Neural networks for solving the quadratic 0-1 programming problem under linear constraints

An extension of the Boolean neural network (BNN) is presented to solve a quadratic 0-1 programming problem under linear constraints. The network is called a QBNN (quadratic Boolean neural network). To design the QBNN, some theoretical results from the integer programming domain are used. This shows the connection between nonlinear and integer programming. The linear constraints are also incorporated into the quadratic objective function by using the penalty methods with a variable parameter. This allows the transformation of the constrained problem into an unconstrained one. The total objective function obtained is then fixed as the energy function for the QBNN. Some simulation results are given to show that the system finds a good optimal solution within a few neural time constants