Approximated and neural network assisted quadratic programming and its applications in structural topology optimization

Abstract

In this article, we present approximated and Neural Network assisted Quadratic Programming (NNaQP) methods to accelerate the solution process for solving the constrained and unconstrained optimization problems using gradient and Hessian matrix of objective function. Firstly, three schemes are presented for the approximation of diagonalizing inversed Hessian matrix; Secondly, the NNaQP method is presented by using the gradient online learning and prediction (GoLap) to learn and predict gradient and approximated inverted Hessian matrix. Several scaling and restoration schemes for GoLap are also proposed. The combination of NNaQP and the three approximation schemes of inversed Hessian matrix reduces the number of routine iterations involving complex derivative computing and thus decreases the total computational time. Thirdly, the three approximation schemes of the Hessian and the NNaQP are used to solve structural topology optimization problems. The performance and the benefits of approximated quadratic programming and NNaQP, in terms of prediction accuracy and the computational efficiency, are demonstrated by numerical results of solving one unconstrained minimization problem, and one 2D and one 3D minimum compliance topology optimization problems. For the selected structural topology optimization problems, the total computational timesaving can reach up to 98 %.