Self-organized combinatorial optimization

Abstract

In this paper, we present a self-organized computing approach to solving hard combinatorial optimization problems, e.g., the traveling salesman problem (TSP). First of all, we provide an analytical characterization of such an approach, by means of formulating combinatorial optimization problems into autonomous multi-entity systems and thereafter examining the microscopic characteristics of optimal solutions with respect to discrete state variables and local fitness functions. Next, we analyze the complexity of searching in the solution space based on the representation of fitness network and the observation of phase transition. In the second part of the paper, following the analytical characterization, we describe a decentralized, self-organized algorithm for solving combinatorial optimization problems. The validation results obtained by testing on a set of benchmark TSP instances have demonstrated the effectiveness and efficiency of the proposed algorithm. The link established between the microscopic characterization of hard computational systems and the design of self-organized computing methods provides a new way of studying and tackling hard combinatorial optimization problems.