This study introduces enhancements to three established swarm intelligence-based optimization algorithms: the Improved Crow Search, Dynamic BAT, and Levy Whale Optimization. Mutation operators, traditionally used in evolutionary-based optimization like genetic algorithms, help escape local optima to converge towards a global solution. This work integrates two novel mutation operators into these algorithms, enhancing their ability to effectively explore and exploit the search space. We employed 12 benchmark functions to analyze performance, observing improvements in global optimal values ranging from 29% to 152%. Furthermore, we applied these algorithms as training optimizers for neural networks, aiming to predict pelvic joint location from fingertips and these data have been used to train a multi-layered feedforward neural network. The algorithms without mutation and with mutation operators have been used as optimizers to train neural networks. A significant decrease in the absolute average percentage from experimental data has been observed. These findings highlight the potential of mutation operators to refine the exploration and exploitation capabilities of swarm intelligence algorithms.