Stochastic neural networks for solving job-shop scheduling. I - Problem representation

An application of neural networks is presented for solving job-shop scheduling, an NP-complete optimization problem with constaint satisfaction. In particular, the authors introduce a neural computation architecture based on a stochastic Hopfield neural-network model. First, the job-shop problem is mapped into a two-dimensional matrix representation of neurons similar to those for solving the traveling salesman problem (TSP). Constant positive and negative current biases are applied to specific neurons as excitations and inhibitions, respectively, to enforce the operation precedence relationships. At the convergence of neural network, the solution to the job-shop problem is represented by a set of cost function trees encoded in the matrix of stable states. Each node in the set of trees represents a job, and each link represents the interdependency between jobs. A computation circuit computes the total completion times (costs) of all jobs, and the cost difference is added to the energy function of the stochastic neural network. Using a simulated annealing algorithm, the temperature of the system is slowly decreased according to an annealing schedule until the energy of the system is at a local or global minimum. By choosing an appropriate annealing schedule, near-optimal and optimal solutions to job-shop problems can be found.