An algorithm based on free search is proposed for the combinatorial optimization problems. In this algorithm, a feasible solution is converted into a full permutation of all the elements and a transformation of one solution into another solution can be interpreted the transformation of one permutation into another permutation. Then, the algorithm is combined with intersection elimination. The discrete free search algorithm greatly improves the convergence rate of the search process and enhances the quality of the results. The experiment results on TSP standard data show that the performance of the proposed algorithm is increased by about 2.7% than that of the genetic algorithm.

Using the analytical and numerical approaches, the nonlinear dynamic behaviors in the vicinity of a compound critical point are studied for a rectangular symmetric cross-ply laminated composite plate with a parametric excitation. The geometric nonlinearity and nonlinear damping are included in the governing equations of motion in this model. Normal form theory, bifurcation and stability theory are used to find closed form solutions for equilibria and periodic motions. Stability conditions of these solutions are obtained explicitly and critical boundaries along which incipient and secondary leading to 2-D tori are also derived. Finally, numerical results are presented to confirm these analytical predictions.