Transiently chaotic neural network based on switched cooling and its application to maximum clique problem

In this paper we propose a new transiently chaotic neural network model based on switched cooling (TCNNSC) for combinatorial optimization problems, which can escape from local minima and has powerful ability to search the globally optimal or near-optimum solution. By introducing the switched cooling mechanism into transiently chaotic neural network, the control granularity becomes small to decide when to terminate the chaotic dynamics, and how to make use of chaotic behavior for convergence to a stable equilibrium point corresponding to an acceptably near-optimal state. A significant property of the new model is that chaotic dynamics can be increased transiently when chaotic searching conditions are satisfied; otherwise chaotic dynamics is decreased quickly to accelerate the convergent process. Therefore the proposed model can be expected to have higher ability to escape from local minima and to search for globally optimal or near-optimal solutions. In addition, since chaotic dynamics can be increased and decreased under the control of the switched cooling mechanism, the searching space of the proposed model for optimization is further reduced. For the reduced search spaces and the accelerating convergent process, the network could use less CPU time to reach a saturated state. A large number of instances on the maximum clique problems have been simulated to verify the proposed model.