Neural computing for optimization and combinatorics by editors, Yoshiyasu Takefuji, Jun Wang.

By editors, Yoshiyasu Takefuji, Jun Wang.

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35] P. L . Hammer, "Some network flow problems solved with pseudo-boolean programming," Operations Research, 13, pp. 388-399. 1965. [36] F. Barahona, M , Junger, and G. Reinelt, "Experiments in quadratic 0-1 programming," Mathematical Programming, 44, pp. 127-137, 1989. [37] M . L . Y u , " A study of the applicability of Hopfield decision neural nets to V L S I C A D , " Proc. 2 6 Appendix , h Design Automation Conference, pp. 412-417, 1989. A: The goal o f the quadratic zero-one programming problem is to minimize the following equation.

Because the graph Gfy] is obtained by adding a node So to the graph G which is the complementary graph of the given graph. Table 6 The C P U lime (seconds! 9 on a D E C 3 1 0 0 machine (13 MIPS). 1 Our algorithm is also compared wilh a partially cnumeraiive algorilhm presented by Carraghan and Pardalos in 1990 112] which is faster than any previously known existing algorithms. Their simulation results were obtained on an I B M 3090 computer. The speed of the 1BM3090 is 30 MIPS. 9 Maximum Clique Problems: Part 1 49 density.

Inspired by the Ising model and the parallelism in the artificial neural network, the maximum neural network is invented. The maximum neural network consists of M clusters where each cluster is composed of n processing elements. The total number of required processing elements is M x n. i = m a x | U m m m j =1 if i, .... U _ (. 0 otherwise. Therefore one and only one processing m n 1 clement among n processing elements per cluster is always encouraged to fire in the maximum neural network. The maximum neural network model has been successfully used to solve the tiling problem [24], the max cut problem [29], the bipartite subgraph problem [30], and the module orientation problem [311.

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