Solving maximum cut problem using improved Hopfield neural network

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E86-A, Issue 3, 2003, Pages 722-729

  Wang, Rong Long ^a   Tang, Zheng ^a   Cao, Qi Ping ^b  

^a UNIVERSITY OF TOYAMA   (Japan)

^b Tateyama Systems Institute   (Japan)

Author keywords

Hopfield type neural network; Internal dynamics; Maximum cut problem; NP complete problem

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; GRAPH THEORY; OPTIMIZATION; PROBABILITY;

HOPFIELD-TYPE NEURAL NETWORK; INTERNAL DYNAMICS; MAXIMUM CUT PROBLEM;

NEURAL NETWORKS;

EID: 0038035681     PISSN: 09168508     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. R.M. Karp, "Reducibility among combinatorial problems," in Complexity of Computer Computations, pp.85-103, Plenum Press, New York, 1972.
2. K. Chang and D. Du, "Efficient algorithm for the layer assignment problem," IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol.6, no.1, pp.67-78, 1987.
3. F. Barahona, M. Grotschel, M. Junger, and G. Reinelt, "An application of combinatorial optimization to statistical physics and circuit layout design," Oper. Res., vol.36, pp.493-513, 1988.
4. R. Pinter, "Optimal layer assignment for interconnect," Proc. Int. Symp. Circuit Syst., pp.398-401, 1982.
5. M.R. Garey, D.S. Johnson, and L.J. Stockmeyer, "Some simplified NP-complete graph problem," Theor. Comput. Sci., vol.1, pp.237-267, 1976.
6. F. Hadlock, "Finding a maximum cut of a planar graph in polynomial time," SIAM J. Comput., vol.4, no.3, pp.221-225, 1975.
7. S. Sahni and T. Gonzalez, "NP-complete approximation problems," J. ACM, vol.23, pp.555-565, 1976.
8. C.-P. Hsu, "Minimum-via topological routing," IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol.2, no.4, pp.235-246, Oct. 1983.
9. F. Alizadeh, "Interior point method in semidefinite programming with applications to combinatorial optimization," SIAM J. Optimization, vol.5, pp.13-51, 1995.
10. M.X. Goemans and D.P. Williamson, "Improved approximation algorithms for the maximum cut and satisfiability problems using semidefinite programming," J. ACM, vol.42, pp.1115-1145, 1995.
11. A. Bertoni, P. Campadelli, and G. Grossi, "An approximation algorithm for the maximum cut problem and its experimental analysis," Proc. Algorithms & Experiments, pp.137-143, Ternto, Italy, Feb. 1998.
12. J.J. Hopfield, "Neurons with graded response have collective computation properties like those of two-state neurons," Proc. Nat. Acad. Sci. U.S., vol.81, pp.3088-3092, 1982.
13. J.J. Hopfield and D.W. Tank, "'Neural' computation of decisions in optimization problems," Biol. Cybern., no. 52, pp.141-152, 1985.
14. K.A. Smith, "Neural network for combinatorial optimization: A review of more than a decade of research," Informs J. Computing, vol.11, no.1, pp.15-34, 1999.
15. M.A. Alberti, A. Bertoni, P. Campadelli, G. Grossi, and R. Posenato, "A neural algorithm for MAX-2SAT: Performance analysis and circuit implementation," Neural Networks, vol.10, no.3, pp.555-560, 1997.
16. S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi, "Optimisation by simulated annealing," Science, vol.220, pp.671-680, 1983.
17. D.E. Goldberg, Genetic algorithm in search, optimization and machine learning, Addison-Wesley, Reading, MA, 1989.
18. J. Mandziuk and B. Macukow, "A neural network designed to solve the N-queens problem," Boil. Cybern., vol.66, pp.375-379, 1992.
19. J. Mandziuk, "Solving the N-queens problem with a binary Hopfield-type network," Boil. Cybern., vol.72, pp.439-445, 1995.
20. Y. Takefuji and K.C. Lee, "Artificial neural networks for four-coloring map problems and K-colorability problems," IEEE Trans. Circuits Syst., vol.38, no.3, pp.326-333, March 1991.
21. W.S. McCulloch and W.H. Pitts, "A logical calculus of ideas immanent in nervous activity," Bull. Math. Biophys, vol.5, pp.115-133, 1943.
22. D.S. Johnson, C.R. Aragon, L.A. McGeoch, and C. Shevon, "Optimization by simulated annealing: An experimental evaluation; Part 1, graph partitioning," Oper. Res., vol.37, no.6, pp.865-892, 1989.
23. A.L. Corcoran and R.L. wainwright, "LibGA: A user-friendly workbench for order-based genetic algorithm research," Proc. 1993 ACM/SIGAPP Symposium on Applied Computing, pp.111-118, ACM Press, New York, 1993.
24. A.L. Corcoran and R.L. wainwright, "Using LibGA to develop genetic algorithm for solving combinatorial optimization problems," in The Application Handbook of Genetic Algorithms, vol.1, ed., Lance Chambers, pp.143-172, CRC Press, 1995.