Neural network approach for minimizing the makespan of the general job-shop

A neural network approach is proposed to minimize the makespan of the job-shop scheduling, which is a combinatorial optimization problem. The present approach is based on the Hopfield interconnected neural networks model. In contrast to the traditional neural network approach based on the Hopfield model, the model changes the threshold values at each transition of neurons in order to make a non-delay schedule in addition to incorporating job- and shop-related constraints. As the modification may lead to non-optimal solutions, the authors increase the temperature of the network according to the Boltzmann machine mechanism and obtain other schedules until no better solution can be obtained within the specified number of tests. From the numerical experiments, 10 out of 15 problems are solved optimally, and the remaining five problems are solved near-optimally within a reasonable computing time.