0-1 constraints satisfaction through recursive neural networks with mixed penalties

This paper presents a new analog neuron-like network for finding feasible solutions to 0-1 constraints satisfaction problems having potentially several thousand of variables. It is based on mixed-penalty functions: exterior penalty functions together with interior penalty functions. Starting from a near-binary solution satisfying each linear inequality, the network generates trial solutions located outside or inside the feasible set, in order to minimize an energy function which measures the total binary infeasibility of the system. The performances of the network are demonstrated on real data sets from an industrial assignment problem of large size with linear inequalities and binary variables.