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
Minimizing conflicts: a heuristic repair method for constraint satisfaction and scheduling problems
Artificial Intelligence - Special volume on constraint-based reasoning
Softmax to Softassign: neural network algorithms for combinatorial optimization
Journal of Artificial Neural Networks - Special issue: neural networks for optimization
Neural Networks for Combinatorial Optimization: a Review of More Than a Decade of Research
INFORMS Journal on Computing
Manufacturing cell formation using a new self-organizing neural network
Computers and Industrial Engineering - 26th International conference on computers and industrial engineering
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
A noisy self-organizing neural network with bifurcation dynamics for combinatorial optimization
IEEE Transactions on Neural Networks
Bifurcations of Renormalization Dynamics in Self-organizing Neural Networks
Neural Information Processing
On conditions for intermittent search in self-organizing neural networks
MICAI'07 Proceedings of the artificial intelligence 6th Mexican international conference on Advances in artificial intelligence
| Hi-index | 0.00 |
Kwok and Smith (2005) 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. It has been hypothesized that the optimal temperature setting corresponds to the 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. It is shown that most fixed points exist in the neighborhood of the maximum entropy equilibrium = (N-1, N-1, ..., N-1), where N is the ISM dimensionality. We calculate the exact rate of decrease in the number of ISM equilibria as one moves away from . Bounds on temperatures guaranteeing different stability types of ISM equilibria are also derived. 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 by trial-and-error 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. It is also shown that no intermittent search can exist in SONN for temperatures greater than one-half.