Incorporating Chaos into the Hopfield Neural Network for Combinatorial Optimisation

Various approaches of incorporating chaos into artificial neural networks have recently been proposed, and used successfully to solve combinatorial optimisation problems. This paper investigates three such approaches: 1) Chen & Aihara's transiently chaotic neural network with chaotic simulated annealing, which has a gradually decaying negative selfcoupling term; 2) Wang & Smith's chaotic simulated annealing, which employs a gradually decreasing time-step; 3) Hayakawa et al's method of adding chaotic noise to a Hopfield network. The N-Queen problem is used as an application to test and compare the performance and robustness of the three methods. The traditional simulated annealing is also included for comparison in order to contrast the effectiveness of the various approaches.