Table 2 Bio-Inspired algorithms comparison.

Particle Swarm Optimization (PSO)⁵⁹

Swarm behavior of birds/fish

Velocity and position updates based on personal and global best positions

Moderate

Strong

Yes (by\(\:w,\:c1,\:c2\))

Grey Wolf Optimizer (GWO)³⁴

Grey wolves’ hunting strategy

Hierarchical role-based movement: α, β, δ guide others; encircling and attacking prey

Moderate

Strong

Yes (by\(\:a\))

Cuckoo Search (CS)⁶⁰

Cuckoo’s parasitic egg-laying

Lévy flights; survival of best nests; discovery probability

Strong

Moderate

Yes (by\(\:\rho\:,\:{a}_{s}\))

Ant Colony Optimization (ACO)⁶¹

Ants’ pheromone-based foraging

Pheromone deposition and evaporation; probabilistic path choice

Moderate

Strong

Yes (by\(\:\alpha\:,\:\beta\:,\:\rho\:\))

Dolphin Optimization Algorithm (DOA)⁶²

Echolocation and cooperative hunting

Sonar exploration, subgroup cooperation, and information sharing

Strong

Strong

Yes (by\(\:P{P}_{1},\:{R}_{e}\))

Crow Search Algorithm (CSA)⁶³

Crows’ food caching and deception

Memory-based tracking, awareness probability APAP, random relocation

Strong

Moderate

Yes (by\(\:AP,\:FL\))

Genetic Algorithm (GA)⁶⁴

Darwinian evolution

Choice, crossover, mutation

Strong (via mutation)

Strong (via choice)

Yes (by\(\:{P}_{c},\:{P}_{m}\))

Whale Optimization Algorithm (WOA)⁶⁵

Humpback whales’ bubble-net hunting

Spiral motion, encircling prey, random search

Moderate

Strong

Yes (by\(\:b,\:a\))

Bat Algorithm (BA)⁶⁶

Bats’ echolocation

Frequency tuning, loudness attenuation, pulse adaptation

Moderate to Strong

Strong

Yes (by

\(\:{f}_{min},\:{f}_{max}\:,\:r,\:A\))

Artificial Bee Colony (ABC)⁶⁷

Foraging behavior of honeybees

Roles of employed, onlooker, and scout bees; solution abandonment and recruitment

Strong

Moderate

Abandonment limit)