Identifying Linkage Groups by Nonlinearity/Non-monotonicity Detection

This paper presents and discusses direct linkage identiication procedures based on nonlinearity/non-monotonicity detection. The algorithm we propose checks arbitrary nonlinearity/non-monotonicity of t-ness change by perturbations in a pair of loci to detect their linkage. We rst discuss condition of the linkage identiication by nonlinearity check (LINC) procedure (Mune-tomo & Goldberg, 1998) and its allowable nonlinearity. Then we propose another condition of the linkage identiication by non-monotonicity detection (LIMD) and prove its equality to the LINC with allowable nonlin-earity (LINC-AN). The procedures can identify linkage groups for problems with at most order-k diiculty by checking O(2 k) strings and the computational cost for each string is O(l 2) where l is the string length.

[1]  H. Kargupta,et al.  Computational processes of evolution and the gene expression messy genetic algorithm , 1996 .

[2]  K. Deb.  Binary and floating-point function optimization using messy genetic algorithms , 1991 .

[3]  Sanza T. Kazadi,et al.  Conjugate Schema in Genetic Search , 1997, ICGA.

[4]  H. Kargupta.  SEARCH , Evolution , And The Gene Expression Messy Genetic Algorithm , 1994 .

[5]  H. Kargupta.  Search, polynomial complexity, and the fast messy genetic algorithm , 1996 .

[6]  M. Pelikán,et al.  The Bivariate Marginal Distribution Algorithm , 1999 .

[7]  Heinz Mühlenbein,et al.  The Equation for Response to Selection and Its Use for Prediction , 1997, Evolutionary Computation.

[8]  David E. Goldberg,et al.  Linkage Problem, Distribution Estimation, and Bayesian Networks , 2000, Evolutionary Computation.

[9]  G. Harik.  Learning gene linkage to efficiently solve problems of bounded difficulty using genetic algorithms , 1997 .

[10]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[11]  Hillol Kargupta,et al.  The Gene Expression Messy Genetic Algorithm , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[12]  Hillol Kargupta,et al.  Extending the class of order-k delineable problems for the gene expression messy genetic algorithm , 1996 .

[13]  Gang Wang,et al.  Revisiting the GEMGA: scalable evolutionary optimization through linkage learning , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).