Computation at the edge of chaos: phase transitions and emergent computation
CNLS '89 Proceedings of the ninth annual international conference of the Center for Nonlinear Studies on Self-organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks on Emergent computation
Neural Networks for Combinatorial Optimization: a Review of More Than a Decade of Research
INFORMS Journal on Computing
Optimization via Intermittency with a Self-Organizing Neural Network
Neural Computation
Performance-enhancing bifurcations in a self-organising neural network
IWANN'03 Proceedings of the Artificial and natural neural networks 7th international conference on Computational methods in neural modeling - Volume 1
Neural techniques for combinatorial optimization with applications
IEEE Transactions on Neural Networks
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Kwok and Smith [1] recently proposed a new kind of optimization dynamics using self-organizing neural networks (SONN) driven by softmax weight renormalization. Such dynamics is capable of powerful intermittent search for high-quality solutions in difficult assignment optimization problems. However, the search is sensitive to temperature setting in the softmax renormalization step of the SONN algorithm. It has been hypothesized that the optimal temperature setting corresponds to symmetry breaking bifurcation of equilibria of the renormalization step, when viewed as an autonomous dynamical system called iterative softmax (ISM). We rigorously analyze equilibria of ISM by determining their number, position and stability types. Moreover, we offer analytical approximations to the critical symmetry breaking bifurcation temperatures that are in good agreement with those found by numerical investigations. So far the critical temperatures have been determined only via numerical simulations. On a set of N-queens problems for a wide range of problem sizes N, the analytically determined critical temperatures predict the optimal working temperatures for SONN intermittent search very well.