Neural network parallel computing for optimization problems

This dissertation presents new parallel computing schemes for solving optimization problems based on the artificial neural network. Optimization problems are generally classified as two types of problems: constraint-satisfied problems and minimization problems. A motion equation approach is provided to solve the constraint-satisfied problems more directly. The demonstrated applications for the constraint-satisfied problems are: (1) four-coloring problems; (2) sorting problems; (3) knight's tour problems and others. The proposed network, the generalized maximum neural network, has the following advantages over the existing models: (1) no tuning parameters are required; (2) no threshold value is needed; (3) the equilibrium state is exactly defined; and (4) a feasible solution is always guaranteed. Several demonstrated applications for the minimization problems are as follows: (1) max cut problems; (2) module orientation problems; (3) maximum clique problems. The analog circuit of the proposed network is also presented.