Abstract
Recently, the first rigorous runtime analyses of ACO algorithms have been presented. These results concentrate on variants of the MAX-MIN ant system by Stützle and Hoos and consider their runtime on simple pseudo-Boolean functions such as OneMax and LeadingOnes. Interestingly, it turns out that a variant called 1-ANT is very sensitive to the choice of the evaporation factor while a recent technical report by Gutjahr and Sebastiani suggests partly opposite results for their variant called MMAS. In this paper, we elaborate on the differences between the two ACO algorithms, generalize the techniques by Gutjahr and Sebastiani and show improved results.
D. S. and C. W. were supported by the Deutsche Forschungsgemeinschaft as a part of the Collaborative Research Center “Computational Intelligence” (SFB 531).
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References
Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)
Dorigo, M., Maniezzo, V., Colorni, A.: The ant system: An autocatalytic optimizing process. Technical Report 91-016 Revised, Politecnico di Milano (1991)
Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theor. Comput. Sci. 276, 51–81 (2002)
Motwani, R., Raghavan, P.: Randomized Algorithms. Cambr. Univ.Press, Cambridge (1995)
Mitzenmacher, M., Upfal, E.: Probability and Computing – Randomized Algorithms and Probabilistic Analysis. Cambr. Univ. Press, Cambridge (2005)
Gutjahr, W.J.: ACO algorithms with guaranteed convergence to the optimal solution. Inform. Process. Lett. 82, 145–153 (2002)
Dorigo, M., Blum, C.: Ant colony optimization theory: A survey. Theor. Comput. Sci. 344, 243–278 (2005)
Gutjahr, W.J.: First steps to the runtime complexity analysis of Ant Colony Optimization. Comput. Oper. Res (to appear)
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) extended version to appear in Algorithmica
Doerr, B., Neumann, F., Sudholt, D., Witt, C.: On the runtime analysis of the 1-ANT ACO algorithm. In: Proc. of GECCO 2007, ACM Press, New York (2007)
Gutjahr, W.J., Sebastiani, G.: Runtime analysis of ant colony optimization. Technical report, Mathematics department, ”Sapienza” Univ. of Rome, 2007/03 (2007)
Gutjahr, W.J.: Mathematical runtime analysis of ACO algorithms: Survey on an emerging issue. Swarm Intelligence (to appear)
Gutjahr, W.J.: On the finite-time dynamics of ant colony optimization. Methodol. Comput. Appli. Probab. 8, 105–133 (2006)
Stützle, T., Hoos, H.H.: MAX-MIN ant system. J. Future Gener. Comput. Syst. 16, 889–914 (2000)
Jansen, T., Wegener, I.: Evolutionary algorithms - how to cope with plateaus of constant fitness and when to reject strings of the same fitness. IEEE Trans. Evolut. Comput. 5(6), 589–599 (2001)
Garnier, J., Kallel, L., Schoenauer, M.: Rigorous hitting times for binary mutations. Evolut. Comput. 7, 173–203 (1999)
Wegener, I., Witt, C.: On the optimization of monotone polynomials by simple randomized search heuristics. Combin. Probab. Comput. 14, 225–247 (2005)
Wegener, I.: Methods for the analysis of evolutionary algorithms on pseudo-boolean functions. In: Sarker, R., Yao, X., Mohammadian, M. (eds.) Evolutionary Optimization, pp. 349–369. Kluwer, Dordrecht (2002)
Rudolph, G.: Convergence Properties of Evolutionary Algorithms. Kovač (1997)
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Neumann, F., Sudholt, D., Witt, C. (2007). Comparing Variants of MMAS ACO Algorithms on Pseudo-Boolean Functions. In: Stützle, T., Birattari, M., H. Hoos, H. (eds) Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics. SLS 2007. Lecture Notes in Computer Science, vol 4638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74446-7_5
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