the pheromone update formula in Ant Colony Optimization (ACO) is updated in each iteration to take into account the effect of the evaporation. Why the evaporation effect is not carried out on the pheromone of the best ant in the previous iteration?
Because if it is, the collective element in the algorithm would be lost. Moreover, there is a possibility that in carrying out the evaporation effect on the pheromone of the best ant, the algorithm would steer away from the path to finding an near optimal solution and head to a local solution instead.
I agree with Galina on this. One note, however, is that using pheromone of the best ant in the previous iteration undermines the effect observed in the current iteration. Therefore, if you use the previous iteration and only the best ant's pheromone, you have 2 drawbacks:
I think there are two things I need to understand first before giving an answer:
Which version/variant of ACO are you considering?
What is the schedule of the activities in each iteration? (e.g, solution construction, pheromone evaporation, pheromone increment, etc)
However, as far as I know, the pheromone management schedule is: evaporation (in all the arcs of the pheromone matrix) and then, depending of which ACO variant you are considering, pheromone is deposited by some ant(s).
About the real ants behavior, all pheromones are evaporated and is relatively slow. There is an experiment of S. Goss where a large-branch bridge is considered. Pheromone is accumulated in the branch and after 30 minutes a shorter branch is added. In general, ants continue crossing by the longest branch.
In the ACO book of Dorigo and Stutzle there is a nice summary
of this kind of experiments (Article Ant Colony Optimization
As ACO is metaheuristic approach so there is emphasis on n trails to find the optimal route or solution. If we skip any one path or node to update its pheromone concentration then if further iteration we don't know whether the worst path will be worst or not. Might that path give the optimal solution in the next iteration. Thats the reason to update the pheromone concentration at each iteration and for each note in ACO