I noticed the ESO uses mutation and the particle are changed/selected using the 'survival of the fittest' while in PSO mutation is not used and all the particle remains the same and follow the best particle's position. Please correct me if I'm wrong.
I infer you mentioned, "in PSO the particles remain the same" due to the fact that "mutation" is not directly used in PSO.
Note that mutation is an exploratory operator. For example, idea behind mutation is to apply some disturbance at the chromosomes of the individual (i.e., the position in the search space) so it wilds unexplored individuals (i.e., unexplored areas). On the other hand, crossover performs exploitation by selecting fit individuals and creating offspring given their genes.
Even though the "mutation operator" is not directly applied in PSO, it has its own methods of exploration and exploitation, and it is directly connected to the way the velocity vector of the particles is adjusted.
what are the main differences between Evolutionary strategy Optimization(ESO) and particle swarm Optimization(PSO)?