Abstract
Classical Genetic Algorithm theory was built on four operators: proportional selection, one-point crossover, mutation and inversion. While the role of inversion was questioned, the use of the other remaining operators has thrived, some of these newly designed operators being motivated by good empirical results, some having a solid theory to support their use. In this paper we present a Simple Inversion Operator, and we investigate its potential mixing capabilities for problems where the optimum consists of juxtaposed Symmetric Building Blocks. Both theoretical investigation and experimental results obtained, indicate that our operator is quite powerful in finding the right building blocks that compose the optimum, whenever symmetrical building blocks play an important role in the discovery of the global solution.
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References
Holland, J.: Adaptation in Natural and Artificial Systems. MIT Press, Cambridge (1992)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)
Whitley, D.: Using Reproductive Evaluations to Improve Genetic Search and Heuristic Discovery. In: Genetic Algorithms and Their Applications - Proceedings of the Second ICGA, pp. 108–115. Lawrence Erlbaum Assoc., Mahwah (1987)
Wienholt, W.: A Refined Genetic Algorithm for Parameter Optimization Problems. In: Proceedings of the Fifth ICGA, pp. 589–596. Morgan Kaufmann, San Francisco (1993)
Syswerda, G.: Uniform Crossover in genetic Algorithms. In: Proceedings of the Third ICGA, pp. 2–9. Morgan Kaufmann, San Francisco (1989)
Sirag, D.J., Weisser, P.T.: Toward a Unified Thermodynamic Genetic Operator. In: Genetic Algorithms and Their Applications - Proceedings of the Second ICGA, pp. 116–122. Lawrence Erlbaum Associates Publ., Mahwah (1987)
Goldberg, D.E.: Don’t Worry, Be Messy. In: Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 24–30. Morgan Kaufmann, San Francisco (1991)
Harik, G., Goldberg, D.E.: Learning linkage. In: Foundations of Genetic Algorithms, vol. 4, pp. 247–262. Morgan Kaufmann, San Francisco (1996)
Lobo, F.G., Deb, K., Goldberg, D.E., Harik, G., Wang, L.: Compressed introns in linkage learning genetic algorithm. In: Proceedings of the Third Annual Conference on Genetic Programming, pp. 551–558. Morgan Kaufmann, San Francisco (1998)
Salman, A., Mehrotra, K., Mohan, C.K.: Linkage Crossover for Genetic Algorithms. In: Proceedings of GECOO 1999, pp. 564–571. Morgan Kaufmann, San Francisco (1999)
Paredis, J.: The Symbiotic Evolution of Solutions and their Representations. In: Proceedings of the Sixth ICGA, pp. 359–365. Morgan Kaufmann, San Francisco (1995)
Munteanu, C., Lazarescu, V.: Simple Inversion Genetic Algorithm an Effective Genetic Strategy. In: Proceedings of ICSC NC 1998, pp. 151–156 (1998)
Munteanu, C., Rosa, A.: Symmetrical Building Blocks and the Simple Inversion Operator. In: Proceedings of GECCO 2000, p. 365. Morgan Kaufmann Publ., San Francisco (2000)
Van Hoyweghen, C., Naudts, B., Goldberg, D.E.: Spin-flip symmetry and synchronization. Evol. Comput. 10, 317–344 (2002)
Choi, S.S., Kwon, Y.-K., Moon, B.-R.: Properties of symmetric fitness functions. In: Proceedings of GECCO 2006, pp. 1117–1124. ACM Press, New York (2006)
Mitchell, M., Forrest, S., Holland, J.: The Royal Road for genetic Algorithms: Fitness Landscapes and GA Performance. In: Proceedings of the First European Conference on Artificial Life, pp. 245–254. MIT Press, Cambridge (1991)
Jones, T.: Evolutionary Algorithms, Fitness Landscapes and Search. PhD thesis, University of New Mexico, Albuquerque NM (1995)
Goldberg, D.E., Deb, K., Clark, J.H.: Genetic algorithms, noise, and the sizing of populations. Complex Systems 6, 333–362 (1992)
Deb, K., Goldberg, D.E.: Sufficient conditions for deceptive and easy binary functions. Annals of mathematics and Artificial Intelligence 10, 385–408 (1994)
Bäck, T., Hoffmeister, F.: Extended Selection Mechanisms in Genetic Algorithms. In: Proceedings of the Fourth ICGA, pp. 92–99. Morgan Kaufmann, San Francisco (1991)
Holland, J.: Royal Road Functions. Genetic Algorithms Digest 7(22) (1993)
Culberson, J.: Holland’s Royal Road and GIGA. GA Digest 7(23) (1993)
Corno, F., Sonza Reorda, M., Squillero, G.: Optimizing Deceptive Functions with the SG-Clans Algorithms. In: Proceedings of IEEE CEC 1999, IEEE Press, Los Alamitos (1999)
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Munteanu, C., Rosa, A. (2007). Symmetry at the Genotypic Level and the Simple Inversion Operator. In: Neves, J., Santos, M.F., Machado, J.M. (eds) Progress in Artificial Intelligence. EPIA 2007. Lecture Notes in Computer Science(), vol 4874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77002-2_18
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DOI: https://doi.org/10.1007/978-3-540-77002-2_18
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