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I read many documents about ant colony optimization but I didn't understand well the process of pheromone update. I know that in the beginning, all the paths have the same pheromone trail. I want to know if, after an iteration, the pheromone will be updated only on the used path or this value will be updated on all paths (I mean if the pheromone trail on the unused path will be equal to (1-r) tau0, where r is the evaporation rate and tau0 is the initial pheromone trail)? thank you in advance

student26
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Pheromone will be updated only on the used paths. However evaporation will be on all paths.

tau0 = (1-r) tau0 + (new_tau)* k, where k is the number of ants using the path.

guroosh
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  • you mean by the formula of tau0, tau_ij (the new value of pheromone between two nodes i and j), since at the beginning the same trail tau0 is deposited on all paths? – student26 Sep 08 '18 at 12:39
  • yes tau0 is the level of pheromone on each path between any i and j – guroosh Sep 09 '18 at 10:09
  • thanks a lot. I have just another question. The selection of a destination j from i is done according to the probability pij= [(mu_ij)^alpha* (tau_ij)^beta]/sum[(mu_ij)^alpha* (tau_ij)^beta]. I want to know if the selected node j is the one that maximize the value of pij. In addition, is it possible to modifiy thi s expression ( sum of mu_ij and tau_ij instead of product)? – student26 Sep 09 '18 at 18:04
  • Yes, node j is the one that maximises the value pij. Since pij is directly proportional to pheromone level and inversely proportional to distance, over iterations the ants start using a combination of higher pheromone level and shorter routes. Also the formula uses multiplication and also has exponential arguments alpha and beta as seen here https://en.wikipedia.org/wiki/Ant_colony_optimization_algorithms#Edge_selection. Alpha and beta can be tuned to give importance to the distance or pheromone level, you could try sum if it works. – guroosh Sep 10 '18 at 05:20