(2) Loop Iteration

In each iteration, ant *k* (*k* = 1, 2, 3, . . . , *m*) determines the direction of their transition based on the pheromone on each path. The tabu table, *tabu<sup>k</sup>* is used to record the location capacity of the ants. The ant determines the transition probability based on the pheromone and path heuristic information on each path. *Pij*(*t*) represents the probability that ant *k* is transferred from position *i* to position *j* at time *t*:

$$p\_{ij}^k = \begin{cases} \frac{[\tau\_{ij}(t)]^a [\eta\_{ij}]^b}{\sum\_{s \in allowed\_k} [\tau\_{is}(t)]^a [\eta\_{is}]^b} & j \in allowed\_k\\ & 0 \end{cases} \tag{26}$$

where *allowed<sup>k</sup>* = {*C* − *tabuk*} (*k* = 1, 2, 3, . . . , *m*) represents the position that the ant *k* next allows to select. *α* is a heuristic information factor, and represents the importance of the motion trajectory, that denotes the role that information accumulated by ants during exercise plays in the selection of ant movements. *α* has a value range of (0,5). *β* is the heuristic factor of expectation, which is the importance of characterizing the visibility of the path, that is, the role that the ant plays in the ant selection path during the movement. The value range of *β* is (0,5).

*τij*(*t*) represents the pheromone strength on the path (*i*, *j*) at time *t*. Where *i* is the beginning location and *j* is the end location. *ηij*(*t*) is a heuristic function, which is generally the reciprocal of the sum of the DG installation cost at location *j* and the distributed power source operating cost.
