Robust design optimization with mathematical programming neural networks

Traditional neural networks involve the training in order to design the layers and neurons and to train the network to find the weights for the neurons such that the difference between the predicted output and the practical output is minimized. The Mathematical Programming Neural Network (MPNN), on the other hand, has a dynamic equation for solving the optimization problem, does not involve training, and therefore, it takes less amount for computations. In this paper, several MPNN models are surveyed, and new MPNN models have been developed and applied to design optimization problems in mechanical motion synthesis and structural design. The MPNN algorithms for unconstrained optimization were developed first. Then, in conjunction with the Augmented Lagrange Multiplier method, new algorithms have been developed for constrained optimization. Compared to the traditional mathematical programming methods, the MPNN algorithms are robust and can have global convergence properties. The numerical examples show that the proposed MPNN algorithms can solve highly nonlinear design optimization problems of mechanical and structural design.