Cooperative updating in the Hopfield model

We propose a new method for updating units in the Hopfield model. With this method two or more units change at the same time, so as to become the lowe st energy state among all possible states. Since this updating algorithm is based on the detailed balance equation, convergence to the Boltzmann distr ibution is guaranteed. If our algorithm is applied to finding the minimum e nergy in constraint satisfaction and combinatorial optimization problems, t hen there is faster convergence than with the usual algorithm in the neural network. This is shown by experiments with the travelling salesman problem (TSP), the four-color problem (4CP), the N-queen problem (4QP), and the gr aph bipartitioning problem (GBP). In constraint satisfaction problems, for which earlier neural networks are effective in some cases, our updating sch eme works fine. Even though we still encounter the problem of ending up in local minima, our updating scheme has a great advantage compared with the u sual updating scheme used in combinatorial optimization problems. Also we d iscuss parallel computing using our updating algorithm.