Nonlinear ant system for large scale search spaces

In this paper we focus on linearity and nonlinearity of learning schemes applied in ant colony optimization algorithms and discuss about the consequences of the two approaches on the overall algorithm´s performance and efficiency. The paper reviews the previously proposed ACO algorithms, talking about the underlying linear philosophy of most of them, and proposes a nonlinear learning scheme by which not only a new flexible view is introduced on ACO, the performance metrics are also considerably improved regarding large scale search spaces. After a theoretical discussion on both linearity and nonlinearity, we applied the nonlinear learning scheme on the travelling salesman problem based on large scale graphs up to 9500 nodes. The simulation is accomplished between the ACS algorithm and the nonlinear method called NLAS on identical randomly generated graphs, to evaluate the performance metrics such as branching factor which implies the algorithm exploration and the generated best tour length which shows the algorithm convergence towards the global optimum. As simulation results show, considerable improvements in the overall convergence and exploration in the nonlinear approach is achieved.