Modelling ACO: Composed Permutation Problems

  • Daniel Merkle
  • Martin Middendorf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2463)


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.


Problem Instance Solution Quality Cost Matrix Pure Competition Pheromone Matrice 
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  1. 1.
    Dorigo, M. (1992). Optimization, Learning and Natural Algorithms (in Italian). PhD thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy.Google Scholar
  2. 2.
    Dorigo, M., and Di Caro, G. (1999). The ant colony optimization meta-heuristic. In Corne, D., Dorigo, M., and Glover, F., editors, New Ideas in Optimization, 11–32, McGraw-Hill, London.Google Scholar
  3. 3.
    Dorigo, M., Maniezzo, V., and Colorni, A. (1996). The Ant System: Optimization by a Colony of Cooperating Agents. IEEE Trans. Systems, Man, and Cybernetics-Part B, 26:29–41.CrossRefGoogle Scholar
  4. 4.
    Gutjahr, W. (2000). A graph-based Ant System and its convergence, Future Generation Computer Systems, 16:873–888.CrossRefGoogle Scholar
  5. 5.
    Gutjahr, W. (2002). ACO algorithms with guaranteed convergence to the optimal solution. Information Processing Letters, 82:145–153.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Merkle, D., and Middendorf, M. (2000). An Ant Algorithm with a new Pheromone Evaluation Rule for Total Tardiness Problems. In Cagnoni, S., et al. (Eds.) Real-World Applications of Evolutionary Computing, LNCS 1803, 287–296, Springer.CrossRefGoogle Scholar
  7. 7.
    Merkle, D., and Middendorf, M. (2001). A New Approach to Solve Permutation Scheduling Problems with Ant Colony Optimization. In Boers, E. J. W., et al. (Eds.) Applications of Evolutionary Computing, LNCS 2037, 213–222, Springer.CrossRefGoogle Scholar
  8. 8.
    Merkle, D., and Middendorf, M. (2001). On the Behaviour of Ant Algorithms: Studies on Simple Problems. In Proceedings of the 4th Metaheuristics International Conference (MIC’2001), Porto, 573–577.Google Scholar
  9. 9.
    Merkle, D., and Middendorf, M. (2001). Modelling the Dynamics of Ant Colony Optimization. TR 412, Institute AIFB, University of Karlsruhe. To appear in Evolutionary Computation.Google Scholar
  10. 10.
    Merkle, D., and Middendorf, M. (2002). Studies on the Dynamics of Ant Colony Optimization Algorithms. To appear in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2002), New York, 2002.Google Scholar
  11. 11.
    Stützle, T. and Dorigo, M. (2000). A short convergence proof for a class of ACO algorithms. TR 2000-35, IRIDIA, Universitè Libre de Bruxelles, Belgium.Google Scholar
  12. 12.
    Stützle, T. and Dorigo, M. (2001). An Experimental Study of the Simple Ant Colony Optimization Algorithm. In Proc. 2001 WSES Int. Conference on Evolutionary Computalution Computation (EC’01), WSES-Press International, 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Daniel Merkle
    • 1
  • Martin Middendorf
    • 2
  1. 1.Institute for Applied Computer Science and Formal Description MethodsUniversity of KarlsruheGermany
  2. 2.Computer Science GroupCatholic University of Eichstätt-IngolstadtGermany

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