1 Lagrangian Relaxation Neural Networks for Job Shop Scheduling

Manufacturing scheduling is an important but difficult task. Building on our previous success in developing optimization-based scheduling methods using Lagrangian relaxation for practical applications, this paper presents a novel Lagrangian relaxation neural network (LRNN) optimization techniques. The convergence of LRNN for separable convex programming problems is established. For separable integer programming problems, LRNN is constructed to obtain near optimal solution in an efficient manner. When applying LRNN to separable job shop scheduling, a new neural dynamic programming method is developed to solve subproblems making innovative use of the dynamic programming structure. The synergy of Lagrangian relaxation and neural dynamic programming leads to a powerful neural optimization method for job shop scheduling. Testing results obtained by software simulation demonstrate that the performance is superior to what has been reported in the neural network literature. Results are also very close to what were obtained by a state-of-the-art optimization algorithm, and should be much improved when the method is refined and implemented in hardware.