Pseudobasin of attraction for combinatorial dynamical systems: Theory and its application to combinatorial optimization

In this brief, a concept of a pseudobasin (a generalized concept of a basin of attraction) for a class of combinatorial dynamical system is introduced. A fairly comprehensive theory of its algebraic and topological structure is developed. A systematic method to solve a combinatorial optimization problem is also developed. Utilizing the theoretical results of pseudobasin, the convergence of the proposed method to a so-called stable local minimum is given.