Ant Colony Optimization: a literature survey - FEP - Working Papers

⎧⎪⎨l =⎪⎩∑τ a /w a∈ A NH (S t−1 ) τ a ′/w a ′ if a ∈ A NH(S t−1 )0 otherwise.(41)This rule, assigns equal weight to the pheromone and the heuristic values, hereby representedby 1/w a , by eliminating parameters α and β from the exponents of the pheromone and heuristicvalues respectively. Given that the probabilistic rule is only triggered whenever a random numberq > 0.8, the search for solutions is in 80% of the cases usually concentrated on relativelygood areas.3.1.6 Parameter ValuesThe setting of an ant based algorithm can take a long time to achieve in order to produce someuseful results. Furthermore, a set of parameter values has also to be defined:• α - parameter related to the weight of the pheromone concentration in the probabilityfunction;• β - parameter weighting the relative importance of heuristic information in the probabilityfunction;• ρ - pheromone evaporation rate, where ρ ∈]0, 1], measures the information that is to betransported to the next iteration;• Q - parameter weighting the quantity of pheromone to be deposited in each componentof the solution;• τ 0 - initial pheromone value to be deposited in every solution component, to guaranteethat every one of them has, at least, a small probability of being chosen;• number of ants in the colony;• stopping criterion - the number of iterations to be performed, the number of solutions tobe evaluated, maximum allowed running time, and so on.For each algorithm developed, there can be other parameters to be set, for example, if boundsare imposed on the pheromone values, a p best parameter, as well as, the limit values have to bedefined. There are other cases where differences in the definition of the probability function, orthe type of ant used, require more parameters. We feel that there is no need to report on theseparameters in a section of their own as they tend to be unique for each algorithm. Nonetheless,almost every work that was reviewed in this paper reports to have tried several combinations ofparameter values before choosing the ones to be used.20