Lower bounds for comparison based evolution strategies using VC-dimension and sign patterns

Algorithmica (New York)

Volumn 59, Issue 3, 2011, Pages 387-408

  Fournier, Hervé ^a   Teytaud, Olivier ^b  

^a UNIVERSITY OF VERSAILLES   (France)

^b CNRS   (France)

Author keywords

Convergence speed; Evolution algorithms; Sign patterns; Sphere function; VC dimension

Indexed keywords

CONVERGENCE SPEED; EVOLUTION ALGORITHMS; SIGN PATTERNS; SPHERE FUNCTION; VC-DIMENSION;

EVOLUTIONARY ALGORITHMS; FUNCTION EVALUATION; SPHERES;

CONVERGENCE OF NUMERICAL METHODS;

EID: 79951672816     PISSN: 01784617     EISSN: 14320541     Source Type: Journal    
DOI: 10.1007/s00453-010-9391-3     Document Type: Article

References (30)

1. Arnold, D.V.: Optimal weighted recombination. In: Foundations of Genetic Algorithms 8. Lecture Notes in Computer Science, vol. 3469, pp. 215-237. Springer, Berlin (2005) (Pubitemid 41313315)
2. A. Auger 2005 Convergence results for (1,λ)-SA-ES using the theory of φ-irreducible Markov chains Theor. Comput. Sci. 334 1-3 35 69 1080.68113 10.1016/j.tcs.2004.11.017 2132943 (Pubitemid 40467294)
3. Auger, A., Schoenauer, M., Teytaud, O.: Local and global order 3/2 convergence of a surrogate evolutionary algorithm. In: GECCO'05: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 857-864. ACM, New York (2005) (Pubitemid 43226386)
4. Bäck, T., Hoffmeister, F., Schwefel, H.-P.: Extended selection mechanisms in genetic algorithms. In: Belew, R.K., Booker, L.B. (eds.) Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 92-99. Morgan Kaufmann, San Mateo (1991)
5. Baker, J.E.: Reducing bias and inefficiency in the selection algorithm. In: Proceedings of the Second International Conference on Genetic Algorithms on Genetic Algorithms and Their Application, pp. 14-21. Lawrence Erlbaum Associates, Mahwah (1987)
6. H.-G. Beyer 1995 Toward a theory of evolution strategies: On the benefit of sex-the (μ/μ,λ)-theory Evol. Comput. 3 1 81 111 10.1162/evco.1995.3.1.81 646496
7. H.-G. Beyer H.-P. Schwefel 2002 Evolution strategies: a comprehensive introduction Nat. Comput. 1 1 3 52 1014.68134 10.1023/A:1015059928466 1907492
8. Devroye, L., Györfi, L., Lugosi, G.: A probabilistic Theory of Pattern Recognition. Springer, Berlin (1997)
9. Droste, S.: Not all linear functions are equally difficult for the compact genetic algorithm. In: Proc. of the Genetic and Evolutionary Computation COnference (GECCO 2005), pp. 679-686 (2005) (Pubitemid 43226360)
10. S. Droste T. Jansen I. Wegener 1998 A rigorous complexity analysis of the (1+1) evolutionary algorithm for separable functions with boolean inputs Evol. Comput. 6 2 185 196 10.1162/evco.1998.6.2.185 (Pubitemid 128692902)
11. S. Gelly S. Ruette O. Teytaud 2007 Comparison-based algorithms are robust and randomized algorithms are anytime Evol. Comput. J. 15 4 411 434 10.1162/evco.2007.15.4.411 Special issue on bridging Theory and Practice
12. Halperin, D.: Arrangements. In: Goodman, J.E., O'Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, pp. 529-562. CRC Press, Boca Raton (2004). Chap. 24
13. N. Hansen A. Ostermeier 2001 Completely derandomized self-adaptation in evolution strategies Evol. Comput. 9 2 159 195 10.1162/106365601750190398
14. R. Hooke T.A. Jeeves 1961 "Direct search" solution of numerical and statistical problems J. ACM 8 2 212 229 0111.12501 10.1145/321062.321069
15. Jägersküpper, J.: Analysis of a simple evolutionary algorithm for minimization in Euclidean spaces. In: 30th International Colloquium on Automata, Languages, and Programming (ICALP 2003). LNCS, vol. 2719, pp. 1068-1079. Springer, Berlin (2003)
16. J. Jägersküpper 2007 Analysis of a simple evolutionary algorithm for minimization in Euclidean spaces Theor. Comput. Sci. 379 3 329 347 1149.90147 10.1016/j.tcs.2007.02.042 Special issue on ICALP 2003 (Pubitemid 46754584)
17. Jägersküpper, J., Witt, C.: Rigorous runtime analysis of a (μ+1)-ES for the sphere function. In: GECCO, pp. 849-856 (2005) (Pubitemid 43226385)
18. Matoušek, J.: Lectures on Discrete Geometry. Graduate Texts in Mathematics, vol. 212. Springer, Berlin (2002)
19. Moraglio, A., Poli, R.: Topological crossover for the permutation representation. In: GECCO'05: Proceedings of the 2005 Workshops on Genetic and Evolutionary Computation, pp. 332-338. ACM, New York (2005)
20. F. Neumann 2008 Expected runtimes of evolutionary algorithms for the Eulerian cycle problem Computers & OR 35 9 2750 2759 1144.90502 10.1016/j.cor.2006.12.009 (Pubitemid 351193082)
21. Rechenberg, I.: Evolutionstrategie: Optimierung Technischer Systeme nach Prinzipien des Biologischen Evolution. Fromman-Holzboog Verlag, Stuttgart (1973)
22. L. Rónyai L. Babai M.K. Ganapathy 2001 On the number of zero-patterns of a sequence of polynomials J. Am. Math. Soc. 14 3 717 735 0978.12001 10.1090/S0894-0347-01-00367-8
23. G. Rudolph 1997 Convergence rates of evolutionary algorithms for a class of convex objective functions Control Cybern. 26 3 375 390 0891.93089 1610995 (Pubitemid 127156689)
24. N. Sauer 1972 On the density of families of sets J. Comb. Theory, Ser. A 13 1 145 147 0248.05005 10.1016/0097-3165(72)90019-2 307902
25. Sudholt, D., Witt, C.: Runtime analysis of binary PSO. In: GECCO'08: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation, pp. 135-142. ACM, New York (2008)
26. Teytaud, O., Gelly, S.: General lower bounds for evolutionary algorithms. In: Proceedings of PPSN, pp. 21-31 (2006) (Pubitemid 44609378)
27. Teytaud, O., Fournier, H.: Lower bounds for evolution strategies using vc-dimension. In: PPSN, pp. 102-111 (2008)
28. V.N. Vapnik A.Ya. Chervonenkis 1971 On the uniform convergence of relative frequencies of events to their probabilities Theory Probab. Appl. XVI 2 264 280 10.1137/1116025 301855
29. Whitley, D.: The GENITOR algorithm and selection pressure: Why rank-based allocation of reproductive trials is best. In: Schaffer, J.D. (ed.) Proceedings of the Third International Conference on Genetic Algorithms, pp. 116-121. Morgan Kaufman, San Mateo (1989)
30. Witt, C.: Theory of randomised search heuristics in combinatorial optimisation: an algorithmic point of view. In: GECCO'09: Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference, pp. 3551-3592. ACM, New York (2009)