MSCSO: A Modified Sand Cat Swarm Algorithm for 3D UAV Path Planning in Complex Environments with Multiple Threats

. 2025 Apr 25;25(9):2730. doi: 10.3390/s25092730

Algorithm 1: The MSCSO

Input:

Population size N

, Max iterations T_{m a x}

, Search space [l b

, u b]

Output:

Global optimal solution X_{g l o b a l}

$Initialize the chaotic Cat Map individual X_{c a t}$ ;
The opposition-based learning individual $X_{o b l}$ , the merged population X;
$The Selected Top X_{g l o b a l}$
$while t < T_{m a x}$ do
$if t < 0.75 T_{m a x}$ then
$X_{n e w} \leftarrow X + 0.1 \cdot L e v y (β) \cdot (u b - l b)$
$Update X via Metropolis criterion with T = T_{0} \cdot {0.95}^{t}$
end
$else if t \geq 0.75 T_{m a x}$ then
$Compute diversity metric d i v = \frac{1}{N} \sum ∥ X i - μ ∥$
for each individual do
$if r a n d < 0.5 + 0.2 (d i v / m a x (d i v))$ then
$X_{n e w} \leftarrow X + δ, δ = 0.05 (u b - l b) (1 - t / T_{m a x}) \cdot N (0, 1)$
end
$else if r a n d \geq 0.5 + 0.2 (d i v / m a x (d i v))$ then
$Update velocity V \leftarrow w V + c_{1} r_{1} (X_{g l o b a l} - X) + c_{2} r_{2} (μ - X)$
$X_{n e w} \leftarrow X + 0.1 V$
end
end
end
Perform mutation: $X_{m u t} \leftarrow X_{e l i t e} + σ_{m u t} \cdot N (0, 1), σ_{m u t} = 0.05 (u b - l b ((1 - t / T_{m a x})$
Replace worst $N_{e l i t e} individuals with X_{m u t}$
$X_{g l o b a l} \leftarrow a r g m i n f (X)$
$t \leftarrow t + 1$
end