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.

Prof. Husein Hadi Abbass is the Dean Assistant post for Scientific Affairs in the Faculty of Computer Science and Mathematics, university of Kufa - Iraq. He obtained master's degree in applied mathematics from the Technology University in Iraq in 1995. He has publications in Algebra, MV-algebra, Image Processing, Algebraic Statistics, Fuzzy maths.