Characteristic updating-normalisation dynamics of a self-organising neural network for enhanced combinatorial optimisation

The optimisation performance of a self-organising neural network with weight normalisation (SONN-WN) is computationally studied in this paper. The SONN-WN is applied to solve the constraint satisfaction problem (CSP) of N-queen, and performance indicators such as feasibility and efficiency are measured in the key parameter space of the Kohonen learning rate β and normalisation temperature T. The measurements reveal regions of high optimisation ability associated with certain β and T combinations, indicating the close coupling of the Kohonen learning and normalisation mechanisms towards effective optimisation. The complex interaction of the two mechanisms is studied by numerically investigating the nonlinear dynamics of a simplified model of the updating-normalisation process. By combining the performance measurements of the SONN-WN with the dynamical study of the simplified model, a range of characteristic convergence dynamics have been identified with the SONN-WN for enhanced optimisation performance.