Abstract
The computational complexity of ant colony optimization (ACO) is a new and rapidly growing research area. The finite-time dynamics of ACO algorithms is assessed with mathematical rigor using bounds on the (expected) time until an ACO algorithm finds a global optimum. We review previous results in this area and introduce the reader into common analysis methods. These techniques are then applied to obtain bounds for different ACO algorithms on classes of pseudo-Boolean problems. The resulting runtime bounds are further used to clarify important design issues from a theoretical perspective. We deal with the question whether the current best-so-far solution should be replaced by new solutions with the same quality. Afterwards, we discuss the hybridization of ACO with local search and present examples where introducing local search leads to a tremendous speed-up and to a dramatic loss in performance, respectively.
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References
Aickelin, U., Burke, E.K., Li, J.: An estimation of distribution algorithm with intelligent local search for rule-based nurse rostering. Journal of the Operational Research Society 58, 1574–1585 (2007)
Attiratanasunthron, N., Fakcharoenphol, J.: A running time analysis of an ant colony optimization algorithm for shortest paths in directed acyclic graphs. Information Processing Letters 105(3), 88–92 (2008)
Balaprakash, P., Birattari, M., Stützle, T., Dorigo, M.: Incremental local search in ant colony optimization: Why it fails for the quadratic assignment problem. In: Dorigo, M., Gambardella, L.M., Birattari, M., Martinoli, A., Poli, R., Stützle, T. (eds.) ANTS 2006. LNCS, vol. 4150, pp. 156–166. Springer, Heidelberg (2006)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Doerr, B., Johannsen, D.: Refined runtime analysis of a basic ant colony optimization algorithm. In: Proceedings of the Congress of Evolutionary Computation (CEC 2007), pp. 501–507. IEEE Computer Society Press, Los Alamitos (2007)
Doerr, B., Neumann, F., Sudholt, D., Witt, C.: On the runtime analysis of the 1-ANT ACO algorithm. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2007), pp. 33–40. ACM Press, New York (2007)
Dorigo, M., Blum, C.: Ant colony optimization theory: A survey. Theoretical Computer Science 344, 243–278 (2005)
Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)
Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science 276, 51–81 (2002)
Droste, S., Jansen, T., Wegener, I.: Upper and lower bounds for randomized search heuristics in black-box optimization. Theory of Computing Systems 39(4), 525–544 (2006)
Garnier, J., Kallel, L., Schoenauer, M.: Rigorous hitting times for binary mutations. Evolutionary Computation 7(2), 173–203 (1999)
Giel, O., Wegener, I.: Evolutionary algorithms and the maximum matching problem. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 415–426. Springer, Heidelberg (2003)
Gutjahr, W.J.: A graph-based ant system and its convergence. Future Generation Computer Systems 16, 873–888 (2000)
Gutjahr, W.J.: A generalized convergence result for the graph-based ant system metaheuristic. Probability in the Engineering and Informational Sciences 17, 545–569 (2003)
Gutjahr, W.J.: Mathematical runtime analysis of ACO algorithms: Survey on an emerging issue. Swarm Intelligence 1, 59–79 (2007)
Gutjahr, W.J.: First steps to the runtime complexity analysis of ant colony optimization. Computers and Operations Research 35(9), 2711–2727 (2008)
Gutjahr, W.J., Sebastiani, G.: Runtime analysis of ant colony optimization with best-so-far reinforcement. Methodology and Computing in Applied Probability 10, 409–433 (2008)
Hart, W.E., Krasnogor, N., Smith, J.E. (eds.): Recent Advances in Memetic Algorithms. Studies in Fuzziness and Soft Computing, vol. 166. Springer, Heidelberg (2004)
Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations & Applications. Elsevier/Morgan Kaufmann (2004)
Jansen, T., Wegener, I.: Evolutionary algorithms—how to cope with plateaus of constant fitness and when to reject strings of the same fitness. IEEE Transactions on Evolutionary Computation 5, 589–599 (2001)
Kennedy, J., Eberhart, R.C., Shi, Y.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001)
Krasnogor, N., Smith, J.: A tutorial for competent memetic algorithms: model, taxonomy, and design issues. IEEE Transactions on Evolutionary Computation 9(5), 474–488 (2005)
Levine, J., Ducatelle, F.: Ant colony optimisation and local search for bin packing and cutting stock problems. Journal of the Operational Research Society 55(7), 705–716 (2004)
Lourenço, H.R., Martin, O., Stützle, T.: Iterated local search. In: Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 57, pp. 321–353. Kluwer Academic Publishers, Dordrecht (2002)
Merkle, D., Middendorf, M.: Modelling the dynamics of Ant Colony Optimization algorithms. Evolutionary Computation 10(3), 235–262 (2002)
Neumann, F., Wegener, I.: Randomized local search, evolutionary algorithms, and the minimum spanning tree problem. Theoretical Computer Science 378(1), 32–40 (2007)
Neumann, F., Witt, C.: Runtime analysis of a simple ant colony optimization algorithm. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, pp. 618–627. Springer, Heidelberg (2006)
Neumann, F., Witt, C.: Ant Colony Optimization and the minimum spanning tree problem. In: Maniezzo, V., Battiti, R., Watson, J.-P. (eds.) LION 2007 II. LNCS, vol. 5313, pp. 153–166. Springer, Heidelberg (2008)
Neumann, F., Sudholt, D., Witt, C.: Rigorous analyses for the combination of ant colony optimization and local search. In: Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A.F.T. (eds.) ANTS 2008. LNCS, vol. 5217, pp. 132–143. Springer, Heidelberg (2008)
Neumann, F., Sudholt, D., Witt, C.: Analysis of different MMAS ACO algorithms on unimodal functions and plateaus. Swarm Intelligence 3, 35–68 (2009)
Stützle, T., Hoos, H.H.: MAX-MIN ant system. Journal of Future Generation Computer Systems 16, 889–914 (2000)
Sudholt, D.: Memetic algorithms with variable-depth search to overcome local optima. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2008), pp. 787–794. ACM Press, New York (2008)
Sudholt, D.: The impact of parametrization in memetic evolutionary algorithms. Theoretical Computer Science (to appear, 2009)
Wegener, I., Witt, C.: On the optimization of monotone polynomials by simple randomized search heuristics. Combinatorics, Probability and Computing 14, 225–247 (2005)
Witt, C.: Worst-case and average-case approximations by simple randomized search heuristics. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 44–56. Springer, Heidelberg (2005)
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Neumann, F., Sudholt, D., Witt, C. (2009). Computational Complexity of Ant Colony Optimization and Its Hybridization with Local Search. In: Lim, C.P., Jain, L.C., Dehuri, S. (eds) Innovations in Swarm Intelligence. Studies in Computational Intelligence, vol 248. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04225-6_6
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DOI: https://doi.org/10.1007/978-3-642-04225-6_6
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