Lagrangian Relaxation Neural Networks for Job Shop Scheduling

Manufacturing scheduling is an important but difficult task. In order to effectively solve such combinatorial optimization problems, this paper presents a novel Lagrangian relaxation neural network (LRNN) for separable optimization problems by combining recurrent neural network optimization ideas with Lagrangian relaxation (LR) for constraint handling. The convergence of the network is proved, and a general framework for neural implementation is established, allowing creative variations. When applying the network for job shop scheduling, the separability of problem formulation is fully exploited, and a new neuron-based dynamic programming is developed making innovative use of the subproblem structure. Testing results obtained by software simulation demonstrate that the method is able to provide near-optimal solutions for practical job shop scheduling problems, and the results are superior to what have been reported in the neural network scheduling literature. In fact, the digital implementation of LRNN for job shop scheduling is similar to the traditional LR approaches. The method, however, has the potential to be implemented in hardware with much improved quality and speed.