Hybrid genetic models based on recombination of allele permutations based on shift and rotations for DHCP

We introduce a genetic model to solve the directed hamiltonian cycle problem (DHCP) for random directed graphs (digraphs) containing a (hidden) superposed random Hamiltonian cycle. The model represents a scheme for hybrid techniques that recombine the genetic material of allele permutation chromosomes merging ideas coming from the most recent progress in the evolutionary algorithm and the traditional combinatorial optimization areas. The methods are interpreted by rephrasing DHCP as determining the compatibility of some quadratic systems over the finite field GF(2). Genetic algorithms implementing some instances of the model and in which the recombination of the alleles is based on shift and rotations of connected traits of the chromosomes are compared with the classic Angulin and Valiant technique designed to find Hamiltonian cycles in random digraphs. The comparison is interpreted taking also into account the results about the main combinatorial techniques, for which theoretical analysis has been developed, to solve DHCP for random digraphs.