Search bias in constructive metaheuristics and implications for ant colony optimisation

Constructive metaheuristics explore a tree of constructive decisions, the topology of which is determined by the way solutions are represented and constructed. Some solution representations allow particular solutions to be reached on a greater number of paths in this construction tree than other solutions, which can introduce a bias to the search. However, the ultimate determinant of search bias is the topology of the construction tree. This is particularly the case in problems where certain solution representations are infeasible. This paper presents an examination of the mechanisms that determine the topologies of construction trees and the implications for ant colony optimisation. The results provide insights into why certain assignment orders perform better in problems such as the quadratic and generalised assignment problems, in terms of both solution quality and avoiding infeasible solutions. Additionally, insight is gained into why certain pheromone representations are more effective than others on different problems.