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Nature Inspired Cooperative Strategies for Optimization (NICSO 2008) pp 1–13Cite as

Exploration in Stochastic Algorithms: An Application on \(\cal M\!AX\!\)–\(\cal MI\!N\!\) Ant System

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 236))

Abstract

In this paper a definition of the exploration performed by stochastic algorithms is proposed. It is based on the observation through cluster analysis of the solutions generated during a run. The probabilities associated by an algorithm to solution components are considered. Moreover, a consequent method for quantifying the exploration is provided. Such a measurement is applied to \(\cal M\!AX\!\)–\(\cal MI\!N\!\) Ant System. The results of the experimental analysis allow to observe the impact of the parameters of the algorithm on the exploration.

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References

  1. Battiti, R.: Reactive Search: Toward Self-Tuning Heuristics. In: Rayward-Smith, V.J., Osman, I.H., Reeves, C.R., Smith, G.D. (eds.) Modern Heuristic Search Methods, pp. 61–83. John Wiley & Sons, Chichester (1996)

    Google Scholar 

  2. Berry, M.J.A., Linoff, G.: Mastering Data Mining. Wiley Computer Publishing, Chichester (2000)

    Google Scholar 

  3. Bianchi, L., Birattari, M., Chiarandini, M., Manfrin, M., Mastrolilli, M., Paquete, L., Rossi-Doria, O., Schiavinotto, T.: Metaheuristics for the Vehicle Routing Problem with Stochastic Demands. Journal of Mathematical Modelling and Algorithms 9, 91–110 (2006)

    Article  MathSciNet  Google Scholar 

  4. Birattari, M., Stützle, T., Paquete, L., Varrentrapp, K.: A Racing Algorithm for Configuring Metaheuristics. In: Langdon, W.B., Cantú-Paz, E., Mathias, K., Roy, R., Davis, D., Poli, R., Balakrishnan, K., Honavar, V., Rudolph, G., Wegener, J., Bull, L., Potter, M.A., Schultz, A.C., Miller, J.F., Burke, E., Jonoska, N. (eds.) GECCO, pp. 11–18 (2002)

    Google Scholar 

  5. Corne, D., Dorigo, M., Glover, F.: The Ant Colony Optimization Meta-Heuristic. In: New Ideas in Optimization. McGraw Hill, New York (1999)

    Google Scholar 

  6. Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)

    MATH  Google Scholar 

  7. Esbensen, H., Kuh, E.: EXPLORER: an interactive floorplanner for design space exploration. In: EURO-DAC 1996/EURO-VHDL 1996: Proceedings of the conference on European design automation, pp. 356–361. IEEE Computer Society Press, Los Alamitos (1996)

    Chapter  Google Scholar 

  8. Everitt, B.: Cluster Analysis. Heinemann Educational Books (1974)

    Google Scholar 

  9. Everitt, B., Landau, S., Leese, M.: Cluster Analysis. Arnold, London (2001)

    Google Scholar 

  10. Glover, F., Kochenberger, G.: Handbook of Metaheuristics. Kluwer Academic Publishers, Dordrecht (2002)

    Google Scholar 

  11. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Publishing Company, Reading (1989)

    MATH  Google Scholar 

  12. Gutjahr, W.J., Sebastiani, G.: Runtime analysis of ant colony optimization with best-so-far reinforcement. In: Methodology and Computing in Applied Probability (2008)

    Google Scholar 

  13. Hanafi, S.: On the Convergence of Tabu Search. Journal of Heuristics 7, 47–58 (2001)

    Article  MATH  Google Scholar 

  14. Hoos, H.H., Stützle, T.: Stochastic Local Search. Foundations and Applications. Morgan Kaufmann Publishers, San Francisco (2004)

    Google Scholar 

  15. Ibaraki, T., Nonobe, K., Yagiura, M.: Metaheuristics: Progress as Real Problem Solvers. Kluwer Academic Publisher, Dordrecht (2005)

    Book  MATH  Google Scholar 

  16. Jardine, N., Sibson, R.: The Construction of Hierarchic and Non-Hierarchic Classifications. The Computer Journal 11, 177–184 (1968)

    MATH  Google Scholar 

  17. Kaufman, L., Rousseeu, P.J.: Finding groups in data. An introduction to cluster analysis. Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics. Wiley, New York (1990)

    Google Scholar 

  18. Kauffman, S.A.: The Origins of Order. In: Self-Organization and Selection in Evolution. Oxford University Press, Oxford (1993)

    Google Scholar 

  19. Larrañaga, P., Lozano, J.A.: Estimation of Distribution Algorithms. A New Tool for Evolutionary Computation. Kluwer Academic Publisher, Dordrecht (2001)

    Google Scholar 

  20. Lorena, L.A.N., Furtado, J.C.: Constructive Genetic Algorithm for Clustering Problems. Evolutionary Computation 9, 309–327 (2001)

    Article  Google Scholar 

  21. Maher, M.L., Poon, J.: Modelling design exploration as co-evolution. Microcomputers in Civil Engineering, 195–210 (1996)

    Google Scholar 

  22. Michalewicz, Z., Fogel, D.B.: How to Solve it: Modern Heuristics. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  23. Osman, I.H., Kelly, J.P.: Meta-Heuristics: The Theory and Applications. Kluwer Academic Publisher, Dordrecht (1996)

    MATH  Google Scholar 

  24. Pellegrini, P., Favaretto, D., Moretti, E.: Multiple Ant Colony Optimization for a Rich Vehicle Routing Problem: a Case Study, Department of Applied Mathematics, Università Ca’ Foscari (2006)

    Google Scholar 

  25. Pellegrini, P.: ACO: parameters, exploration and quality of solutions. Phd Thesis. Università Ca’ Foscari (2007)

    Google Scholar 

  26. Rizzoli, A.E., Montemanni, R., Lucibello, E., Gambardella, L.M.: Ant Colony Optimisation for real world vehicle routing problems: from theory to applications. Swarm Intelligence 1, 135–151 (2007)

    Article  Google Scholar 

  27. Stützle, T., Hoos, H.H.: The \(\cal MAX\)–\(\cal MIN\) Ant System and Local Search for the Traveling Salesman Problem. In: Bäck, T., Michalewicz, Z., Yao, X. (eds.) ICEC 1997, pp. 309–314 (1997)

    Google Scholar 

  28. Stützle, T., Hoos, H.H.: Improvements on the Ant System: Introducing the \(\cal MAX\)–\(\cal MIN\) Ant System. In: Smith, G.D., Steele, N.C., Albrecht, R.F. (eds.) Artificial Neural Networks and Genetic Algorithms, pp. 245–249. Springer, Heidelberg (1998)

    Google Scholar 

  29. Stützle, T., Hoos, H.H.: \(\cal MAX\)–\(\cal MIN\) Ant System and Local Search for Combinatorial Optimization Problems. In: Voss, S., Martello, S., Osman, I.H., Roucairol, C. (eds.) Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pp. 137–154. Kluwer Academic Publishers, Dordrecht (1999)

    Google Scholar 

  30. Stützle, T., Hoos, H.H.: \(\cal MAX\)–\(\cal MIN\) Ant System. Future Generation Computer Systems 16, 889–914 (2000)

    Article  Google Scholar 

  31. Toussaint, M.: The structure of evolutionary exploration: On crossover, buildings blocks, and Estimation-Of-Distribution Algorithms. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 1444–1456. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  32. Voss, S., Martello, S., Osman, I.H., Roucairol, C.: Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization. Kluwer Academic Publishers, Dordrecht (1999)

    MATH  Google Scholar 

  33. Watson, J.P., Whitley, L.D., Howe, A.E.: Linking Search Space Srtucture, Run-Time Dynamics, and Problem Difficulty: A Step Toward Demystifying Tabu Search. Journal of Artificial Intelligence Research 24, 221–261 (2005)

    Article  MATH  Google Scholar 

  34. Xu, J., Chiu, S.Y., Glover, F.: Fine-Tuning a tabu search algorithm with statistical tests. International Transactions in Operational Research 5, 233–244 (1998)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Dorsoduro 3825/E, I-30123, Venezia, Italy

    Paola Pellegrini, Daniela Favaretto & Elena Moretti

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  1. Paola Pellegrini
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  2. Daniela Favaretto
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  3. Elena Moretti
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Editor information

Editors and Affiliations

  1. School of Computer Sciences and Information Technology, University of Nottingham, Jubilee Campus, NG81BB, Nottingham, UK

    Natalio Krasnogor

  2. Universidad de La Laguna, Tenerife, Spain

    María Belén Melián-Batista

  3. DEIOC, Facultad de Matemáticas, Universidad de La Laguna, 38271, La Laguna, Tenerife, Spain

    José Andrés Moreno Pérez  & J. Marcos Moreno-Vega  & 

  4. Department of Computer Science and Artificial Intelligence, E.T.S.I Informática y de Telecomunicación, University of Granada, C/ Periodista Daniel Saucedo Aranda s/n, 18071, Granada, Spain

    David Alejandro Pelta

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Pellegrini, P., Favaretto, D., Moretti, E. (2009). Exploration in Stochastic Algorithms: An Application on \(\cal M\!AX\!\)–\(\cal MI\!N\!\) Ant System. In: Krasnogor, N., Melián-Batista, M.B., Pérez, J.A.M., Moreno-Vega, J.M., Pelta, D.A. (eds) Nature Inspired Cooperative Strategies for Optimization (NICSO 2008). Studies in Computational Intelligence, vol 236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03211-0_1

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  • DOI: https://doi.org/10.1007/978-3-642-03211-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03210-3

  • Online ISBN: 978-3-642-03211-0

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