Modelling ACO: Composed Permutation Problems
The behaviour of Ant Colony Optimization (ACO) algorithms is studied on optimization problems that are composed of different types of subproblems. Numerically exact results are derived using a deterministic model for ACO that is based on the average expected behaviour of the artificial ants. These computations are supplemented by test runs with an ACO algorithm on the same problem instances. It is shown that different scaling of the objective function on isomorphic subproblems has a strong influence on the optimization behaviour of ACO. Moreover, it is shown that ACOs behaviour on a subproblem depends heavily on the type of the other subproblems. This is true even when the subproblems are independent in the sense that the value of the objective function is the sum of the qualities of the solutions of the subproblems. We propose two methods for handling scaling problems (pheromone update masking and rescaling of the objective function) that can improve ACOs behaviour. Consequences of our findings for using ACO on real-world problems are pointed out.
KeywordsProblem Instance Solution Quality Cost Matrix Pure Competition Pheromone Matrice
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