Research and Application of Back Propagation Neural Network-Based Linear Constrained Optimization Method

Abstract

A back propagation (BP) neural network-based linear constrained optimization method(BPNN-LCOM) was proposed for to solve the problems in linear constraint black box in this paper,hoping to improve the shortcoming of BP neural network-based constrained optimization method (BPNN-COM). In view of minimizing the mathematic model of network output, the basic ideas of BPNN-LCOM wereilluminated,includingmodel design and training, and BP neural network-based global optimization. Firstly, the iteration step size was calculated by optimal step size, and the adjustment step size was calculated by interpolation method, also the iteration speed was accelerated. Secondly, the search direction that iteration point locates on the boundary offeasible region was determined by gradient projection method, which ensured that the iteration process continued along a feasible search direction, and effectively solved the defect of BPNN-COM that sometimes fails to find thetrue optimal solutions. At the same time, the iteration step size along the gradient projection direction was calculated by the optimal constraint step size, which ensured the new iteration point located in the feasible region. Thirdly, the Kuhn-Tucker conditions were introduced to verify whether the iteration point is theoptimization solution that locates on the boundary of feasible region, and it made the termination criterion perfect for BPNN-LCOM.The computation results of two examples showed the effectiveness and feasibility of BPNN-LCOM. The BPNN-LOCM was used to optimize the roller-type bailing mechanism,and the optimal parameters were obtained as follows: round disc diameter was 360 mm, rotationalspeed of the steel rollerwas 250 rpm, feeding quantity was1.7 kg/s, and length-width ratio was 0.8. The corresponding minimum power consumption was 45.8 kJ/bundle. The optimization results were superior to regression analysis and BPNN-COM.The verification test was carried out and the optimization results could improve roller-type bailing mechanism. Verification results showed that the BPNN-LCOM is a feasible method for solving problems in linear constraint black box.

Keywords

• BP neural network
• optimization method
• linear constraint
• gradient projection method