**4. ACOR algorithm**

The metaheuristic Ant Colony Optimization (ACO) system, inspired by foraging behavior of ants, was first developed by Dorigo et al. [16] for discrete optimization problems. In the discrete ACO the ants represent stochastic procedures toward establishing set of candidate solutions in presence of a pheromone model. The pheromone model encompasses numerical values as pheromones being updated in iterations leading ants to promising solution regions of the search space. Hence, in the discrete ACO, pheromone information is used in a sampling process to construct a discrete probability function based on the sorted solutions. Later on for solving continuous domains, Socha and Dorigo [17] developed the continuous ACO (ACOR) which can utilize continuous multimodal probability functions such as weighted Gaussian functions over the search space to solve a non-linear function optimization problem as Min f xð Þ : a≤ x≤b where vector x ¼ ð Þ x1, … , xn represents the decision variables having vectors a and b as the lower and upper search space boundaries, respectively [18]. To this end, it produces a probability density function for each iteration using solution archives as an explicit memory of the search history in the pheromone model. Accordingly, the ACOR used in this study includes three main phases as:

