Sunn Pest Optimization (SPO): A Phase-Differentiated Bio-Inspired Metaheuristic for Global Optimization with Application to Precision Agriculture Monitoring Networks

. 2026 Sep 19;11(9):676. doi: 10.3390/biomimetics11090676

Algorithm 1 Sunn Pest Optimization (SPO)

Require:

f (x)

, D,

l b

u b

, N, T, all parameters
Ensure:

X_{b e s t}

f_{b e s t}

1:
$X_{i} \sim U (l b, u b)$ , $i = 1 \dots N$ ▹ Initial population
2:
$f i t_{i} \leftarrow f (X_{i}) \forall i$
3:
$X_{b e s t} \leftarrow X_{\arg \min_{i} f i t_{i}}$ , $f_{b e s t} \leftarrow \min_{i} f i t_{i}$
4:
$Δ (0) \leftarrow \frac{1}{N} \sum_{i} {∥ X_{i} - μ (0) ∥}_{2}$ ▹ Equation (8), $t = 0$
5:
$d i v_t h r e s h o l d \leftarrow \max (Δ (0) \cdot ε, 10^{- 10})$ ▹ Equation (9)
6:
$s t a g \leftarrow 0$ , $f_{p r e v} \leftarrow f_{b e s t}$
7:
for $t = 0$ to $T - 1$ do
8:
$w (t) \leftarrow w_{m a x} - t \cdot (w_{m a x} - w_{m i n}) / T$ ▹ Equation (2)
9:
if $t < 0.4 T$ then
10:
$X \leftarrow$ LevyMigration(X, $X_{b e s t}$ , $w (t)$ ) ▹ Equations (3)–(5)
11:
else
12:
$X \leftarrow$ DifferentialMigration(X, $X_{b e s t}$ , $w (t)$ ) ▹ Equation (6)
13:
end if
14:
$f i t_{i} \leftarrow f (X_{i}) \forall i$ ; update $X_{b e s t}$ , $f_{b e s t}$
15:
$Δ (t) \leftarrow \frac{1}{N} \sum_{i} {∥ X_{i} - μ (t) ∥}_{2}$ ▹ Equation (8)
16:
$s t a g \leftarrow (f_{b e s t} < f_{p r e v} - 10^{- 10}) ? 0 : s t a g + 1$ ▹ Equation (7)
17:
if $Δ (t) < d i v_t h r e s h o l d$ then
18:
$s t a g \leftarrow \max (s t a g, 24)$ ▹ diversity-override
19:
end if
20:
if $s t a g \geq 8$ then
21:
$[X, f i t] \leftarrow$ Carabid( $X, f i t$ ) ▹ Equations (10) and (11)
22:
end if
23:
if $s t a g \geq 16$ then
24:
$[X, f i t] \leftarrow$ Beauveria( $X, f i t, X_{b e s t}$ ) ▹ Equations (12)–(14)
25:
end if
26:
if $s t a g \geq 24$ then
27:
$[X, f i t] \leftarrow$ Parasitoid( $X, f i t$ ); $s t a g \leftarrow 0$ ▹ Equations (15)–(17)
28:
end if
29:
Elitism: worst $0.1 N \leftarrow$ best $0.1 N$ ▹ Equation (18)
30:
$f_{p r e v} \leftarrow f_{b e s t}$
31:
end for
32:
return $X_{b e s t}$ , $f_{b e s t}$