*3.5. Population Mutation*

To enhance the ability to jump out of local extremes, we introduce the mutation operator from the genetic algorithm into the PSO [43]. This can expand the search space of the particles themselves, enhance the diversity of the population and further increase the possibility of finding the optimal solution. The particles will reset with a certain probability after each evolution. When the mutation condition is met, the mutation jumps out of the current position; otherwise, the original position remains unchanged. The particle variation can be expressed as:

$$\times\_{id}(t) = r \times (\mathbf{U}\_{\mathbf{x}} - L\_{\mathbf{x}})/n + (\mathbf{U}\_{\mathbf{x}} - L\_{\mathbf{x}})/2,\tag{13}$$

where *r* is uniformly distributed in the range [ −1, 1], **U***x* and *Lx* are the upper and lower limits of a given position and *n* is 4. The mutation condition is random mutation, and the mutation probability is 10%.
