Automatic path planning of unmanned combat aerial vehicle based on double-layer coding method with enhanced grey wolf optimizer

Abstract

The unmanned combat aerial vehicle (UCAV) technology has to deal with a lot of challenges in complex battlefield environments. The UCAV requires a high number of points to build the path to avoid dangers in order to achieve a safe and low-energy flying path, which increases the issue dimension and uses more computer resources while producing unstable results. To address the issue, this paper proposes a double-layer (DLC) model for path planning, which reduces the outputting dimension of path-forming points, reduces the computational cost and enhances the path stability. Meanwhile, this paper improves the grey wolf optimizer (K-FDGWO) by introducing adaptive K-neighbourhood-based learning strategy and differential “hunger-hunting strategy”, and using fitness distance correlation (FDC) to balance the global exploration and local exploitation. Besides, the K-FDGWO and Differential Evolution (DE) algorithm are jointly used for the DLC model (DLC-K-FDGWO). The experimental results indicated that the proposed DLC-K-FDGWO method for path planning always generated the ideal flight path in complicated environments.

Appendix

Function expression	Range	D	$f_{min}$
$F1(x)=\sum ^{n}_{i=1}{x^{2}}$	$[-100,100]$	30	0
$F2(x)=\sum ^{n}_{i=1}{\mid x_{i} \mid }+\prod ^{n}_{i=1}{\mid x_{i} \mid }$	$[-10,10]$	30	0
$F3(x)=\sum ^{n}_{i=1}{\left( \sum ^{i}_{j-1}{x_{j}}\right) ^{2}}$	$[-100,100]$	30	0
$F4(x)=\max \{x_{i}\mid 1\le i \le n\}$	$[-100,100]$	30	0
$F5(x)=\sum ^{n-1}_{i=1}{[100(x_{i+1}-x^{2}_{i})+(x_{i}-1)^{2}]}$	$[-30,30]$	30	0
$F6(x)=\sum ^{n}_{i=1}{([x_{i}+0.5])^{2}}$	$[-100,100]$	30	0
$F7(x)=\sum ^{n}_{i=1}{-x_{i}\sin (\sqrt{(\vert x_{i}\vert )})}$	$[-500,500]$	30	$-418.9829\cdot$ D
$F8(x)=\sum ^{n}_{i=1}{[x^{2}_{i}-10\cos (2\pi x_{i})+10]}$	$[-5.12,5.12]$	30	0
$F9(x)=-20\exp \left( {-0.2\sqrt{\frac{1}{n}\sum ^{n}_{i=1}{x^{2}_{i}}}}\right) -\exp \left( \frac{1}{n}\right.$
$\left. \sum ^{2}_{i=1}{\cos (2\pi x_{i})}\right) +20+e$	$[-32,32]$	30	0
$F10(x)=\frac{1}{4000}\sum ^{n}_{i=1}{x^{2}_{i}}-\prod ^{n}_{i=1}{\cos \left( \frac{x_{i}}{\sqrt{i}}\right) }+1$	$[-600,600]$	30	0
$F11(x)==\frac{\pi }{n}\{10\sin (\pi y_{1})+\sum ^{n-1}_{i=1}{(y_{i}-1)^{2}[1+10\sin ^{2}(\pi y_{i}+1)]}$
$+(y_{n}-1)^{2}\}+\sum ^{n}_{i=1}{u(x_{i},a,k,m)},$
$y_{i}=1+\frac{1}{4}(x_{i}+1),$
$u(x_{i},a,k,m)=\left\{ \begin{array}{ll} k(x_{i}-a)^{m},&{}ifx_{i}>a\\ 0, &{}if-a\le x_{i}\le a\\ k(-x_{i}-a)^{m}, &{}ifx_{i}<-a \end{array} \right.$	$[-50,50]$	30	0
$F12(x)=0.1\{ \sin ^{2}(3\pi x_{1})+\sum ^{n}_{i=1}[(x_{i}-1)^{2}[1+\sin ^{2}(3\pi x_{i}+1)]$
$+(x_{n}-1)^{2}[1+\sin ^{2}(2\pi x_{n})]]+\sum ^{n}_{i=1}u(x_{i},5,100,4)\}$	$[-50,50]$	30	0
$F13(x)=\sum ^{n}_{i=1}{\mid x_{i}\sin (x_{i})+0.1x_{i}\mid }$	$[-10,10]$	30	0
$F14(x)=(x^{2}_{1}+x_{2}-11)^{2}+(x_{1}+x^{2}_{2}-7)^{2}$	$[-6,6]$	2	0
$F15(x)=\left( \frac{1}{500}+\sum ^{25}_{j=1}\frac{1}{j+\sum ^{2}_{i=1}{(x_{i}-a_{i,j})^{6}}}\right) ^{-1}$	$[-65,65]$	2	1
$F16(x)=\sum ^{11}_{i=1}{\left[ a_{i}-\frac{x_{1}(b^{2}_{i}+b_{i}x_{2})}{b^{2}_{i}+b_{i}x_{3}+x_{4}}\right] ^{2}}$	$[-5,5]$	4	0.0003
$F17(x)=4x_{1}^{2}-2.1x_{1}^{4}+\frac{1}{3}x_{1}^{6}+x{1}x_{2}-4x_{2}^{2}+4x_{2}^{4}$	$[-5,5]$	2	$-1.0316$
$F18(x)=\left( x_{2}-\frac{5.1}{4\pi ^{2}}+\frac{5}{\pi }-6\right) ^{2}+10\left( 1-\frac{1}{8\pi }\right) \cos x_{1}+10$	$[-5,5]$	2	0.398
$F15(x)=[1+(x_{1}+x_{2}+1)^{2}(19-14x_{1}+3x^{2}_{1}-14x_{2}+6x_{1}x_{2}+3x^{2}_{2})]$
$[30+(2x_{1}-3x_{2})^{2}(18-32x_{1}+12x^{2}_{1}+48x_{2}-36x_{1}x_{2}+27x^{2}_{2})]$	$[-2,2]$	2	3
$F19(x)=-\sum ^{4}_{i=1}c_{i}\exp \left( -\sum ^{3}_{j=1}a_{ij}(x_{j}-p_{ij})^{2}\right)$	[1, 3]	3	$-3.86$
$F20(x)=-\sum ^{4}_{i=1}c_{i}\exp \left( -\sum ^{6}_{j=1}a_{ij}(x_{j}-p_{ij})^{2}\right)$	[0, 1]	6	$-3.32$
$F21(x)=-\sum ^{5}_{i=1}[(X-a_{i})(X-a_{i})^{T}+c_{i}]^{-1}$	[0, 10]	4	$-10.1532$
$F22(x)=-\sum ^{7}_{i=1}[(X-a_{i})(X-a_{i})^{T}+c_{i}]^{-1}$	[0, 10]	4	$-10.4028$
$F23(x)=-\sum ^{10}_{i=1}[(X-a_{i})(X-a_{i})^{T}+c_{i}]^{-1}$	[0, 10]	4	$-10.5363$