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.<
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