Cooperative Global Path Planning for Multiple Unmanned Aerial Vehicles Based on Improved Fireworks Algorithm Using Differential Evolution Operation

Abstract

Multiple unmanned aerial vehicles’ (multi-UAVs) cooperative global path planning is considered as a complexed nonlinear optimization problem. The improved hybrid fireworks algorithm with differential evolution (HDEFWA) is put forward herein to handle the problem and yield optimal flyable paths for multi-UAVs. The UAV paths are expected to be safe and short, of which the cost function is modeled according to realistic scenarios. The proposed HDEFWA can generate the extra DE-sparks through the mutation, crossover, and selection operators using the highly ranked individuals, which greatly enhances the information sharing capacity among the better individuals and thus effectively strengthen the capacity to escape from local optima. To handle the multi-UAVs cooperative planning, the whole firework population in HDEFWA is divided into a series of parallel firework groups, and the information interaction mechanism is established to calculate the cooperative cost of solutions to achieve the collision-free among UAV paths. Simulation results demonstrate that our HDEFWA can effectively settle multi-UAVs cooperative path planning with the better performance than other population-based algorithms.

Appendix

1.1 Definitions of the Test Functions:

• 1. Sphere function: $f_{1} (x) = \sum\nolimits_{i = 1}^{D} {x_{i}^{2} }$.

• 2. Rosenbrock function: $f_{2} (x) = \sum\nolimits_{i = 2}^{D - 1} (100(x_{i}^{2} - x_{i - 1} )^{2}+$ $(x_{i} - 1)^{2})$.

• 3. Griewank function: $f_{3} (x) = \sum\nolimits_{i = 1}^{D} \frac{x_{i}^{2}}{4000}$ $- \prod\nolimits_{i = 1}^{D} \cos \left(\frac{x_{i}}{\sqrt i}\right)+1$.

• 4. Rastrigin function: $f_{4} \left( x \right) = \sum\limits_{{i - 1}}^{D} {\left( {x_{i}^{2} - 10\cos \left( {2\pi x_{i} } \right) + 10} \right)}$ .

• 5. Schwefel function: $f_{5} = \sum\nolimits_{i = 1}^{n} {\left( {\sum\nolimits_{j = 1}^{i} {x_{i} } } \right)^{2} }$.

• 6. Ackley function: $f_{6} (x) = - 20\exp \left( { - 0.2\sqrt {\frac{1}{D}\sum\nolimits_{i = 1}^{D} {x_{i}^{2} } } } \right) - \exp \left( {\frac{1}{D}\sum\nolimits_{i = 1}^{D} {\cos (2\pi x_{i} )} } \right) + 20 + e$.

• 7. Axis parallel hyper-ellipsoid function: $f_{7} (x) = \sum\nolimits_{i = 1}^{D} {\left( {\sum\nolimits_{j1}^{D} {x_{j} } } \right)^{2} }$.

• 8. Rotated hyper-ellipsoid function: $f_{8} (x) = \sum\nolimits_{i = 1}^{D} {\left( {\sum\nolimits_{j = 1}^{i} {x_{j}^{2} } } \right)^{2} }$.

• 9. Schaffer function: $f_{9} (x) = 0.5 + \frac{{\sin^{2} \left( {\sqrt {\sum\nolimits_{i = 1}^{D} {x_{i}^{2} } } } \right) - 0.5}}{{\left( {1 + 0.001\left( {\sqrt {\sum\nolimits_{i = 1}^{D} {x_{i}^{2} } } } \right)} \right)^{2} }}$.

• 10. Perm function: $f_{10} (x) = \sum\nolimits_{i = 1}^{D} \left(\sum\nolimits_{j = 1}^{D} (j^{i} + 0.5)\right.$ $\left.\left( \left( \frac{x_{j}}{j}\right)^{i} - 1\right) \right)^{2}$.

• 11. Michalewicz function: $f_{11} (x) = - \sum\nolimits_{i = 1}^{D} \sin (x_{i} )$ $\sin^{2*10}\left(\frac{{ix_{i}^{2} }}{\pi }\right)$.