Path Planning of UAV Using Levy Pelican Optimization Algorithm In Mountain Environment

Figures & data

Figure 1. Logistic chaotic mapping distribution.

Figure 2. Schematic diagram of Levy’s flight.

Figure 3. Flow chart of improved LPOA.

Figure 4. The parameter space diagram of the benchmark function.

Table 1. Details of the benchmark functions.

Function	Range	Dim	${\mathit{F}}_{\mathit{min}}$
$f_1\left(\mathit{x}\right)=\sum _{\mathit{i}=1}^m{x}_i^2$	$\left[-100,100\right]$	30	0
$f_2\left(\mathit{x}\right)=\sum _{\mathit{i}=1}^m\left|x_i\right|+\prod _{\mathit{i}=1}^m\left|x_i\right|$	$\left[-10,10\right]$	30	0
$f_3\left(\mathit{x}\right)=\sum _{\mathit{i}=1}^m{\left(\sum _{\mathit{j}=1}^i{x}_i\right)}^2$	$\left[-100,100\right]$	30	0
$f_4\left(\mathit{x}\right)=\mathit{max}\left\{\left|x_i\right|,1\le \mathit{i}\text{lem}\right\}$	$\left[-100,100\right]$	30	0
$f_8\left(\mathit{x}\right)=\sum _{\mathit{i}=1}^m-x_{i}sin\left(\sqrt{\left|x_i\right|}\right)$	$\left[-500,500\right]$	30	$-12,569$
$f_{11}\left(\mathit{x}\right)=\frac{1}{4000}\sum _{\mathit{i}=1}^m{x}_i^2-\prod _{\mathit{i}=1}^{m}cos\left(\frac{x_i}{\sqrt{\mathit{i}}}\right)+1$	$\left[-600,600\right]$	30	0

Figure 5. Algorithm comparison iteration diagram.

Table 2. Comparison of the performance of the algorithms in the benchmark function.

		GA	PSO	GWO	WOA	MPA	POA	LPOA
F1	avg	11.6364	4.1543 × 10^−4	1.1643 × 10^−57	5.29 × 10^−62	3.2583 × 10^−20	2.27 × 10^−213	0
	std	2.6142 × 10^−11	3.1673 × 10^−21	5.2363 × 10^−74	2.6142 × 10^−78	2.6142 × 10^−19	2.612 × 10^−11	0
F2	avg	4.2362	0.2578	2.2366 × 10^−32	2.36 × 10^−56	6.3214 × 10^−11	5.4322 × 10^−107	3.4511 × 10^−291
	std	5.2354 × 10^−14	4.4667 × 10^−16	5.9353 × 10^−30	5.23 × 10^−59	3.356 × 10^−11	2.1925 × 10^−106	0
F3	avg	1435.1356	567.3467	4.4561 × 10^−14	6.2356 × 10^−10	0.0819	2.0210 × 10^−210	0
	std	6.6096 × 10^−12	9.7117 × 10^−12	6.3467 × 10^−28	1.23 × 10^−18	0.1370	0	0
F4	avg	2.0315	4.3578	1.9925 × 10^−13	0.0013	5.234 × 10^−8	8.9656 × 10^−105	1.3226 × 10^−227
	std	4.3456 × 10^−14	4.2019 × 10^−15	1.8235 × 10^−28	0.0877	2.3687 × 10^−9	4.9070 × 10^−104	0
F8	avg	−8210.3415	−6899.9556	−5903.3711	−7239.1	−3611.2271	−9336.7304	−1.2513 × 10^4
	std	833.5126	625.4286	467.8216	261.0117	811.1459	2.64 × 10^−12	111
F11	avg	0.0469	0.4792	0.0364	0.007728	0.0815	0.0583	0
	std	1.7456 × 10^−14	9.3071 × 10^−15	1.3604 × 10^−13	8.07 × 10^−5	0.0162	2.73 × 10^−16	0

Table 3. Order by Friedman test in dimensions D = 30.

Function	GA	PSO	GWO	WOA	MPA	POA	LPOA
F1	7	6	4	3	5	2	1
F2	7	6	4	3	5	2	1
F3	7	6	4	3	5	2	1
F4	7	6	4	3	5	2	1
F8	6.5	5.5	3.67	3.33	5	1.67	1.33
F11	6.5	5.5	3.67	3.33	5	2	1
Overall Rank	7	6	4	3	5	2	1

Figure 6. Simulation result graph.

Figure 7. Comparison of algorithm iterations.

Table 4. Partial parameters of the algorithm.

Basic Data	Symbol	Coordinate range
Start	$x_s$	（5,95）
End	$x_t$	（145,5）
Rough navigation point	$z_n$	5
Navigation points obtained by interpolation	$z_m$	100
Penalty Factor	${\gamma }_b$	10^4
Obstacle Coordinate	$x_{\mathit{z}1}{x}_{\mathit{z}2}{x}_{\mathit{z}3}{x}_{\mathit{z}4}$	（30,80）、（50,65）、（70,60）、（100,30）
Obstacle radius	Radius	8,11,6,8
Flight line length weighting	$v_1$	0.3
Smoothing index weighting	$v_2$	0.2
Flight altitude-related weighting	$v_3$	0.2
Crash threat indicator weighting	$v_4$	0.3
Population size	$\mathit{n}$	30
Maximum number of iterations	$\mathit{T}$	200
Logistic control parameter	$\mathit{\mu }$	3.6

Table 5. Statistics of experimental results.

Experimental Algorithm	Average cost	Average shortest path	Average iterations	Average computing time/s	Standard deviation
POA	103.23	73.26	63.79	12.57	4.78
LPOA	93.16	58.39	83.16	14.06	2.17

Data Availability Statement

The data used to support the findings of this study are included within the article.