Path Planning of Unmanned Aerial Vehicles Based on an Improved Bio-Inspired Tuna Swarm Optimization Algorithm
Abstract
:1. Introduction
- (1)
- A mathematical model was established by reviewing existing drone path optimization strategies.
- (2)
- A new unmanned aerial vehicle path optimization strategy was created using an improved tuna optimization algorithm, and it was improved through sine and Levy’s flight.
- (3)
- The simulation results were used to confirm the efficiency and effectiveness of the proposed technology.
- (4)
- The performance indicators of the proposed algorithm were compared with seven other algorithms.
2. Relate Works
3. Mathematical Model for Path Planning of UAVs
3.1. The Problem with Trajectory Planning
3.2. Path Encoding
3.3. Constraint Condition
3.4. Optimization Objectives
3.4.1. Fuel Consumption
3.4.2. Threats
3.5. Path Planning Model for UAVs
4. Tuna Swarm Optimization Algorithm (TSO)
Standard Tuna Swarm Optimization Algorithm (TSO)
- (1)
- Population Initialization
- (2)
- Tuna school spiral feeding
- (3)
- Tuna parabolic foraging
5. Improved TSO Algorithm Based on the Sine Strategy and Levy Flight (SLTSO)
5.1. Elite Opposition-Based Learning Mechanism
5.2. Introducing the Levy Flight Strategy and the Greedy Strategy to Update Positions
5.3. Introducing the Golden Sine Strategy to Update Individual Positions
5.4. The Workflow for the Proposed SLTSO Algorithm
5.5. Time Complexity Analysis of the SLTSO Algorithm
6. Simulation Experiments and Result Analysis
6.1. Comparison of Test Function Results
6.2. Comparison of Engineering Application
- (1)
- Welding beam design problem
- (2)
- Gear train design problem
6.3. Comparison of UAV Path Planning
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
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Function | PSO | DBO | SMA | HHO | SABO | SCSO | TSO | SLTSO | |
---|---|---|---|---|---|---|---|---|---|
F1 | Min | 1.16 × 102 | 1.02 × 102 | 9.92 × 102 | 3.00 × 105 | 8.98 × 106 | 2.59 × 104 | 1.01 × 102 | 1.05 × 102 |
Std | 1.28 × 107 | 1.75 × 107 | 3.92 × 103 | 5.84 × 105 | 6.34 × 108 | 5.55 × 108 | 2.57 × 103 | 2.03 × 103 | |
Mean | 2.34 × 106 | 5.55 × 106 | 7.43 × 103 | 1.11 × 106 | 4.84 × 108 | 2.79 × 108 | 1.59 × 103 | 2.05 × 103 | |
F3 | Min | 3.00 × 102 | 3.00 × 102 | 3.00 × 102 | 3.06 × 102 | 7.68 × 102 | 3.17 × 102 | 3.00 × 102 | 3.00 × 102 |
Std | 7.73 × 10−1 | 1.55 × 103 | 6.75 × 10−1 | 3.12 × 102 | 1.61 × 103 | 2.49 × 103 | 1.06 × 100 | 7.02 × 100 | |
Mean | 3.00 × 102 | 1.37 × 103 | 3.00 × 102 | 6.16 × 102 | 3.09 × 103 | 2.87 × 103 | 3.00 × 102 | 3.02 × 102 | |
F4 | Min | 4.01 × 102 | 4.01 × 102 | 4.00 × 102 | 4.00 × 102 | 4.07 × 102 | 4.03 × 102 | 4.00 × 102 | 4.00 × 102 |
Std | 4.21 × 101 | 3.28 × 101 | 3.21 × 101 | 3.54 × 101 | 2.22 × 101 | 3.89 × 101 | 1.30 × 101 | 2.01 × 101 | |
Mean | 4.23 × 102 | 4.23 × 102 | 4.22 × 102 | 4.27 × 102 | 4.43 × 102 | 4.41 × 102 | 4.06 × 102 | 4.11 × 102 | |
F5 | Min | 5.05 × 102 | 5.17 × 102 | 5.09 × 102 | 5.24 × 102 | 5.34 × 102 | 5.12 × 102 | 5.12 × 102 | 5.02 × 102 |
Std | 8.53 × 100 | 1.37 × 101 | 6.52 × 100 | 1.72 × 101 | 1.03 × 101 | 1.55 × 101 | 1.24 × 101 | 2.37 × 100 | |
Mean | 5.14 × 102 | 5.40 × 102 | 5.20 × 102 | 5.59 × 102 | 5.54 × 102 | 5.41 × 102 | 5.27 × 102 | 5.07 × 102 | |
F6 | Min | 6.00 × 102 | 6.01 × 102 | 6.00 × 102 | 6.14 × 102 | 6.09 × 102 | 6.03 × 102 | 6.02 × 102 | 6.00 × 102 |
Std | 2.89 × 10−1 | 8.23 × 100 | 6.09 × 10−1 | 1.25 × 101 | 1.03 × 101 | 1.07 × 101 | 6.83 × 100 | 9.05 × 10−9 | |
Mean | 6.00 × 102 | 6.13 × 102 | 6.00 × 102 | 6.42 × 102 | 6.20 × 102 | 6.18 × 102 | 6.11 × 102 | 6.00 × 102 | |
F7 | Min | 7.13 × 102 | 7.30 × 102 | 7.19 × 102 | 7.62 × 102 | 7.39 × 102 | 7.39 × 102 | 7.22 × 102 | 7.06 × 102 |
Std | 6.44 × 100 | 1.45 × 101 | 5.96 × 100 | 1.83 × 101 | 1.39 × 101 | 1.68 × 101 | 1.57 × 101 | 3.46 × 100 | |
Mean | 7.23 × 102 | 7.49 × 102 | 7.29 × 102 | 7.91 × 102 | 7.67 × 102 | 7.68 × 102 | 7.48 × 102 | 7.16 × 102 | |
F8 | Min | 8.05 × 102 | 8.07 × 102 | 8.05 × 102 | 8.15 × 102 | 8.32 × 102 | 8.18 × 102 | 8.06 × 102 | 8.02 × 102 |
Std | 4.71 × 100 | 1.58 × 101 | 8.80 × 100 | 8.53 × 100 | 9.17 × 100 | 7.51 × 100 | 7.37 × 100 | 2.10 × 100 | |
Mean | 8.13 × 102 | 8.37 × 102 | 8.20 × 102 | 8.30 × 102 | 8.49 × 102 | 8.31 × 102 | 8.22 × 102 | 8.07 × 102 | |
F9 | Min | 9.00 × 102 | 9.02 × 102 | 9.00 × 102 | 9.82 × 102 | 9.18 × 102 | 9.15 × 102 | 9.11 × 102 | 9.00 × 102 |
Std | 1.16 × 10−1 | 1.14 × 102 | 2.94 × 100 | 2.14 × 102 | 9.53 × 101 | 2.33 × 102 | 7.82 × 101 | 8.29 × 10−2 | |
Mean | 9.00 × 102 | 9.98 × 102 | 9.01 × 102 | 1.58 × 103 | 1.04 × 103 | 1.12 × 103 | 9.96 × 102 | 9.00 × 102 | |
F10 | Min | 1.02 × 103 | 1.28 × 103 | 1.14 × 103 | 1.27 × 103 | 2.34 × 103 | 1.37 × 103 | 1.37 × 103 | 1.05 × 103 |
Std | 2.55 × 102 | 3.10 × 102 | 2.52 × 102 | 3.65 × 102 | 1.98 × 102 | 3.20 × 102 | 3.00 × 102 | 1.71 × 102 | |
Mean | 1.58 × 103 | 1.98 × 103 | 1.59 × 103 | 2.03 × 103 | 2.81 × 103 | 2.08 × 103 | 1.96 × 103 | 1.49 × 103 | |
F11 | Min | 1.10 × 103 | 1.11 × 103 | 1.11 × 103 | 1.11 × 103 | 1.14 × 103 | 1.11 × 103 | 1.11 × 103 | 1.10 × 103 |
Std | 2.97 × 101 | 1.22 × 102 | 1.04 × 102 | 5.38 × 101 | 1.37 × 103 | 4.90 × 101 | 2.38 × 101 | 3.01 × 100 | |
Mean | 1.12 × 103 | 1.23 × 103 | 1.21 × 103 | 1.18 × 103 | 1.86 × 103 | 1.16 × 103 | 1.14 × 103 | 1.10 × 103 | |
F12 | Min | 3.65 × 103 | 1.93 × 103 | 6.40 × 103 | 5.05 × 104 | 1.41 × 105 | 1.79 × 104 | 2.27 × 103 | 1.98 × 103 |
Std | 1.49 × 106 | 5.67 × 106 | 6.24 × 105 | 2.98 × 106 | 1.72 × 106 | 1.95 × 106 | 9.44 × 103 | 1.20 × 104 | |
Mean | 2.96 × 105 | 3.41 × 106 | 4.68 × 105 | 2.46 × 106 | 2.01 × 106 | 1.78 × 106 | 9.76 × 103 | 1.35 × 104 | |
F13 | Min | 1.38 × 103 | 1.51 × 103 | 1.55 × 103 | 2.45 × 103 | 3.56 × 103 | 2.47 × 103 | 1.58 × 103 | 1.36 × 103 |
Std | 9.29 × 103 | 1.19 × 104 | 1.24 × 104 | 8.47 × 103 | 6.16 × 103 | 1.05 × 104 | 6.04 × 103 | 1.32 × 104 | |
Mean | 9.63 × 103 | 1.45 × 104 | 1.12 × 104 | 1.42 × 104 | 1.30 × 104 | 1.43 × 104 | 1.00 × 104 | 1.24 × 104 | |
F14 | Min | 1.43 × 103 | 1.45 × 103 | 1.43 × 103 | 1.50 × 103 | 1.51 × 103 | 1.46 × 103 | 1.43 × 103 | 1.41 × 103 |
Std | 8.39 × 102 | 5.29 × 102 | 2.57 × 103 | 9.72 × 102 | 1.05 × 103 | 2.03 × 103 | 3.96 × 101 | 2.49 × 102 | |
Mean | 1.76 × 103 | 1.97 × 103 | 2.16 × 103 | 2.09 × 103 | 2.21 × 103 | 3.48 × 103 | 1.50 × 103 | 1.56 × 103 | |
F15 | Min | 1.51 × 103 | 1.63 × 103 | 1.53 × 103 | 1.78 × 103 | 2.75 × 103 | 1.58 × 103 | 1.52 × 103 | 1.51 × 103 |
Std | 2.35 × 103 | 2.45 × 103 | 3.62 × 103 | 3.00 × 103 | 5.27 × 103 | 1.80 × 103 | 3.86 × 102 | 7.64 × 102 | |
Mean | 3.10 × 103 | 4.34 × 103 | 5.19 × 103 | 7.92 × 103 | 9.55 × 103 | 4.92 × 103 | 1.81 × 103 | 1.86 × 103 | |
F16 | Min | 1.60 × 103 | 1.61 × 103 | 1.60 × 103 | 1.63 × 103 | 1.79 × 103 | 1.62 × 103 | 1.60 × 103 | 1.60 × 103 |
Std | 1.37 × 102 | 1.45 × 102 | 9.73 × 101 | 1.49 × 102 | 1.23 × 102 | 1.34 × 102 | 1.19 × 102 | 4.60 × 101 | |
Mean | 1.76 × 103 | 1.82 × 103 | 1.70 × 103 | 1.93 × 103 | 2.06 × 103 | 1.82 × 103 | 1.79 × 103 | 1.63 × 103 | |
F17 | Min | 1.71 × 103 | 1.73 × 103 | 1.72 × 103 | 1.75 × 103 | 1.76 × 103 | 1.73 × 103 | 1.72 × 103 | 1.70 × 103 |
Std | 3.24 × 101 | 4.04 × 101 | 3.63 × 101 | 5.87 × 101 | 7.79 × 101 | 2.98 × 101 | 2.32 × 101 | 2.49 × 101 | |
Mean | 1.75 × 103 | 1.78 × 103 | 1.76 × 103 | 1.80 × 103 | 1.87 × 103 | 1.77 × 103 | 1.75 × 103 | 1.72 × 103 | |
F18 | Min | 2.23 × 103 | 2.18 × 103 | 4.46 × 103 | 2.89 × 103 | 2.55 × 103 | 4.08 × 103 | 2.01 × 103 | 1.97 × 103 |
Std | 1.52 × 104 | 1.62 × 104 | 1.40 × 104 | 1.33 × 104 | 1.21 × 104 | 1.77 × 104 | 7.14 × 103 | 7.76 × 103 | |
Mean | 2.27 × 104 | 1.91 × 104 | 2.57 × 104 | 1.89 × 104 | 1.88 × 104 | 2.41 × 104 | 9.01 × 103 | 8.51 × 103 | |
F19 | Min | 1.96 × 103 | 1.97 × 103 | 1.93 × 103 | 1.94 × 103 | 3.05 × 103 | 1.95 × 103 | 1.94 × 103 | 1.91 × 103 |
Std | 6.92 × 103 | 2.06 × 104 | 1.05 × 104 | 1.87 × 104 | 5.33 × 103 | 6.89 × 103 | 7.06 × 102 | 9.75 × 102 | |
Mean | 6.29 × 103 | 1.14 × 104 | 1.49 × 104 | 2.08 × 104 | 8.90 × 103 | 8.01 × 103 | 2.56 × 103 | 2.57 × 103 | |
F20 | Min | 2.00 × 103 | 2.03 × 103 | 2.00 × 103 | 2.04 × 103 | 2.12 × 103 | 2.04 × 103 | 2.01 × 103 | 2.00 × 103 |
Std | 5.44 × 101 | 7.86 × 101 | 5.01 × 101 | 6.89 × 101 | 6.66 × 101 | 6.78 × 101 | 6.41 × 101 | 2.23 × 101 | |
Mean | 2.05 × 103 | 2.12 × 103 | 2.05 × 103 | 2.18 × 103 | 2.23 × 103 | 2.14 × 103 | 2.10 × 103 | 2.01 × 103 | |
F21 | Min | 2.20 × 103 | 2.20 × 103 | 2.10 × 103 | 2.20 × 103 | 2.33 × 103 | 2.20 × 103 | 2.20 × 103 | 2.20 × 103 |
Std | 4.09 × 101 | 5.52 × 101 | 5.58 × 101 | 7.04 × 101 | 1.52 × 101 | 5.48 × 101 | 4.02 × 101 | 5.17 × 101 | |
Mean | 2.30 × 103 | 2.23 × 103 | 2.31 × 103 | 2.32 × 103 | 2.35 × 103 | 2.31 × 103 | 2.22 × 103 | 2.27 × 103 | |
F22 | Min | 2.23 × 103 | 2.24 × 103 | 2.22 × 103 | 2.26 × 103 | 2.31 × 103 | 2.30 × 103 | 2.24 × 103 | 2.20 × 103 |
Std | 2.93 × 101 | 2.31 × 101 | 2.72 × 102 | 2.10 × 102 | 5.19 × 101 | 7.85 × 101 | 1.60 × 101 | 1.95 × 101 | |
Mean | 2.31 × 103 | 2.31 × 103 | 2.41 × 103 | 2.35 × 103 | 2.34 × 103 | 2.34 × 103 | 2.30 × 103 | 2.30 × 103 | |
F23 | Min | 2.61 × 103 | 2.62 × 103 | 2.61 × 103 | 2.62 × 103 | 2.63 × 103 | 2.61 × 103 | 2.61 × 103 | 2.61 × 103 |
Std | 1.22 × 101 | 1.78 × 101 | 7.85 × 100 | 2.99 × 101 | 2.01 × 101 | 1.52 × 101 | 1.42 × 101 | 2.89 × 100 | |
Mean | 2.63 × 103 | 2.64 × 103 | 2.62 × 103 | 2.68 × 103 | 2.66 × 103 | 2.64 × 103 | 2.63 × 103 | 2.61 × 103 | |
F24 | Min | 2.50 × 103 | 2.50 × 103 | 2.74 × 103 | 2.50 × 103 | 2.53 × 103 | 2.50 × 103 | 2.50 × 103 | 2.50 × 103 |
Std | 4.93 × 101 | 1.06 × 102 | 1.26 × 101 | 1.43 × 102 | 4.98 × 101 | 7.23 × 101 | 8.02 × 101 | 9.11 × 101 | |
Mean | 2.76 × 103 | 2.72 × 103 | 2.76 × 103 | 2.78 × 103 | 2.78 × 103 | 2.75 × 103 | 2.73 × 103 | 2.70 × 103 | |
F25 | Min | 2.90 × 103 | 2.90 × 103 | 2.90 × 103 | 2.90 × 103 | 2.94 × 103 | 2.91 × 103 | 2.90 × 103 | 2.90 × 103 |
Std | 3.18 × 101 | 2.48 × 101 | 3.78 × 101 | 2.17 × 101 | 2.25 × 101 | 3.08 × 101 | 2.42 × 101 | 2.33 × 101 | |
Mean | 2.93 × 103 | 2.94 × 103 | 2.94 × 103 | 2.94 × 103 | 2.97 × 103 | 2.94 × 103 | 2.93 × 103 | 2.92 × 103 | |
F26 | Min | 2.60 × 103 | 2.82 × 103 | 2.90 × 103 | 2.61 × 103 | 3.11 × 103 | 2.86 × 103 | 2.60 × 103 | 2.60 × 103 |
Std | 3.36 × 102 | 2.31 × 102 | 4.42 × 102 | 6.56 × 102 | 4.02 × 102 | 2.28 × 102 | 1.43 × 102 | 1.29 × 102 | |
Mean | 3.08 × 103 | 3.17 × 103 | 3.19 × 103 | 3.56 × 103 | 3.47 × 103 | 3.17 × 103 | 2.96 × 103 | 2.92 × 103 | |
F27 | Min | 3.09 × 103 | 3.09 × 103 | 3.09 × 103 | 3.11 × 103 | 3.10 × 103 | 3.09 × 103 | 3.09 × 103 | 3.07 × 103 |
Std | 2.52 × 101 | 1.02 × 101 | 1.91 × 100 | 4.97 × 101 | 1.84 × 101 | 2.84 × 101 | 2.55 × 101 | 2.26 × 100 | |
Mean | 3.12 × 103 | 3.10 × 103 | 3.09 × 103 | 3.17 × 103 | 3.11 × 103 | 3.11 × 103 | 3.11 × 103 | 3.07 × 103 | |
F28 | Min | 3.10 × 103 | 3.17 × 103 | 3.17 × 103 | 3.10 × 103 | 3.23 × 103 | 3.17 × 103 | 3.10 × 103 | 3.10 × 103 |
Std | 1.22 × 102 | 1.27 × 102 | 1.30 × 102 | 1.12 × 102 | 1.38 × 102 | 1.18 × 102 | 1.61 × 102 | 4.61 × 101 | |
Mean | 3.39 × 103 | 3.35 × 103 | 3.41 × 103 | 3.38 × 103 | 3.50 × 103 | 3.32 × 103 | 3.40 × 103 | 3.26 × 103 | |
F29 | Min | 3.14 × 103 | 3.16 × 103 | 3.13 × 103 | 3.21 × 103 | 3.20 × 103 | 3.17 × 103 | 3.16 × 103 | 3.15 × 103 |
Std | 4.47 × 101 | 8.95 × 101 | 5.93 × 101 | 8.34 × 101 | 9.03 × 101 | 8.41 × 101 | 6.59 × 101 | 1.27 × 101 | |
Mean | 3.20 × 103 | 3.30 × 103 | 3.22 × 103 | 3.36 × 103 | 3.34 × 103 | 3.29 × 103 | 3.25 × 103 | 3.17 × 103 | |
F30 | Min | 6.30 × 103 | 6.66 × 103 | 6.71 × 103 | 1.68 × 104 | 5.59 × 104 | 5.04 × 103 | 4.67 × 103 | 3.23 × 103 |
Std | 5.61 × 105 | 1.44 × 106 | 6.02 × 105 | 2.77 × 106 | 4.55 × 106 | 1.31 × 106 | 2.12 × 106 | 1.25 × 103 | |
Mean | 4.25 × 105 | 1.21 × 106 | 3.66 × 105 | 2.07 × 106 | 2.52 × 106 | 1.11 × 106 | 7.61 × 105 | 3.71 × 103 |
Function | PSO | DBO | SMA | HHO | SABO | SCSO | TSO | SLTSO | |
---|---|---|---|---|---|---|---|---|---|
F1 | Min | 2.18 × 103 | 5.32 × 107 | 4.58 × 104 | 8.83 × 107 | 3.71 × 109 | 8.02 × 108 | 1.11 × 106 | 1.06 × 102 |
Std | 3.09 × 109 | 1.77 × 108 | 4.53 × 104 | 2.43 × 108 | 5.66 × 109 | 3.97 × 109 | 1.49 × 107 | 9.81 × 103 | |
Mean | 2.00 × 109 | 2.59 × 108 | 1.05 × 105 | 4.30 × 108 | 1.34 × 1010 | 9.08 × 109 | 1.07 × 107 | 7.75 × 103 | |
F3 | Min | 3.99 × 104 | 6.29 × 104 | 1.39 × 104 | 3.80 × 104 | 4.59 × 104 | 3.58 × 104 | 2.48 × 104 | 7.14 × 104 |
Std | 2.50 × 104 | 9.19 × 103 | 1.55 × 104 | 8.27 × 103 | 1.02 × 104 | 1.10 × 104 | 1.51 × 104 | 3.48 × 104 | |
Mean | 7.43 × 104 | 8.57 × 104 | 3.52 × 104 | 5.76 × 104 | 6.57 × 104 | 6.07 × 104 | 6.08 × 104 | 1.43 × 105 | |
F4 | Min | 4.92 × 102 | 5.34 × 102 | 4.76 × 102 | 5.96 × 102 | 9.13 × 102 | 5.31 × 102 | 4.86 × 102 | 4.18 × 102 |
Std | 3.86 × 102 | 1.63 × 102 | 1.50 × 101 | 9.82 × 101 | 1.10 × 103 | 4.74 × 102 | 2.51 × 101 | 3.41 × 101 | |
Mean | 7.68 × 102 | 6.68 × 102 | 5.02 × 102 | 7.29 × 102 | 2.21 × 103 | 9.90 × 102 | 5.31 × 102 | 4.73 × 102 | |
F5 | Min | 5.40 × 102 | 6.68 × 102 | 5.61 × 102 | 7.24 × 102 | 7.64 × 102 | 6.84 × 102 | 6.00 × 102 | 5.60 × 102 |
Std | 2.33 × 101 | 5.76 × 101 | 4.59 × 101 | 2.64 × 101 | 3.60 × 101 | 4.98 × 101 | 3.02 × 101 | 1.75 × 101 | |
Mean | 5.83 × 102 | 7.59 × 102 | 6.37 × 102 | 7.70 × 102 | 8.27 × 102 | 7.67 × 102 | 6.65 × 102 | 5.94 × 102 | |
F6 | Min | 6.02 × 102 | 6.18 × 102 | 6.07 × 102 | 6.58 × 102 | 6.37 × 102 | 6.40 × 102 | 6.25 × 102 | 6.00 × 102 |
Std | 6.16 × 100 | 1.09 × 101 | 1.02 × 101 | 5.11 × 100 | 1.47 × 101 | 1.08 × 101 | 7.91 × 100 | 1.19 × 10−2 | |
Mean | 6.08 × 102 | 6.46 × 102 | 6.18 × 102 | 6.69 × 102 | 6.67 × 102 | 6.62 × 102 | 6.44 × 102 | 6.00 × 102 | |
F7 | Min | 7.93 × 102 | 8.54 × 102 | 8.32 × 102 | 1.18 × 103 | 1.04 × 103 | 9.62 × 102 | 9.61 × 102 | 8.03 × 102 |
Std | 4.86 × 101 | 9.67 × 101 | 3.99 × 101 | 6.13 × 101 | 5.97 × 101 | 1.07 × 102 | 7.92 × 101 | 1.98 × 101 | |
Mean | 8.44 × 102 | 1.02 × 103 | 8.93 × 102 | 1.30 × 103 | 1.13 × 103 | 1.16 × 103 | 1.08 × 103 | 8.36 × 102 | |
F8 | Min | 8.44 × 102 | 9.21 × 102 | 8.73 × 102 | 9.26 × 102 | 1.04 × 103 | 9.56 × 102 | 8.67 × 102 | 8.56 × 102 |
Std | 2.69 × 101 | 5.11 × 101 | 2.86 × 101 | 3.00 × 101 | 2.60 × 101 | 2.88 × 101 | 3.19 × 101 | 1.69 × 101 | |
Mean | 8.90 × 102 | 1.02 × 103 | 9.19 × 102 | 9.92 × 102 | 1.08 × 103 | 1.01 × 103 | 9.30 × 102 | 8.83 × 102 | |
F9 | Min | 9.24 × 102 | 3.52 × 103 | 2.16 × 103 | 6.48 × 103 | 3.84 × 103 | 3.65 × 103 | 2.46 × 103 | 9.01 × 102 |
Std | 7.47 × 102 | 1.86 × 103 | 1.65 × 103 | 1.38 × 103 | 1.74 × 103 | 1.58 × 103 | 1.36 × 103 | 3.57 × 102 | |
Mean | 1.55 × 103 | 6.49 × 103 | 4.75 × 103 | 8.78 × 103 | 6.71 × 103 | 6.47 × 103 | 4.58 × 103 | 1.08 × 103 | |
F10 | Min | 2.71 × 103 | 4.41 × 103 | 3.98 × 103 | 5.31 × 103 | 7.90 × 103 | 4.80 × 103 | 4.12 × 103 | 3.89 × 103 |
Std | 7.57 × 102 | 1.14 × 103 | 5.90 × 102 | 7.52 × 102 | 3.81 × 102 | 6.72 × 102 | 1.14 × 103 | 4.80 × 102 | |
Mean | 4.58 × 103 | 6.84 × 103 | 4.94 × 103 | 6.39 × 103 | 8.77 × 103 | 6.10 × 103 | 6.09 × 103 | 5.12 × 103 | |
F11 | Min | 1.16 × 103 | 1.29 × 103 | 1.18 × 103 | 1.28 × 103 | 2.31 × 103 | 1.52 × 103 | 1.18 × 103 | 1.15 × 103 |
Std | 1.17 × 102 | 1.10 × 103 | 7.79 × 101 | 2.41 × 102 | 2.16 × 103 | 1.46 × 103 | 4.32 × 101 | 2.73 × 101 | |
Mean | 1.31 × 103 | 2.10 × 103 | 1.29 × 103 | 1.59 × 103 | 5.60 × 103 | 3.25 × 103 | 1.26 × 103 | 1.18 × 103 | |
F12 | Min | 1.85 × 105 | 1.28 × 106 | 3.26 × 105 | 5.54 × 106 | 1.09 × 108 | 2.43 × 107 | 4.06 × 105 | 4.83 × 104 |
Std | 1.46 × 108 | 1.40 × 108 | 3.58 × 106 | 7.73 × 107 | 7.16 × 108 | 7.65 × 108 | 2.85 × 106 | 1.81 × 106 | |
Mean | 7.63 × 107 | 9.69 × 107 | 4.34 × 106 | 6.83 × 107 | 9.74 × 108 | 4.87 × 108 | 3.16 × 106 | 1.79 × 106 | |
F13 | Min | 7.28 × 103 | 1.10 × 104 | 1.46 × 104 | 3.30 × 105 | 2.55 × 106 | 2.46 × 104 | 4.30 × 103 | 1.36 × 103 |
Std | 2.68 × 108 | 1.73 × 107 | 5.33 × 104 | 7.42 × 105 | 2.92 × 108 | 8.98 × 107 | 1.29 × 104 | 1.73 × 104 | |
Mean | 7.66 × 107 | 6.67 × 106 | 6.64 × 104 | 1.04 × 106 | 1.50 × 108 | 3.83 × 107 | 1.93 × 104 | 1.86 × 104 | |
F14 | Min | 5.00 × 103 | 1.32 × 104 | 1.43 × 104 | 2.16 × 104 | 4.68 × 104 | 1.57 × 104 | 3.38 × 103 | 3.82 × 103 |
Std | 9.64 × 104 | 4.69 × 105 | 2.88 × 105 | 1.07 × 106 | 8.95 × 105 | 8.53 × 105 | 4.70 × 104 | 6.49 × 104 | |
Mean | 1.04 × 105 | 3.84 × 105 | 2.84 × 105 | 1.15 × 106 | 1.17 × 106 | 6.35 × 105 | 3.83 × 104 | 6.54 × 104 | |
F15 | Min | 2.20 × 103 | 9.46 × 103 | 3.45 × 103 | 3.16 × 104 | 1.45 × 105 | 2.43 × 104 | 1.80 × 103 | 1.66 × 103 |
Std | 2.49 × 104 | 2.35 × 106 | 1.62 × 104 | 1.08 × 105 | 5.09 × 106 | 2.58 × 106 | 1.16 × 104 | 1.12 × 104 | |
Mean | 2.11 × 104 | 5.86 × 105 | 2.15 × 104 | 1.40 × 105 | 3.13 × 106 | 2.06 × 106 | 7.75 × 103 | 1.22 × 104 | |
F16 | Min | 1.95 × 103 | 2.59 × 103 | 2.00 × 103 | 2.28 × 103 | 3.75 × 103 | 2.43 × 103 | 2.37 × 103 | 2.14 × 103 |
Std | 2.99 × 102 | 4.02 × 102 | 3.34 × 102 | 5.15 × 102 | 2.86 × 102 | 3.67 × 102 | 2.95 × 102 | 2.36 × 102 | |
Mean | 2.60 × 103 | 3.25 × 103 | 2.67 × 103 | 3.71 × 103 | 4.17 × 103 | 3.30 × 103 | 2.85 × 103 | 2.60 × 103 | |
F17 | Min | 1.79 × 103 | 1.92 × 103 | 1.91 × 103 | 1.81 × 103 | 2.44 × 103 | 1.89 × 103 | 1.97 × 103 | 1.79 × 103 |
Std | 1.67 × 102 | 3.43 × 102 | 2.64 × 102 | 3.16 × 102 | 2.42 × 102 | 2.48 × 102 | 2.11 × 102 | 1.78 × 102 | |
Mean | 2.11 × 103 | 2.68 × 103 | 2.32 × 103 | 2.71 × 103 | 2.92 × 103 | 2.38 × 103 | 2.38 × 103 | 2.13 × 103 | |
F18 | Min | 1.70 × 105 | 7.87 × 104 | 3.53 × 105 | 1.83 × 105 | 2.69 × 105 | 5.12 × 104 | 4.72 × 104 | 1.83 × 105 |
Std | 1.14 × 106 | 4.03 × 106 | 2.78 × 106 | 4.47 × 106 | 6.12 × 106 | 7.48 × 106 | 2.06 × 105 | 6.45 × 105 | |
Mean | 1.31 × 106 | 3.11 × 106 | 2.99 × 106 | 4.09 × 106 | 4.56 × 106 | 4.71 × 106 | 2.93 × 105 | 1.06 × 106 | |
F19 | Min | 1.98 × 103 | 2.93 × 103 | 2.14 × 103 | 1.18 × 105 | 2.75 × 105 | 1.55 × 105 | 2.05 × 103 | 1.99 × 103 |
Std | 1.10 × 105 | 6.97 × 107 | 1.99 × 104 | 1.37 × 106 | 4.73 × 106 | 1.59 × 106 | 9.15 × 103 | 1.44 × 104 | |
Mean | 5.21 × 104 | 1.69 × 107 | 1.98 × 104 | 1.75 × 106 | 5.32 × 106 | 1.89 × 106 | 1.05 × 104 | 1.32 × 104 | |
F20 | Min | 2.07 × 103 | 2.30 × 103 | 2.09 × 103 | 2.54 × 103 | 2.80 × 103 | 2.30 × 103 | 2.23 × 103 | 2.16 × 103 |
Std | 1.75 × 102 | 2.38 × 102 | 2.20 × 102 | 1.96 × 102 | 1.50 × 102 | 2.02 × 102 | 2.01 × 102 | 1.25 × 102 | |
Mean | 2.42 × 103 | 2.71 × 103 | 2.54 × 103 | 2.84 × 103 | 3.08 × 103 | 2.69 × 103 | 2.58 × 103 | 2.37 × 103 | |
F21 | Min | 2.35 × 103 | 2.42 × 103 | 2.38 × 103 | 2.47 × 103 | 2.54 × 103 | 2.46 × 103 | 2.39 × 103 | 2.37 × 103 |
Std | 3.43 × 101 | 5.40 × 101 | 2.56 × 101 | 5.86 × 101 | 3.77 × 101 | 4.58 × 101 | 3.06 × 101 | 1.20 × 101 | |
Mean | 2.41 × 103 | 2.55 × 103 | 2.43 × 103 | 2.60 × 103 | 2.60 × 103 | 2.53 × 103 | 2.44 × 103 | 2.39 × 103 | |
F22 | Min | 2.30 × 103 | 2.37 × 103 | 2.30 × 103 | 3.12 × 103 | 3.39 × 103 | 2.52 × 103 | 2.31 × 103 | 2.30 × 103 |
Std | 1.69 × 103 | 2.27 × 103 | 9.37 × 102 | 1.45 × 103 | 8.31 × 102 | 9.93 × 102 | 1.78 × 103 | 2.33 × 103 | |
Mean | 4.76 × 103 | 4.97 × 103 | 6.16 × 103 | 7.37 × 103 | 4.29 × 103 | 3.71 × 103 | 3.01 × 103 | 4.77 × 103 | |
F23 | Min | 2.73 × 103 | 2.84 × 103 | 2.71 × 103 | 3.01 × 103 | 2.99 × 103 | 2.85 × 103 | 2.79 × 103 | 2.72 × 103 |
Std | 1.01 × 102 | 7.20 × 101 | 2.66 × 101 | 1.30 × 102 | 9.77 × 101 | 5.56 × 101 | 6.34 × 101 | 2.39 × 101 | |
Mean | 2.91 × 103 | 2.99 × 103 | 2.77 × 103 | 3.30 × 103 | 3.20 × 103 | 2.94 × 103 | 2.92 × 103 | 2.77 × 103 | |
F24 | Min | 2.91 × 103 | 3.02 × 103 | 2.87 × 103 | 3.25 × 103 | 3.13 × 103 | 3.00 × 103 | 2.95 × 103 | 2.91 × 103 |
Std | 1.06 × 102 | 6.97 × 101 | 3.91 × 101 | 1.53 × 102 | 1.11 × 102 | 5.13 × 101 | 1.19 × 102 | 2.15 × 101 | |
Mean | 3.09 × 103 | 3.21 × 103 | 2.96 × 103 | 3.50 × 103 | 3.30 × 103 | 3.08 × 103 | 3.15 × 103 | 2.95 × 103 | |
F25 | Min | 2.88 × 103 | 2.90 × 103 | 2.88 × 103 | 2.95 × 103 | 3.20 × 103 | 3.00 × 103 | 2.89 × 103 | 2.88 × 103 |
Std | 6.07 × 101 | 5.33 × 101 | 1.54 × 101 | 3.37 × 101 | 1.47 × 102 | 2.00 × 102 | 2.13 × 101 | 1.12 × 101 | |
Mean | 2.93 × 103 | 2.98 × 103 | 2.90 × 103 | 3.01 × 103 | 3.36 × 103 | 3.19 × 103 | 2.93 × 103 | 2.89 × 103 | |
F26 | Min | 2.80 × 103 | 3.95 × 103 | 4.58 × 103 | 4.28 × 103 | 6.90 × 103 | 4.12 × 103 | 3.07 × 103 | 2.91 × 103 |
Std | 9.35 × 102 | 9.96 × 102 | 3.06 × 102 | 1.29 × 103 | 6.01 × 102 | 1.47 × 103 | 1.21 × 103 | 5.16 × 102 | |
Mean | 4.77 × 103 | 7.04 × 103 | 5.01 × 103 | 8.12 × 103 | 8.38 × 103 | 6.69 × 103 | 6.36 × 103 | 4.69 × 103 | |
F27 | Min | 3.21 × 103 | 3.22 × 103 | 3.21 × 103 | 3.23 × 103 | 3.30 × 103 | 3.27 × 103 | 3.23 × 103 | 3.20 × 103 |
Std | 7.48 × 101 | 1.17 × 102 | 1.37 × 101 | 2.26 × 102 | 1.12 × 102 | 8.28 × 101 | 7.43 × 101 | 1.93 × 10−4 | |
Mean | 3.29 × 103 | 3.40 × 103 | 3.23 × 103 | 3.56 × 103 | 3.49 × 103 | 3.40 × 103 | 3.34 × 103 | 3.20 × 103 | |
F28 | Min | 3.23 × 103 | 3.23 × 103 | 3.21 × 103 | 3.36 × 103 | 3.53 × 103 | 3.36 × 103 | 3.21 × 103 | 3.26 × 103 |
Std | 1.19 × 102 | 4.86 × 102 | 5.37 × 101 | 6.91 × 101 | 3.50 × 102 | 3.80 × 102 | 2.78 × 101 | 1.01 × 101 | |
Mean | 3.35 × 103 | 3.52 × 103 | 3.27 × 103 | 3.47 × 103 | 4.24 × 103 | 3.83 × 103 | 3.30 × 103 | 3.30 × 103 | |
F29 | Min | 3.37 × 103 | 3.75 × 103 | 3.59 × 103 | 4.22 × 103 | 5.07 × 103 | 3.99 × 103 | 3.72 × 103 | 3.26 × 103 |
Std | 2.45 × 102 | 2.65 × 102 | 2.69 × 102 | 4.61 × 102 | 4.37 × 102 | 4.24 × 102 | 3.12 × 102 | 1.48 × 102 | |
Mean | 3.79 × 103 | 4.47 × 103 | 4.01 × 103 | 4.94 × 103 | 5.71 × 103 | 4.73 × 103 | 4.29 × 103 | 3.51 × 103 | |
F30 | Min | 8.84 × 103 | 3.24 × 104 | 2.45 × 104 | 7.63 × 105 | 2.99 × 106 | 2.09 × 106 | 9.31 × 103 | 3.23 × 103 |
Std | 1.58 × 106 | 6.06 × 106 | 7.86 × 104 | 1.21 × 107 | 2.72 × 107 | 1.60 × 107 | 2.19 × 104 | 5.10 × 103 | |
Mean | 4.54 × 105 | 3.03 × 106 | 1.10 × 105 | 9.77 × 106 | 3.50 × 107 | 1.94 × 107 | 3.77 × 104 | 7.70 × 103 |
Function | PSO | DBO | SMA | HHO | SABO | SCSO | TSO | SLTSO | |
---|---|---|---|---|---|---|---|---|---|
F1 | Min | 1.20 × 109 | 3.66 × 108 | 2.19 × 106 | 2.19 × 109 | 2.49 × 1010 | 1.48 × 1010 | 3.12 × 108 | 1.75 × 102 |
Std | 5.83 × 109 | 1.05 × 1010 | 2.67 × 106 | 1.55 × 109 | 1.04 × 1010 | 6.99 × 109 | 5.57 × 108 | 6.13 × 105 | |
Mean | 7.50 × 109 | 6.57 × 109 | 7.26 × 106 | 5.36 × 109 | 4.32 × 1010 | 2.77 × 1010 | 1.02 × 109 | 1.25 × 105 | |
F3 | Min | 1.26 × 105 | 1.78 × 105 | 1.11 × 105 | 1.41 × 105 | 1.56 × 105 | 9.28 × 104 | 1.51 × 105 | 2.45 × 105 |
Std | 5.42 × 104 | 6.59 × 104 | 5.67 × 104 | 1.87 × 104 | 1.50 × 104 | 2.26 × 104 | 3.25 × 104 | 4.52 × 104 | |
Mean | 2.22 × 105 | 2.57 × 105 | 2.05 × 105 | 1.75 × 105 | 1.83 × 105 | 1.36 × 105 | 2.04 × 105 | 3.47 × 105 | |
F4 | Min | 5.73 × 102 | 7.37 × 102 | 5.16 × 102 | 1.05 × 103 | 3.73 × 103 | 1.30 × 103 | 7.22 × 102 | 4.51 × 102 |
Std | 5.59 × 102 | 1.31 × 103 | 6.20 × 101 | 3.77 × 102 | 2.17 × 103 | 1.41 × 103 | 9.90 × 101 | 6.43 × 101 | |
Mean | 1.14 × 103 | 1.57 × 103 | 6.17 × 102 | 1.69 × 103 | 7.56 × 103 | 4.02 × 103 | 8.55 × 102 | 5.55 × 102 | |
F5 | Min | 6.51 × 102 | 7.48 × 102 | 7.30 × 102 | 8.80 × 102 | 1.02 × 103 | 8.67 × 102 | 7.63 × 102 | 6.96 × 102 |
Std | 4.99 × 101 | 9.11 × 101 | 5.50 × 101 | 2.95 × 101 | 4.90 × 101 | 3.88 × 101 | 3.73 × 101 | 2.56 × 101 | |
Mean | 7.21 × 102 | 9.61 × 102 | 8.21 × 102 | 9.33 × 102 | 1.11 × 103 | 9.50 × 102 | 8.39 × 102 | 7.42 × 102 | |
F6 | Min | 6.09 × 102 | 6.34 × 102 | 6.19 × 102 | 6.74 × 102 | 6.61 × 102 | 6.57 × 102 | 6.49 × 102 | 6.00 × 102 |
Std | 6.61 × 100 | 1.13 × 101 | 1.26 × 101 | 3.45 × 100 | 1.10 × 101 | 7.62 × 100 | 7.98 × 100 | 2.26 × 100 | |
Mean | 6.19 × 102 | 6.62 × 102 | 6.49 × 102 | 6.79 × 102 | 6.87 × 102 | 6.75 × 102 | 6.63 × 102 | 6.02 × 102 | |
F7 | Min | 9.60 × 102 | 1.14 × 103 | 1.05 × 103 | 1.65 × 103 | 1.51 × 103 | 1.52 × 103 | 1.26 × 103 | 9.87 × 102 |
Std | 9.28 × 101 | 1.54 × 102 | 8.94 × 101 | 8.43 × 101 | 1.04 × 102 | 1.03 × 102 | 1.35 × 102 | 3.87 × 101 | |
Mean | 1.09 × 103 | 1.40 × 103 | 1.17 × 103 | 1.89 × 103 | 1.66 × 103 | 1.72 × 103 | 1.62 × 103 | 1.06 × 103 | |
F8 | Min | 9.46 × 102 | 1.06 × 103 | 9.58 × 102 | 1.15 × 103 | 1.32 × 103 | 1.15 × 103 | 1.01 × 103 | 9.80 × 102 |
Std | 4.78 × 101 | 1.16 × 102 | 5.33 × 101 | 3.68 × 101 | 5.70 × 101 | 4.93 × 101 | 4.53 × 101 | 2.79 × 101 | |
Mean | 1.02 × 103 | 1.28 × 103 | 1.09 × 103 | 1.23 × 103 | 1.45 × 103 | 1.30 × 103 | 1.12 × 103 | 1.05 × 103 | |
F9 | Min | 1.67 × 103 | 1.10 × 104 | 7.93 × 103 | 2.63 × 104 | 1.82 × 104 | 1.40 × 104 | 7.24 × 103 | 1.57 × 103 |
Std | 8.27 × 103 | 6.69 × 103 | 3.85 × 103 | 2.70 × 103 | 4.68 × 103 | 4.00 × 103 | 4.32 × 103 | 3.09 × 103 | |
Mean | 1.11 × 104 | 3.05 × 104 | 1.58 × 104 | 3.16 × 104 | 3.14 × 104 | 2.17 × 104 | 1.39 × 104 | 7.42 × 103 | |
F10 | Min | 6.32 × 103 | 7.54 × 103 | 6.63 × 103 | 8.83 × 103 | 1.41 × 104 | 8.43 × 103 | 6.91 × 103 | 8.27 × 103 |
Std | 1.02 × 103 | 2.51 × 103 | 8.59 × 102 | 9.50 × 102 | 5.07 × 102 | 9.19 × 102 | 1.77 × 103 | 5.71 × 102 | |
Mean | 8.17 × 103 | 1.24 × 104 | 8.44 × 103 | 1.04 × 104 | 1.50 × 104 | 1.04 × 104 | 1.03 × 104 | 9.19 × 103 | |
F11 | Min | 1.37 × 103 | 2.00 × 103 | 1.29 × 103 | 1.84 × 103 | 7.04 × 103 | 3.15 × 103 | 1.45 × 103 | 1.30 × 103 |
Std | 3.72 × 102 | 4.68 × 103 | 8.00 × 101 | 5.80 × 102 | 2.42 × 103 | 2.85 × 103 | 2.12 × 102 | 2.50 × 102 | |
Mean | 1.72 × 103 | 5.77 × 103 | 1.43 × 103 | 3.02 × 103 | 1.12 × 104 | 7.89 × 103 | 1.75 × 103 | 1.59 × 103 | |
F12 | Min | 1.59 × 107 | 2.63 × 108 | 1.05 × 107 | 3.63 × 108 | 3.47 × 109 | 3.74 × 108 | 1.24 × 107 | 2.16 × 106 |
Std | 2.73 × 109 | 7.38 × 108 | 1.73 × 107 | 5.56 × 108 | 5.06 × 109 | 3.45 × 109 | 3.18 × 107 | 1.58 × 107 | |
Mean | 2.58 × 109 | 1.16 × 109 | 3.66 × 107 | 8.49 × 108 | 1.09 × 1010 | 4.41 × 109 | 4.90 × 107 | 1.95 × 107 | |
F13 | Min | 4.15 × 104 | 2.37 × 105 | 6.65 × 104 | 6.35 × 106 | 3.39 × 108 | 1.37 × 107 | 1.53 × 104 | 2.11 × 103 |
Std | 1.61 × 109 | 1.18 × 108 | 7.42 × 104 | 3.22 × 107 | 1.85 × 109 | 4.70 × 108 | 3.80 × 104 | 7.69 × 103 | |
Mean | 9.04 × 108 | 1.08 × 108 | 1.79 × 105 | 2.59 × 107 | 2.05 × 109 | 5.38 × 108 | 6.98 × 104 | 1.00 × 104 | |
F14 | Min | 2.23 × 105 | 3.18 × 105 | 1.51 × 105 | 3.63 × 105 | 3.65 × 105 | 9.14 × 104 | 1.21 × 104 | 1.32 × 105 |
Std | 6.21 × 106 | 4.03 × 106 | 6.75 × 105 | 4.51 × 106 | 6.59 × 106 | 5.48 × 106 | 2.59 × 105 | 3.75 × 105 | |
Mean | 2.30 × 106 | 4.03 × 106 | 9.15 × 105 | 4.92 × 106 | 7.15 × 106 | 3.41 × 106 | 2.71 × 105 | 6.21 × 105 | |
F15 | Min | 3.80 × 103 | 3.86 × 104 | 1.18 × 104 | 4.18 × 105 | 5.74 × 106 | 3.54 × 104 | 4.07 × 103 | 1.71 × 103 |
Std | 1.30 × 107 | 2.30 × 108 | 2.79 × 104 | 8.83 × 105 | 2.47 × 108 | 5.61 × 108 | 8.91 × 103 | 3.99 × 104 | |
Mean | 2.41 × 106 | 6.15 × 107 | 4.73 × 104 | 1.37 × 106 | 2.06 × 108 | 3.44 × 108 | 1.50 × 104 | 2.32 × 104 | |
F16 | Min | 2.46 × 103 | 3.44 × 103 | 2.67 × 103 | 4.01 × 103 | 4.81 × 103 | 3.50 × 103 | 3.20 × 103 | 2.98 × 103 |
Std | 5.04 × 102 | 6.49 × 102 | 4.64 × 102 | 6.60 × 102 | 5.06 × 102 | 5.01 × 102 | 3.77 × 102 | 3.26 × 102 | |
Mean | 3.55 × 103 | 4.84 × 103 | 3.59 × 103 | 4.90 × 103 | 5.95 × 103 | 4.68 × 103 | 3.93 × 103 | 3.83 × 103 | |
F17 | Min | 2.61 × 103 | 3.31 × 103 | 2.44 × 103 | 3.34 × 103 | 3.63 × 103 | 3.14 × 103 | 2.86 × 103 | 2.89 × 103 |
Std | 3.78 × 102 | 5.32 × 102 | 4.11 × 102 | 4.29 × 102 | 5.37 × 102 | 7.09 × 102 | 2.95 × 102 | 2.29 × 102 | |
Mean | 3.32 × 103 | 4.20 × 103 | 3.37 × 103 | 3.90 × 103 | 4.73 × 103 | 4.00 × 103 | 3.45 × 103 | 3.54 × 103 | |
F18 | Min | 3.31 × 105 | 3.82 × 105 | 1.04 × 106 | 1.54 × 106 | 2.95 × 106 | 3.06 × 105 | 1.59 × 105 | 9.43 × 105 |
Std | 7.38 × 106 | 9.51 × 106 | 4.22 × 106 | 1.09 × 107 | 2.47 × 107 | 1.52 × 107 | 1.60 × 106 | 4.91 × 106 | |
Mean | 6.70 × 106 | 9.41 × 106 | 7.12 × 106 | 1.19 × 107 | 3.73 × 107 | 1.57 × 107 | 1.96 × 106 | 5.78 × 106 | |
F19 | Min | 1.15 × 104 | 6.83 × 104 | 3.65 × 103 | 3.07 × 105 | 7.71 × 106 | 1.49 × 105 | 4.46 × 103 | 2.04 × 103 |
Std | 3.16 × 106 | 7.56 × 106 | 1.71 × 104 | 2.35 × 106 | 6.45 × 107 | 2.16 × 107 | 1.34 × 104 | 1.61 × 104 | |
Mean | 1.56 × 106 | 7.93 × 106 | 2.63 × 104 | 2.35 × 106 | 6.26 × 107 | 1.23 × 107 | 2.52 × 104 | 1.90 × 104 | |
F20 | Min | 2.24 × 103 | 3.04 × 103 | 2.95 × 103 | 2.88 × 103 | 3.61 × 103 | 2.83 × 103 | 2.60 × 103 | 2.97 × 103 |
Std | 4.11 × 102 | 3.48 × 102 | 2.89 × 102 | 3.21 × 102 | 2.21 × 102 | 3.17 × 102 | 3.70 × 102 | 1.78 × 102 | |
Mean | 3.14 × 103 | 3.79 × 103 | 3.42 × 103 | 3.57 × 103 | 4.24 × 103 | 3.60 × 103 | 3.35 × 103 | 3.44 × 103 | |
F21 | Min | 2.44 × 103 | 2.66 × 103 | 2.48 × 103 | 2.77 × 103 | 2.84 × 103 | 2.67 × 103 | 2.53 × 103 | 2.48 × 103 |
Std | 5.72 × 101 | 8.41 × 101 | 5.54 × 101 | 8.53 × 101 | 4.58 × 101 | 6.23 × 101 | 6.01 × 101 | 3.47 × 101 | |
Mean | 2.54 × 103 | 2.88 × 103 | 2.57 × 103 | 2.94 × 103 | 2.94 × 103 | 2.79 × 103 | 2.65 × 103 | 2.56 × 103 | |
F22 | Min | 3.94 × 103 | 9.20 × 103 | 7.75 × 103 | 9.98 × 103 | 1.54 × 104 | 1.01 × 104 | 8.64 × 103 | 9.57 × 103 |
Std | 1.92 × 103 | 2.28 × 103 | 9.69 × 102 | 8.65 × 102 | 4.95 × 102 | 1.17 × 103 | 1.55 × 103 | 7.37 × 102 | |
Mean | 1.04 × 104 | 1.25 × 104 | 9.48 × 103 | 1.25 × 104 | 1.71 × 104 | 1.23 × 104 | 1.13 × 104 | 1.10 × 104 | |
F23 | Min | 3.11 × 103 | 3.35 × 103 | 2.92 × 103 | 3.69 × 103 | 3.61 × 103 | 3.20 × 103 | 3.12 × 103 | 2.89 × 103 |
Std | 1.70 × 102 | 1.37 × 102 | 5.72 × 101 | 2.12 × 102 | 1.85 × 102 | 1.06 × 102 | 1.83 × 102 | 5.64 × 101 | |
Mean | 3.35 × 103 | 3.57 × 103 | 3.04 × 103 | 4.01 × 103 | 3.91 × 103 | 3.39 × 103 | 3.43 × 103 | 3.01 × 103 | |
F24 | Min | 3.27 × 103 | 3.46 × 103 | 3.02 × 103 | 3.96 × 103 | 3.61 × 103 | 3.23 × 103 | 3.39 × 103 | 3.11 × 103 |
Std | 1.96 × 102 | 1.24 × 102 | 9.09 × 101 | 2.16 × 102 | 1.59 × 102 | 1.25 × 102 | 3.11 × 102 | 5.05 × 101 | |
Mean | 3.53 × 103 | 3.67 × 103 | 3.19 × 103 | 4.31 × 103 | 3.93 × 103 | 3.54 × 103 | 3.78 × 103 | 3.24 × 103 | |
F25 | Min | 3.08 × 103 | 3.16 × 103 | 3.04 × 103 | 3.34 × 103 | 4.26 × 103 | 4.26 × 103 | 3.14 × 103 | 2.94 × 103 |
Std | 1.12 × 102 | 1.74 × 103 | 3.88 × 101 | 2.23 × 102 | 1.15 × 103 | 5.79 × 102 | 9.71 × 101 | 4.86 × 101 | |
Mean | 3.23 × 103 | 3.79 × 103 | 3.10 × 103 | 3.79 × 103 | 6.96 × 103 | 5.15 × 103 | 3.32 × 103 | 3.02 × 103 | |
F26 | Min | 3.71 × 103 | 8.28 × 103 | 2.94 × 103 | 7.59 × 103 | 1.10 × 104 | 6.36 × 103 | 8.07 × 103 | 5.33 × 103 |
Std | 1.66 × 103 | 1.35 × 103 | 2.28 × 103 | 1.39 × 103 | 9.68 × 102 | 2.24 × 103 | 1.32 × 103 | 5.11 × 102 | |
Mean | 7.15 × 103 | 1.10 × 104 | 5.42 × 103 | 1.18 × 104 | 1.36 × 104 | 1.08 × 104 | 1.11 × 104 | 6.64 × 103 | |
F27 | Min | 3.45 × 103 | 3.60 × 103 | 3.32 × 103 | 3.87 × 103 | 3.94 × 103 | 3.73 × 103 | 3.58 × 103 | 3.20 × 103 |
Std | 2.45 × 102 | 2.42 × 102 | 1.05 × 102 | 7.13 × 102 | 4.89 × 102 | 2.87 × 102 | 2.39 × 102 | 1.78 × 10−4 | |
Mean | 3.74 × 103 | 4.01 × 103 | 3.54 × 103 | 4.94 × 103 | 4.74 × 103 | 4.31 × 103 | 3.95 × 103 | 3.20 × 103 | |
F28 | Min | 3.42 × 103 | 3.52 × 103 | 3.32 × 103 | 3.99 × 103 | 6.01 × 103 | 4.30 × 103 | 3.49 × 103 | 3.30 × 103 |
Std | 1.04 × 103 | 2.49 × 103 | 4.71 × 101 | 3.91 × 102 | 8.66 × 102 | 6.50 × 102 | 1.34 × 102 | 2.05 × 10−4 | |
Mean | 4.47 × 103 | 6.67 × 103 | 3.38 × 103 | 4.77 × 103 | 7.52 × 103 | 5.55 × 103 | 3.84 × 103 | 3.30 × 103 | |
F29 | Min | 3.82 × 103 | 4.69 × 103 | 4.26 × 103 | 5.69 × 103 | 7.09 × 103 | 5.32 × 103 | 4.86 × 103 | 3.99 × 103 |
Std | 4.26 × 102 | 8.66 × 102 | 3.00 × 102 | 8.53 × 102 | 1.70 × 103 | 8.62 × 102 | 4.73 × 102 | 2.11 × 102 | |
Mean | 4.66 × 103 | 6.20 × 103 | 4.98 × 103 | 7.06 × 103 | 9.83 × 103 | 6.86 × 103 | 5.52 × 103 | 4.37 × 103 | |
F30 | Min | 1.31 × 106 | 4.69 × 106 | 7.83 × 106 | 3.61 × 107 | 2.02 × 108 | 9.52 × 107 | 1.46 × 106 | 3.34 × 103 |
Std | 8.05 × 106 | 6.09 × 107 | 3.82 × 106 | 7.68 × 107 | 2.23 × 108 | 1.92 × 108 | 1.69 × 106 | 6.54 × 103 | |
Mean | 7.40 × 106 | 6.37 × 107 | 1.35 × 107 | 1.38 × 108 | 5.29 × 108 | 2.84 × 108 | 3.75 × 106 | 9.58 × 103 |
Algorithm | l | t | b | h | fmin |
---|---|---|---|---|---|
PSO | 0.125 | 6.3202 | 8.4483 | 0.2661 | 3.4293 |
DBO | 0.3469 | 3.8941 | 5.6022 | 0.5353 | 2.7293 |
SMA | 0.1956 | 3.4175 | 3.4175 | 0.1989 | 1.6925 |
HHO | 0.1708 | 3.7218 | 9.5616 | 0.1953 | 1.7859 |
SABO | 0.2759 | 2.7468 | 7.8187 | 0.2889 | 2.5531 |
SLTSO | 0.1981 | 3.3528 | 9.1916 | 0.1988 | 1.6713 |
TSO | 0.1962 | 3.4175 | 9.1995 | 0.1989 | 1.6931 |
SCSO | 0.1913 | 3.5671 | 9.1924 | 0.1985 | 1.6897 |
Algorithm | l | t | b | h | fmin |
---|---|---|---|---|---|
PSO | 12 | 23.869 | 51.1725 | 38.7949 | 1.7009 × 10−14 |
DBO | 16.592 | 12 | 48.651 | 28.3652 | 9.9416 × 10−28 |
SMA | 12 | 16.3463 | 36.245 | 37.5114 | 2.6689 × 10−11 |
HHO | 15.2728 | 27.4423 | 53.8562 | 53.9388 | 1.2646 × 10−24 |
SABO | 27.5857 | 14.3694 | 49.5786 | 55.4162 | 1.4442 × 10−11 |
SLTSO | 12 | 24.0508 | 38.6095 | 51.8098 | 1.9259 × 10−32 |
TSO | 15.2097 | 34.1496 | 54.3547 | 55.1563 | 1.2646 × 10−27 |
SCSO | 21.0187 | 33.6516 | 78.4484 | 62.5337 | 9.4023 × 10−9 |
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Wang, Q.; Xu, M.; Hu, Z. Path Planning of Unmanned Aerial Vehicles Based on an Improved Bio-Inspired Tuna Swarm Optimization Algorithm. Biomimetics 2024, 9, 388. https://doi.org/10.3390/biomimetics9070388
Wang Q, Xu M, Hu Z. Path Planning of Unmanned Aerial Vehicles Based on an Improved Bio-Inspired Tuna Swarm Optimization Algorithm. Biomimetics. 2024; 9(7):388. https://doi.org/10.3390/biomimetics9070388
Chicago/Turabian StyleWang, Qinyong, Minghai Xu, and Zhongyi Hu. 2024. "Path Planning of Unmanned Aerial Vehicles Based on an Improved Bio-Inspired Tuna Swarm Optimization Algorithm" Biomimetics 9, no. 7: 388. https://doi.org/10.3390/biomimetics9070388