A Novel Chaotic Neural Network With the Ability to Characterize Local Features and Its Application

Abstract

To provide an ability to characterize local features for the chaotic neural network (CNN), Gauss wavelet is used for the self-feedback of the CNN with the dilation parameter acting as the bifurcation parameter. The exponentially decaying dilation parameter and the chaotically varying translation parameter not only govern the wavelet self-feedback transform but also enable the CNN to generate complex dynamics behavior preventing the network from being trapped in the local minima. Analysis of the energy function of the CNN indicates that the local characterization ability of the proposed CNN is effectively provided by the wavelet self-feedback in the manner of inverse wavelet transform and that the proposed CNN can achieve asymptotical stability. The experimental results on traveling salesman problem (TSP) suggest that the proposed CNN has a higher average success rate for obtaining globally optimal or near-optimal solutions.

Application of the edge of chaos in combinatorial optimization*

“…In order to clarify the superiority of our algorithm further, we firstly compare ECNN algorithm to several other recent works on TSP with improved algorithms based on CNN. The globally optimal probability for TSP of 30-city is 46% with the algorithm based on CNN with Gauss wavelet self-feedback, [22] 30.5% with the FCSCNN algorithm, [23] and 49% with the HFCSCNN algorithm. [24] ECNN algorithm can drive the network away from local optimal states.…”

“…Then, studies have been focused on the approximate algorithms or heuristic algorithms to seek near-optimal solutions of the problem with limited amount of computing time. Many algorithms were therefore proposed, such as stochastic simulated annealing (SSA) algorithm, [6][7][8] some algorithms based on biological phenomena, [3,[8][9][10][11][12][13] and artificial neural network algorithms, [14][15][16][17][18][19][20][21][22][23][24] which have brought about some achievement in different scale problems.…”

“…However, the probabilities of the globally optimal solutions for the two TSPs were not given in their work. [21] Besides, several other improved algorithms were proposed based on CNN, such as chaotic neural network with Gauss wavelet self-feedback, [22] frequency conversion sinusoidal chaotic neural network (FCSCNN), [23] and FCSCNN with hysteretic noise (HNFCSCNN). [24] Those algorithms enhanced the globally optimal probability in the TSPs of no more than 30 cities in certain degrees.…”

“…However, no globally optimal solutions of larger scale problems were reported. [21][22][23][24] Studies show that the algorithms based on chaotic neural networks have higher searching efficiency than many other algorithms. [20][21][22][23][24] At the initial stage of optimization, a chaotic neural network is in chaotic states.…”

“…[21][22][23][24] Studies show that the algorithms based on chaotic neural networks have higher searching efficiency than many other algorithms. [20][21][22][23][24] At the initial stage of optimization, a chaotic neural network is in chaotic states. As time evolves, the chaotic neural network gradually degenerates into a stable state, optimization then is achieved.…”