Experimental Characterization of Emergent Behavior in Bio-Inspired Swarm Intelligence Algorithms

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. 2026 Aug 12;11(8):576. doi: 10.3390/biomimetics11080576

Algorithm 3 Pseudocode of the DLO algorithm

1:
Initialize DLO parameters and initialize the population.
2:
Calculate the fitness value of the agents
3:
Update global optimal fitness value $f_{g b e s t}$ and the optimal individual position $\vec{x b e s t}$
4:
while $t < T_{m a x}$ do
5:
for $i \leftarrow 1$ to N do
Exploration phase
6:
if $(t < \frac{T_{m a x}}{2})$ then
7:
$A = round (1 + rand (0, 1))$
8:
initialize the direction vector $\vec{D L}$
9:
for $j \leftarrow 1$ to D do
10:
update $D L^{(j)}$
11:
end for
12:
if ${\vec{x b e s t}}_{i} > {\vec{x b e s t}}_{m}$ then
13:
${\vec{x}}_{i}^{(t + 1)} = {\vec{x b e s t}}_{i} + r \cdot ({\vec{x}}_{m}^{(t)} - A \cdot {\vec{x b e s t}}_{i}) + \vec{D L} \cdot r \cdot ({\vec{x}}_{m}^{(t)} - {\vec{x}}_{n}^{(t)})$
14:
else
15:
${\vec{x}}_{i}^{(t + 1)} = {\vec{x b e s t}}_{i} + r \cdot ({\vec{x b e s t}}_{i} - {\vec{x}}_{m}^{(t)}) + \vec{D L} \cdot r \cdot ({\vec{x}}_{m}^{(t)} - {\vec{x}}_{n}^{(t)})$
16:
end if
Exploitation phase
17:
else
18:
update Lévy flight search strategy
19:
if $r a n d (0, 1) < p$ then
20:
${\vec{x}}_{i}^{(t + 1)} = \vec{g b e s t} + l e v y (D) \cdot (\vec{g b e s t} - {\vec{x}}_{l}^{(t)})$
21:
else
22:
${\vec{x}}_{i}^{(t + 1)} = \vec{g b e s t} + g \cdot (1 - \frac{t}{T_{\max}}) \cdot ({\vec{x b e s t}}_{i} - {\vec{x}}_{l}^{(t)})$
23:
end if
24:
end if
25:
update $\vec{x b e s t_{i}}$ using greedy selection strategy
26:
update $\vec{g b e s t}$ using greedy selection strategy
27:
end for
28:
$t = t + 1$
29:
end while
30:
Output: the global optimal fitness value $f_{g b e s t}$ and the global optimal position $\vec{g b e s t}$