New Models of Genetic Algorithms Using the Dihedral Group

In this book, we find a Markov basis B and toric ideals for (n^2-3n)/3×3×n/3 - contingency tables with fixed two dimensional marginals, n is a multiple of 3 greater than or equal 6, also we give a new model of permutation the pieces of nucleotides in aligned DNA sequences. Then we used the action of the largest subgroup H of dihedral group D_n on these contingency tables and B to find six types of (n^2-3n)/3×3×n/3 - contingency tables with fixed two dimensional marginal, such that the Markov basis B for (n^2-3n)/3×3×n/3 - contingency tables is H invariant, from these types a new model of genetic algorithm of permutation of the pieces of Nucleotides in aligned DNA sequences is given.