An Ant Colony Approach For The Steiner Tree Problem

One ant is placed initially at each of the given terminal vertices that are to be connected. In each iteration, an ant is moved to a new location via an edge, determined stochastically, but biased in such a manner that the ants get drawn to the paths traced out by one another. Each ant maintains its own separate list of vertices already visited to avoid revisiting it. When any ant collides with another ant, or even with the path of another, it merges into the latter. An ant m , currently at a vertex i , selects a vertex j not in its tabu list ) (m T , to move to, only if E j i ∈ ) , ( . In order to ensure that the ants merge with one another as quickly as possible, we define a potential for each vertex j in V , with respect to an ant m as follows,