Adaptiveness in monotone pseudo-boolean optimization and stochastic neural computation

International Journal of Neural Systems

Volumn 19, Issue 4, 2009, Pages 241-252

  Grossi, Giuliano ^a  

^a UNIVERSITY OF MILAN   (Italy)

Author keywords

Heuristics; Hopfield neural networks; Nonlinear pseudo Boolean optimization; Penalty strategies; Stochastic dynamics

Indexed keywords

BENCHMARKING; BOOLEAN FUNCTIONS; COMPUTATION THEORY; COMPUTATIONAL COMPLEXITY; COST FUNCTIONS; GRAPH THEORY; MARKOV PROCESSES; OPTIMIZATION; POLYNOMIAL APPROXIMATION; RANDOM PROCESSES; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

HEURISTICS; HOPFIELD NEURAL NETWORKS (HNN); NONLINEAR COMPUTATIONAL MODEL; PENALTY STRATEGY; PSEUDO-BOOLEAN FUNCTION; PSEUDO-BOOLEAN OPTIMIZATION; STATE-SPACE DISTRIBUTIONS; STOCHASTIC DYNAMICS;

HOPFIELD NEURAL NETWORKS;

ANIMAL; ARTICLE; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; COMPUTER SIMULATION; HUMAN; NONLINEAR SYSTEM; STATISTICS;

ANIMALS; COMPUTER SIMULATION; HUMANS; MODELS, NEUROLOGICAL; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; STOCHASTIC PROCESSES;

EID: 70149109891     PISSN: 01290657     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129065709001999     Document Type: Article

References (32)

1. E. Aarts and J. Korst, Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing (John Wiley & Sons, Inc., New York, NY, USA, 1989).
2. D. H. Ackley, G. E. Hinton and T. J. Sejnowski, A learning algorithm for boltzmann machines, Cognitive Science 9 (1985).
3. H. Adeli and H. S. Park, Optimization of space structures by neural dynamics, Neural Networks 8(5) (1995) 769-781.
4. R. Bar-Yehuda and S. Even, A local-ratio theorem for approximating the weighted vertex cover problem, Annals of Discrete Mathematics 25 (1985) 27-45.
5. A. Bertoni, P. Campadelli and G. Grossi, A neural algorithm for the maximum clique problem: Analysis, experiments and circuit implementation, Algo-ritmica 33(1) (2002) 71-88.
6. E. Boros and P. L. Hammer, Pseudo-boolean optimization, DAMATH: Discrete Applied Mathematics and Combinatorial Operations Research and Computer Science 123 (2002).
7. Y. Y. Chen and K. Y. Young, An som-based algorithm for optimization with dynamic weight updating, International Journal of Neural Systems 17(3) (2007) 171-181.
8. K. L. Clarkson, A modification of the greedy algorithm for vertex cover, Information Processing Letters 16 (1983) 23-25.
9. G. Gaĺan-Maŕin, E. Ḿerida-Casermeiro and J. Munoz-Ṕerez, Modelling competitive hopfield networks for the maximum clique problem, Comput. Oper. Res. 30(4) (2003) 603-624.
10. M. R. Garey and D. S. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness (W. H. Freeman & Co., San Francisco, CA, 1979).
11. F. Gavril, Quoted in Ref. 10, p. 134.
12. R. J. Glauber, Time-dependent statistics of the Ising model, Journal of Mathematical Physics 4(2) (1963) 294-307.
13. G. Grossi, A discrete adaptive stochastic neural model for constrained optimization, in 16th International Conference on Artificial Neural Networks (ICANN '06), Springer (2006), pp. 641-650.
14. G. Grossi and F. Pedersini, FPGA implementation of a stochastic neural network for monotonic pseudo-boolean optimization, Neural Networks 21(6) (2008) 872-879.
15. G. Grossi and R. Posenato, A distributed algorithm for max independent set problem based on Hopfield networks, in Neural Nets: 13th Italian Workshop on Neural Nets (WIRN '02), Springer-Verlag (2002), pp. 64-74.
16. P. L. Hammer, I. Rozemberg and S. Rudeanu, Application of discrete linear programming to the minimization of boolean functions, Rev. Mat. Pures App. 8 (1963) 459-475.
17. P.L. Hammer and S. Rudeanu, Boolean Methods in Operations Research and Related Areas (Springer-Verlag, 1968).
18. J. Hertz, A. Krogh and R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, 1991).
19. J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proceedings of the National Academy of Sciences of the United States of America 79(8) (1982) 2554-2558.
20. J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, in Proceedings of the National Academy of Sciences 81 (NAS, 1984) 3088-3092.
21. J. J. Hopfield and D. W. Tank, Neural computation of decision in optimization problems, Biological Cybernetics 52 (1985) 141-152.
22. D. S. Johnson and M. A. Trick, Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science (American Mathematical Society, 1996).
23. R. M. Karp, Reducibility among combinatorial problems, Complexity of Computer Computations (Plenum Press, New York, 1972), pp. 85-103.
24. S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Optimization by simulated annealing, Science 220 (1983) 671-680.
25. P. J. M. Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications, Mathematics and Its Applications (Reidel Publisching Company, 1987).
26. D. Matula, On the complete subgraph of a random graph, Combinatory Mathematics and Its Applications (1970), pp. 356-369.
27. R. V. Mayorga and M. Arriaga, Non-linear global optimization via parameterization and inverse function approximation: An artificial neural networks approach, International Journal of Neural Systems 17 (5) (2007) 353-368.
28. G. Serpen, Hopfield network as static optimizer: Learning the weights and eliminating the guesswork, Neural Process. Lett. 27(1) (2008) 1-15.
29. K. Smith, Neural networks for combinatorial optimization: A review of more than a decade of research, INFORMS Journal on Computing 11 (1999) 15-34.
30. Y. Takefuji, Neural Network Parallel Computing (Kluwer Academic Publishers, Norwell, MA, USA, 1992).
31. J. Wang and Y. Zhou, Stochastic optimal competitive hopfield network for partitional clustering, Expert Systems with Applications 36 (2009) 2072-2080.
32. R. L. Wang, P. Zhang and K. Okazaki, An efficient learning algorithm of the hopfield neural network for the minimum set cover problem, IJCSNS International Journal of Computer Science and Network Security 6(9) (2007) 28-31.