Adjusting the Algorithm Parameters

Marco Dorigo ( inventor of Ant Colony Optimization) provides a very useful discussion of the problem parameters in his article "The Ant System: Optimization by a Colony of Cooperating Agents" [Dorigo et al. 1996]. This section will summarize his findings for the most common adjustable parameters.

Alpha ( ± )/Beta ( ² )

A number of ± / ² combinations were found to yield good solutions in a reasonable amount of time. These are found in Table 4.1.

 

Table 4.1: ± / ² Parameter Combinations.

±	²
0.5	5.0
1.0	1.0
1.0	2.0
1.0	5.0

The ± parameter is associated with pheromone levels (from Equation 4.1), where the ² parameter is associated with visibility (distance for the edge). Therefore, whichever value is higher indicates the importance of the parameter within the edge selection probability equation. Note that in one case, the parameters are of equal importance. In all other cases, the visibility of the path is a greater determinant of the path to take.

Rho ( )

Recall that while represents the coefficient applied to new pheromone on a path, (1.0 - ) represents the coefficient of evaporation of existing pheromone on the trail. Tests were run with > 0.5, all of which yielded interesting solutions. Setting to a value less than 0.5 resulted in less than satisfactory results.

This parameter primarily determines the concentration of pheromone that will remain on the edges over time.

Number of Ants

The quantity of ants in the simulation had an effect on the quality of solutions that resulted. While more ants may sound like a reasonable idea, setting the number of ants in the simulation to the number of cities yields the best result.