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Full-Text Articles in Physical Sciences and Mathematics
Optimization By Varied Beam Search In Hopfield Networks, Tony R. Martinez, Xinchuan Zeng
Optimization By Varied Beam Search In Hopfield Networks, Tony R. Martinez, Xinchuan Zeng
Faculty Publications
This paper shows that the performance of the Hopfield network for solving optimization problems can be improved by a varied beam search algorithm. The algorithm varies the beam search size and beam intensity during the network relaxation process. It consists of two stages: increasing the beam search parameters in the flrst stage and then decreasing them in the second stage. The purpose of using such a scheme is to provide the network with a better chance to find more and better solutions. A large number of simulation results based on 200 randomly generated city distributions of the 10-city traveling salesman …
Improved Hopfield Networks By Training With Noisy Data, Fred Clift, Tony R. Martinez
Improved Hopfield Networks By Training With Noisy Data, Fred Clift, Tony R. Martinez
Faculty Publications
A new approach to training a generalized Hopfield network is developed and evaluated in this work. Both the weight symmetricity constraint and the zero self-connection constraint are removed from standard Hopfield networks. Training is accomplished with Back-Propagation Through Time, using noisy versions of the memorized patterns. Training in this way is referred to as Noisy Associative Training (NAT). Performance of NAT is evaluated on both random and correlated data. NAT has been tested on several data sets, with a large number of training runs for each experiment. The data sets used include uniformly distributed random data and several data sets …
Improving The Hopfield Network Through Beam Search, Tony R. Martinez, Xinchuan Zeng
Improving The Hopfield Network Through Beam Search, Tony R. Martinez, Xinchuan Zeng
Faculty Publications
In this paper we propose a beam search mechanism to improve the performance of the Hopfield network for solving optimization problems. The beam search readjusts the top M (M > 1) activated neurons to more similar activation levels in the early phase of relaxation, so that the network has the opportunity to explore more alternative, potentially better solutions. We evaluated this approach using a large number of simulations (20,000 for each parameter setting), based on 200 randomly generated city distributions of the 10-city traveling salesman problem. The results show that the beam search has the capability of significantly improving the network …
Rescaling The Energy Function In Hopfield Networks, Tony R. Martinez, Xinchuan Zeng
Rescaling The Energy Function In Hopfield Networks, Tony R. Martinez, Xinchuan Zeng
Faculty Publications
In this paper we propose an approach that rescales the distance matrix of the energy function in the Hopfield network for solving optimization problems. We rescale the distance matrix by normalizing each row in the matrix and then adjusting the parameter for the distance term. This scheme has the capability of reducing the effects of clustering in data distributions, which is one of main reasons for the formation of invalid solutions. We evaluate this approach through a large number (20,000) simulations based on 200 randomly generated city distributions of the 10-city traveling salesman problem. The result shows that, compared to …
Extending The Power And Capacity Of Constraint Satisfaction Networks, Tony R. Martinez, Xinchuan Zeng
Extending The Power And Capacity Of Constraint Satisfaction Networks, Tony R. Martinez, Xinchuan Zeng
Faculty Publications
This work focuses on improving the Hopfield network for solving optimization problems. Although much work has been done in this area, the performance of the Hopfield network is still not satisfactory in terms of valid convergence and quality of solutions. We address this issue in this work by combing a new activation function (EBA) and a new relaxation procedure (CR) in order to improve the performance of the Hopfield network. Each of EBA and CR has been individually demonstrated capable of substantially improving the performance. The combined approach has been evaluated through 20,000 simulations based on 200 randomly generated city …