Finding the Global Minimum of a Low-Dimensional Spin-Glass Model

We present a search method based on a variation of natural molecular evolution to find the global minimum of low-dimensional spin-glasses. A group of different machines operates on a population of suitably defined data strings. Consecutive selection of ”better” strings allows to find the global minimum of the energy landscape.

[1]  W. Ebeling,et al.  Boltzmann and Darwin strategies in complex optimization , 1987 .

[2]  P. W. Anderson,et al.  Suggested model for prebiotic evolution: the use of chaos. , 1983, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Hans-Paul Schwefel,et al.  Numerical Optimization of Computer Models , 1982 .

[4]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[5]  P. Rujan Searching for optimal configurations by simulated tunneling , 1988 .

[6]  Hermann Haken,et al.  Neural and Synergetic Computers , 1988 .

[7]  M. Mézard,et al.  Spin Glass Theory and Beyond , 1987 .

[8]  W Banzhaf,et al.  Population processing--a powerful class of parallel algorithms. , 1989, Bio Systems.

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

[10]  P. Schuster,et al.  A computer model of evolutionary optimization. , 1987, Biophysical chemistry.

[11]  H. Scheraga,et al.  Monte Carlo-minimization approach to the multiple-minima problem in protein folding. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[12]  P. Wolynes,et al.  Spin glasses and the statistical mechanics of protein folding. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[13]  S. Isola Understanding complex behaviour. Some remarks on method and intepretation, in `Chaos and Complexity', (Torino, October 5-11, 1987), R. Livi, S. Ruffo, S. Ciliberto and M. Buiatti eds., World Scientific. , 1988 .

[14]  Heinz Mühlenbein,et al.  Evolution algorithms in combinatorial optimization , 1988, Parallel Comput..

[15]  W. Ebeling,et al.  Models of darwinian processes and evolutionary principles. , 1982, Bio Systems.

[16]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[17]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[18]  M. Mézard,et al.  A replica analysis of the travelling salesman problem , 1986 .

[19]  D. Ackley A connectionist machine for genetic hillclimbing , 1987 .

[20]  Nicholas Carriero,et al.  Distributed data structures in Linda , 1986, POPL '86.

[21]  R. Brady Optimization strategies gleaned from biological evolution , 1985, Nature.

[22]  S. Kirkpatrick,et al.  Solvable Model of a Spin-Glass , 1975 .

[23]  G. Toulouse,et al.  Ultrametricity for physicists , 1986 .