Maximiliano Tabacman
Natalio Krasnogor
Jaume Bacardit
ABSTRACT
This paper presents a set of experiments on the use of Learning Classifier Systems for the purpose of solving combinatorial optimisation problems. We demonstrate our approach with a set of Fractal Travelling Salesman Problem (TSP) instances for which it is possible to know by construction the optimal tour regardless of the number of cities in them. This special type of TSP instances are ideal for testing new methods as they are well characterised in their solvability and easy to use for scalability studies. Our results show that an LCS is capable of learning rules to recognise to which family of instances a set containing a sample of the cities in the problem belongs to and hence automatically select the best heuristic to solve it. Moreover, we have also trained the LCS to recognise links belonging to the optimal tour.
- J. Bacardit. Pittsburgh Genetics-Based Machine Learning in the Data Mining era: Representations, generalization, and run-time. PhD thesis, Ramon Llull University, Barcelona, Catalonia, Spain, 2004.Google Scholar
- J. Bacardit. Analysis of the initialization stage of a pittsburgh approach learning classifier system. In GECCO 2005: Proceedings of the Genetic and Evolutionary Computation Conference, volume 2, pages 1843--1850. ACM Press, 2005. Google ScholarDigital Library
- J. Bacardit and N. Krasnogor. Empirical evaluation of ensemble techniques for a pittsburgh learning classifier system. In Proceedings of the 9th International Workshop on Learning Classifier Systems. (to appear), LNAI, Springer-Verlag, 2008. Google ScholarDigital Library
- J. H. Holland and J. S. Reitman. Cognitive systems based on adaptive algorithms. In D. Hayes-Roth and F. Waterman, editors, Pattern-directed Inference Systems, pages 313--329. Academic Press, New York, 1978.Google ScholarCross Ref
- A. Mariano, P. Moscato, and M. Norman. Arbitrarily large planar etsp instances with known optimal tours. Pesquisa Operacional, 15:89--96, 1995.Google Scholar
- A. Mariano, P. Moscato, and M. Norman. Using l-systems to generate arbitrarily large instances of the euclidean traveling salesman problem with known optimal tours. In Anales del XXVII Simposio Brasileiro de Pesquisa Operacional, Vitoria, Brazil, 6-8 Nov. 1995.Google Scholar
- P. Moscato and M. Norman. An analysis of the performance of traveling salesman heuristics on infinite-size fractal instances in the euclidean plane. Technical report, CeTAD - Universidad Nacional de La Plata, 1994.Google Scholar
- M. Norman and P. Moscato. The euclidean traveling salesman problem and a space-filling curve. Chaos, Solitons and Fractals, 6:389--397, 1995.Google ScholarCross Ref
- H. Peitgen, H. Jürgens, and D. Saupe. Chaos and Fractals. Springer, February 2004. Google ScholarDigital Library
- S. Smith. A Learning System Based on Genetic Algorithms. PhD thesis, University of Pittsburgh, 1980. Google ScholarDigital Library
- M. Stout, J. Bacardit, J. D. Hirst, and N. Krasnogor. Prediction of recursive convex hull class assignments for protein residues. Bioinformatics, In press, 2008. Google ScholarDigital Library
- M. Stout, J. Bacardit, J. D. Hirst, R. E. Smith, and N. Krasnogor. Prediction of topological contacts in proteins using learning classifier systems. Soft Computing, Special Issue on Evolutionary and Metaheuristic-based Data Mining (EMBDM), In Press, 2008. Google ScholarDigital Library
- D. Wolpert and W. Macready. No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1(1):67--82, April 1997. Google ScholarDigital Library
Index Terms
- Learning classifier systems for optimisation problems: a case study on fractal travelling salesman problem
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