Abstract
There is a lot of experimental evidence that crossover is, for some functions, an essential operator of evolutionary algorithms. Nevertheless, it was an open problem to prove for some function that an evolutionary algorithm using crossover is essentially more efficient than evolutionary algorithms without crossover. In this paper, such an example is presented and its properties are proved.
This work was supported by the Deutsche Forschungsgemeinschaft (DFG) as part of the Collaborative Research Center “Computational Intelligence” (531).
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References
Baum, E. B., Boneh, D., and Garret, C.: On genetic algorithms. In Proceedings of the 8th Conference on Computational Learning Theory (COLT’ 95), (1995) 230–239.
Droste, S., Jansen, Th., and Wegener, I.: On the Analysis of the (1+1) Evolutionary Algorithm. Tech. Report CI-21/98. Collaborative Research Center 531, Reihe Computational Intelligence, Univ. of Dortmund, Germany, (1998).
Droste, S., Jansen, Th., Wegener, I.: A rigorous complexity analysis of the (1+1) evolutionary algorithm for separable functions with Boolean inputs. Evolutionary Computation 6(2) (1998) 185–196.
Fogel, L. J., Owens, A. J., and Walsh, M. J.: Artificial Intelligence Through Simulated Evolutions. (1966) Wiley, NewYork.
Forrest, S. and Mitchell, M.: Relative building block fitness and the building block hypothesis. In D. Whitley (Ed.): Foundations of Genetic Algorithms 2, (1993) 198–226, Morgan Kaufmann, San Mateo, CA.
Goldberg, D. E.: Genetic Algorithms in Search, Optimization, and Machine Learning. (1989) AddisonWesley, Reading, Mass.
Holland, J. H.: Adaption in Natural and Artificial Systems. (1975) Univ. of Michigan.
Horn, J., Goldberg, D. E., and Deb, K.: Long Path problems. In Y. Davidor, H.-P. Schwefel, and R. Männer (Eds.): Parallel Problem Solving from Nature (PPSN III), (1994) 149–158, Springer, Berlin, Germany.
Jerrum, M. and Sinclair, A.: The Markov Chain Monte Carlo method: An approach to approximate counting and integration. In D. S. Hochbaum (Ed.): Approximation Algorithms for NP-hard Problems. (1997) 482–520, PWS Publishers, Boston, MA.
Jerrum, M. and Sorkin, G. B.: The Metropolis algorithm for graph bisection. Discrete Applied Mathematics 82 (1998) 155–175.
Juels, A. and Wattenberg, M.: Stochastic Hillclimbing as a Baseline Method for Evaluating Genetic Algorithms, Tech. Report CSD-94-834, (1994), Univ. of California.
van Laarhoven, P. J. M. and Aarts, E. H. L.: Simulated Annealing. Theory and Applications, (1987), Reidel, Dordrecht, The Netherlands.
Mitchell, M. and Forrest, S.: Royal Road functions. In Th. Bäck, D. B. Fogel and Z. Michalewicz (Eds.): Handbook of Evolutionary Computation, (1997) B2.7:20–B2.7:25, Oxford University Press, Oxford UK.
Mitchell, M., Forrest, S., and Holland, J. H.: The Royal Road function for genetic algorithms: Fitness landscapes and GA performance. In F. J. Varela and P. Bourgine (Eds.): Proceedings of the First European Conference on Artificial Life, (1992) 245–254, MIT Press, Cambridge, MA.
Mitchell, M., Holland, J. H., and Forrest, S.: When will a genetic algorithm outperform hill climbing? In J. Cowan, G. Tesauro, and J. Alspector (Eds.): Advances in Neural Information Processing Systems, (1994), Morgan Kaufmann, San Francisco, CA.
Motwani, R. and Raghavan, P.: Randomized Algorithms. (1995) Cambridge University Press, Cambridge.
Rabani, Y., Rabinovich, Y., and Sinclair, A.: A computational view of population genetics. Random Structures and Algorithms 12(4) (1998) 314–334.
Rabinovich, Y., Sinclair, A., and Wigderson, A.: Quadratical dynamical systems (preliminary version). In Proceedings of the 33rd IEEE Symposium on Foundations of Computer Science (FOCS’ 92), (1992) 304–313, IEEE Press Piscataway, NJ.
Ronald, S.: Duplicate genotypes in a genetic algorithm. In Proceedings of the IEEE International Conference on Evolutionary Computation (ICEC’ 98), (1998) 793–798, IEEE Press Piscataway, NJ.
Rudolph, G.: How mutation and selection solve long path problems in polynomial expected time. Evolutionary Computation 4(2) (1997) 195–205.
Sarma J. and De Jong, K.: Generation gap methods. In Th. Bäck, D. B. Fogel and Z. Michalewicz (Eds.): Handbook of Evolutionary Computation, (1997) C2.7, Oxford University Press, UK.
Schwefel, H.-P.: Evolution and Optimum Seeking. (1995) Wiley, New-York, NY.
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Jansen, T., Wegener, I. (1999). On the Analysis of Evolutionary Algorithms — A Proof That Crossover Really Can Help. In: Nešetřil, J. (eds) Algorithms - ESA’ 99. ESA 1999. Lecture Notes in Computer Science, vol 1643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48481-7_17
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DOI: https://doi.org/10.1007/3-540-48481-7_17
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