 1.51 × 101 | 7.58 × 100 | 6.38 × 100 | |
F27 | Mean | 8.40 × 102 | 8.33 × 102 | 8.32 × 102 | 8.26 × 102 | 8.31 × 102 | 8.53 × 102 | 8.30 × 102 | 8.25 × 102 |
Std | 1.34 × 101 | 1.14 × 101 | 1.46 × 101 | 9.95 × 100 | 9.50 × 100 | 1.97 × 101 | 9.01 × 100 | 6.95 × 100 | |
F28 | Mean | 1.24 × 103 | 1.21 × 103 | 1.29 × 103 | 1.16 × 103 | 1.27 × 103 | 3.95 × 103 | 1.25 × 103 | 1.19 × 103 |
Std | 9.53 × 101 | 6.19 × 101 | 1.66 × 102 | 3.52 × 101 | 9.64 × 101 | 2.75 × 103 | 1.91 × 102 | 8.29 × 101 | |
F29 | Mean | 1.62 × 104 | 2.08 × 104 | 3.63 × 104 | 1.67 × 104 | 2.37 × 104 | 1.71 × 106 | 2.00 × 104 | 1.49 × 104 |
Std | 1.24 × 104 | 1.50 × 104 | 4.62 × 104 | 1.48 × 104 | 1.56 × 104 | 5.19 × 106 | 1.43 × 104 | 1.07 × 104 | |
F30 | Mean | 2.89 × 103 | 1.84 × 103 | 5.10 × 103 | 3.41 × 103 | 5.19 × 103 | 4.23 × 103 | 2.81 × 103 | 2.30 × 103 |
Std | 1.51 × 103 | 5.71 × 102 | 8.37 × 103 | 2.90 × 103 | 4.29 × 103 | 1.99 × 103 | 2.18 × 103 | 1.18 × 103 | |
F31 | Mean | 1.03 × 104 | 7.22 × 103 | 1.32 × 104 | 2.52 × 103 | 6.17 × 103 | 1.14 × 104 | 7.66 × 103 | 5.87 × 103 |
Std | 8.92 × 103 | 3.30 × 103 | 1.57 × 104 | 1.89 × 103 | 4.23 × 103 | 9.14 × 103 | 4.54 × 103 | 2.68 × 103 | |
F32 | Mean | 1.81 × 103 | 1.80 × 103 | 1.82 × 103 | 1.79 × 103 | 1.78 × 103 | 1.85 × 103 | 1.78 × 103 | 1.75 × 103 |
Std | 6.61 × 101 | 9.01 × 101 | 7.58 × 101 | 5.61 × 101 | 3.93 × 101 | 1.01 × 102 | 3.05 × 101 | 2.47 × 101 | |
F33 | Mean | 2.22 × 103 | 2.17 × 103 | 2.15 × 103 | 2.13 × 103 | 2.15 × 103 | 2.20 × 103 | 2.14 × 103 | 2.12 × 103 |
Std | 7.67 × 101 | 6.23 × 101 | 7.84 × 101 | 6.98 × 101 | 7.15 × 101 | 6.13 × 101 | 5.96 × 101 | 4.28 × 101 | |
F34 | Mean | 2.40 × 103 | 2.39 × 103 | 2.44 × 103 | 2.35 × 103 | 2.90 × 103 | 2.64 × 103 | 2.31 × 103 | 2.28 × 103 |
Std | 2.91 × 102 | 3.26 × 102 | 3.61 × 102 | 1.96 × 102 | 6.75 × 102 | 3.79 × 102 | 1.46 × 101 | 1.03 × 101 | |
F35 | Mean | 2.67 × 103 | 2.68 × 103 | 2.65 × 103 | 2.66 × 103 | 2.64 × 103 | 2.71 × 103 | 2.65 × 103 | 2.63 × 103 |
Std | 3.08 × 101 | 2.49 × 101 | 1.36 × 101 | 3.40 × 101 | 1.55 × 101 | 4.05 × 101 | 2.17 × 101 | 1.10 × 101 | |
F36 | Mean | 2.77 × 103 | 2.78 × 103 | 2.79 × 103 | 2.75 × 103 | 2.76 × 103 | 2.82 × 103 | 2.75 × 103 | 2.74 × 103 |
Std | 5.46 × 101 | 1.37 × 102 | 6.99 × 101 | 6.44 × 101 | 1.03 × 101 | 4.71 × 101 | 7.79 × 101 | 9.31 × 101 | |
F37 | Mean | 2.96 × 103 | 2.94 × 103 | 2.94 × 103 | 2.93 × 103 | 2.95 × 103 | 3.08 × 103 | 2.93 × 103 | 2.93 × 103 |
Std | 2.26 × 101 | 1.97 × 101 | 3.33 × 101 | 3.39 × 101 | 1.78 × 101 | 1.46 × 102 | 2.37 × 101 | 2.85 × 101 | |
F38 | Mean | 3.59 × 103 | 3.70 × 103 | 3.06 × 103 | 3.17 × 103 | 3.40 × 103 | 3.81 × 103 | 3.07 × 103 | 3.02 × 103 |
Std | 5.53 × 102 | 6.43 × 102 | 3.87 × 102 | 4.41 × 102 | 4.74 × 102 | 5.67 × 102 | 2.31 × 102 | 2.24 × 102 | |
F39 | Mean | 3.15 × 103 | 3.20 × 103 | 3.14 × 103 | 3.12 × 103 | 3.10 × 103 | 3.19 × 103 | 3.11 × 103 | 3.10 × 103 |
Std | 4.24 × 101 | 5.91 × 101 | 6.34 × 101 | 3.09 × 101 | 2.59 × 100 | 4.75 × 101 | 5.94 × 100 | 1.26 × 101 | |
F40 | Mean | 3.42 × 103 | 3.38 × 103 | 3.29 × 103 | 3.26 × 103 | 3.25 × 103 | 3.34 × 103 | 3.28 × 103 | 3.24 × 103 |
Std | 1.23 × 102 | 9.08 × 101 | 8.14 × 101 | 7.89 × 101 | 8.40 × 101 | 1.18 × 102 | 6.74 × 101 | 4.18 × 101 |
Fn | WOA | HHO | SSA | MVO | STOA | TSA | AO | IHSSAO |
---|---|---|---|---|---|---|---|---|
F24 | 7 | 5 | 2 | 3 | 6 | 8 | 4 | 1 |
F25 | 6 | 7 | 5 | 1 | 3 | 8 | 4 | 2 |
F26 | 8 | 7 | 5 | 1 | 2 | 6 | 4 | 3 |
F27 | 7 | 6 | 5 | 2 | 4 | 8 | 3 | 1 |
F28 | 4 | 3 | 7 | 1 | 6 | 8 | 5 | 2 |
F29 | 2 | 6 | 8 | 3 | 7 | 4 | 5 | 1 |
F30 | 4 | 1 | 7 | 5 | 8 | 6 | 3 | 2 |
F31 | 6 | 4 | 8 | 1 | 3 | 7 | 5 | 2 |
F32 | 6 | 5 | 7 | 4 | 3 | 8 | 2 | 1 |
F33 | 8 | 6 | 5 | 2 | 4 | 7 | 3 | 1 |
F34 | 5 | 4 | 6 | 3 | 8 | 7 | 2 | 1 |
F35 | 6 | 7 | 3 | 5 | 2 | 7 | 4 | 1 |
F36 | 5 | 6 | 7 | 2 | 4 | 8 | 3 | 1 |
F37 | 7 | 4 | 5 | 2 | 6 | 8 | 3 | 1 |
F38 | 6 | 7 | 2 | 4 | 5 | 8 | 3 | 1 |
F39 | 6 | 8 | 5 | 4 | 1 | 7 | 3 | 2 |
F40 | 8 | 7 | 5 | 3 | 2 | 6 | 4 | 1 |
Threat Sequence | Center Coordinates (km) | Radius (km) |
---|---|---|
1 | (60, 160) | 20 |
2 | (80, 100) | 20 |
3 | (100, 40) | 20 |
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Yao, J.; Sha, Y.; Chen, Y.; Zhang, G.; Hu, X.; Bai, G.; Liu, J. IHSSAO: An Improved Hybrid Salp Swarm Algorithm and Aquila Optimizer for UAV Path Planning in Complex Terrain. Appl. Sci. 2022, 12, 5634. https://doi.org/10.3390/app12115634
Yao J, Sha Y, Chen Y, Zhang G, Hu X, Bai G, Liu J. IHSSAO: An Improved Hybrid Salp Swarm Algorithm and Aquila Optimizer for UAV Path Planning in Complex Terrain. Applied Sciences. 2022; 12(11):5634. https://doi.org/10.3390/app12115634
Chicago/Turabian StyleYao, Jinyan, Yongbai Sha, Yanli Chen, Guoqing Zhang, Xinyu Hu, Guiqiang Bai, and Jun Liu. 2022. "IHSSAO: An Improved Hybrid Salp Swarm Algorithm and Aquila Optimizer for UAV Path Planning in Complex Terrain" Applied Sciences 12, no. 11: 5634. https://doi.org/10.3390/app12115634