Application of Inhomogeneous Markov Chain Monte Carlo to a Genetic Algorithm

There has been active study on the genetic algorithm based on the homogeneous Markov chain Monte Carlo method. Noticing that a convergence of the Markov chain to an invariant distribution is possible even for an inhomogeneous one, we propose a new method using the inhomogeneous Markov chain Monte Carlo for the genetic algorithm. In this method we separate solutions to an object and a supporter. The former is the solution that should converge to the invariant distribution, while the latter is used for keeping a diversity of solutions. After presenting experiments for convergences in our method, we apply this method for the optimization for the deceptive problem and the binary quadratic programming problem. By experimental results we confirm that it is quite effective for the optimization.