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

An application of neural networks is presented for solving job-shop scheduling, and NP-complete optimization problem with constraint 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 the neural network, solution to the job-shop problem is represented by a set of cost function trees encoded in the matrix of stable states. Each node represents a job, and each link represents the interdependency between jobs. The cost attached to each link is a function of the processing time of a particular job. The starting time of each job can be determined by traversing the paths leading to the root node of the tree. Near-optimal and optimal solutions are found by simulated annealing.<>