A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing

Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.

[1]  Kazuyuki Aihara,et al.  Chaotic simulated annealing by a neural network model with transient chaos , 1995, Neural Networks.

[2]  Kazuyuki Aihara,et al.  Adaptive annealing for chaotic optimization , 1996 .

[3]  Kenya Jin'no,et al.  Analysis of bifurcation phenomena in a 3-cells hysteresis neural network , 1999 .

[4]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[5]  Kate Smith-Miles,et al.  On chaotic simulated annealing , 1998, IEEE Trans. Neural Networks.

[6]  Kazuyuki Aihara,et al.  A modified algorithm for the quadratic assignment problem using chaotic-neuro-dynamics for VLSI implementation , 2001, IJCNN'01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222).

[7]  Kotaro Hirasawa,et al.  Chaos control on universal learning networks , 2000, IEEE Trans. Syst. Man Cybern. Part C.

[8]  Kazuyuki Aihara,et al.  Combination of Chaotic Neurodynamics with the 2-opt Algorithm to Solve Traveling Salesman Problems , 1997 .

[9]  Zhenya He,et al.  A chaos-generator: analyses of complex dynamics of a cell equation in delayed cellular neural networks , 1998 .

[10]  L. Wang,et al.  Oscillations and chaos in neural networks: an exactly solvable model. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[11]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[12]  Yong Yao,et al.  Model of biological pattern recognition with spatially chaotic dynamics , 1990, Neural Networks.

[13]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Emile H. L. Aarts,et al.  Simulated annealing and Boltzmann machines - a stochastic approach to combinatorial optimization and neural computing , 1990, Wiley-Interscience series in discrete mathematics and optimization.

[15]  Lipo Wang,et al.  Oscillatory and chaotic dynamics in neural networks under varying operating conditions , 1996, IEEE Trans. Neural Networks.

[16]  Kazuyuki Aihara,et al.  Global searching ability of chaotic neural networks , 1999 .

[17]  D. Kunz,et al.  Channel assignment for cellular radio using neural networks , 1991 .

[18]  Dietmar Kunz,et al.  Channel assignment for cellular radio using simulated annealing , 1993 .

[19]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[20]  Lipo Wang,et al.  Artificial neural networks - oscillations, chaos, and sequence processing , 1993 .

[21]  G. Pawley,et al.  On the stability of the Travelling Salesman Problem algorithm of Hopfield and Tank , 2004, Biological Cybernetics.

[22]  Nasser M. Nasrabadi,et al.  Cellular radio channel assignment using a modified Hopfield network , 1997 .

[23]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[24]  H. Nozawa,et al.  Solution of the optimization problem using the neural network model as a globally coupled map , 1994 .

[25]  S. Haykin,et al.  Making sense of a complex world [chaotic events modeling] , 1998, IEEE Signal Process. Mag..

[26]  Hiroshi Nozawa,et al.  A neural network model as a globally coupled map and applications based on chaos. , 1992, Chaos.

[27]  Yoshihiko Horio,et al.  Experimental verification of signal transmission using synchronized SC chaotic neural networks , 1995 .

[28]  A. Gamst,et al.  Some lower bounds for a class of frequency assignment problems , 1986, IEEE Transactions on Vehicular Technology.

[29]  DeLiang Wang,et al.  Incremental learning of complex temporal patterns , 1996, IEEE Trans. Neural Networks.

[30]  Yoshiyasu Takefuji,et al.  A neural network parallel algorithm for channel assignment problems in cellular radio networks , 1992 .

[31]  Marimuthu Palaniswami,et al.  Static and Dynamic Channel Assignment Using Neural Networks , 1997, IEEE J. Sel. Areas Commun..

[32]  Robert Kozma,et al.  Encoding and recall of noisy data as chaotic spatio-temporal memory patterns in the style of the brains , 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium.

[33]  Kate Smith-Miles,et al.  A unified framework for chaotic neural-network approaches to combinatorial optimization , 1999, IEEE Trans. Neural Networks.