Table 3.

Optimization techniques: a detailed comparative analysis.

Optimization method	Description
Adagrad (Adaptive Gradient Algorithm)48	Adapts learning rates for each parameter based on historical gradient information
Adam (Adaptive Moment Estimation)49	Combines advantages of Adagrad and Root Mean Squared Propagation (RMSprop) and adapts the learning rates individually for each parameter
Adadelta50	Extension of Adagrad addressing diminishing learning rate
ADAPLUS51	Integrates Nesterov momentum and precise step size adjustment on an AdamW basis
Adan52	Adaptive Nesterov momentum algorithm for optimizing deep models faster
Phasor Particle Swarm Optimization (PPSO)53	Replaces control parameters with a scalar phasor angle based on trigonometric functions
Fitness-based Multirole PSO (FMPSO)54	Integrates a sub-social learning part into standard PSO to enhance search mechanisms
Multi-Swarm PSO (MSPSO)55	Utilizes dynamic strategies to divide swarms, regroup them, and avoid local minima based on historical information
Expanded PSO (XPSO)56	Integrates forgetting ability and multi-exemplar concept into standard PSO for improved optimization