Integer linear programming neural networks for job-shop scheduling

The authors present an integer linear programming neural network (ILPNN) based on a modified Tank and Hopfield neural network model to solve job-shop scheduling, an NP-complete constraint satisfaction problem. The constraints of the job-shop problem are formulated as a set of integer linear equations. The cost function for minimization is the total starting times of all jobs subject to precedence constraints. In the authors´ approach, the set of integer linear equations is solved by an iterative linear programming with integer adjustments (ILPIA) technique, without a branch-and-bound search. In particular, the linear and nonlinear zero-one variables are represented by linear sigmoid and nonlinear high-gain amplifiers with a response of a step function, respectively. Simulations based on solving a linear differential equation show that the ILPNN approach produces optimal or near-optimal solutions, although it does not guarantee optimal solutions. The authors also analyze the hardware implementation of ILPNNs and study the feasibility of this approach for large-scale problems.<>