Transient Chaotic Neural Network with Negative Self-feedback Memory for Continuous Optimisation Problems

In this paper we present a transient chaotic neural network model which incorporates negative self-feedback memory. This allows the chaotic driving term in the neural network model the ability to adapt to the energy state of the network and hence drive the system towards the global minimum avoiding the issue of being trapped in local minima. The model framework also reduces the number of parameters that require tuning to the particular optimisation problem since the self-feedback bias, \(I_0\) , is no longer a tunable parameter and instead evolves with the neurodynamics. We apply the model on a continuous optimisation problem, in doing so we outline the procedure for mapping the continuous energy function onto the neuron state space and embedding the energy function into the network equations. We compare performance with the Chen and Aihara model and confirm that the self-feedback memory model does outperform the Chen & Aihara model in terms of robustness, i.e., finds the global minimum for all initial values of the self-feedback bias, \(I_0\) , and still has comparable convergence rate. We also perform a parameter investigation and demonstrate that the input scaling parameter, \(\alpha \) , can induce non-transient chaos even in the non-chaotic Hopfield network, highlighting the importance of this parameter for problem specific considerations.