To effectively tackle large-scale optimization problems, numerous efforts have been made by various swarm intelligence methodologies to strike a balance between two critical functions: exploration and exploitation. However, in the majority of existing particle swarm optimizers, these two functions often remain indistinguishable throughout the optimization process. To mitigate the mutual interference between exploration and exploitation, designers of optimizers have attempted to design these functions separately. Nonetheless, there has been limited research into analyzing the roles and the relationship between exploration and exploitation. Building upon our previous work, we have redesigned several state-of-the-art large-scale particle swarm optimizers using a decoupled learning pattern. Through comprehensive experimental analysis on the synergistic effect of exploitation and exploration, we delve into the optimization performance and introduce a mathematical model to illustrate their interrelationship. Our investigation and analysis reveal that most existing algorithms exhibit sensitivity in the parameter settings for exploration and exploitation, an aspect that has not been adequately addressed before. Based on the proposed mathematical analysis of the parameters, we provide clear balance model for algorithm designers and users on how to balance these two factors when solving large-scale optimization problems.