An SQP Algorithm for Structural Topology Optimization Based on Majorization–Minimization Method

When applying the sequential quadratic programming (SQP) algorithm to topology optimization, using the quasi-Newton methods or calculating the Hessian matrix directly will result in a considerable amount of calculation, making it computationally infeasible when the number of optimization variables i...

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Bibliographic Details
Published in:Applied sciences Vol. 12; no. 13; p. 6304
Main Authors: Liao, Weilong, Zhang, Qiliang, Meng, Huanli
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.07.2022
Subjects:
Algorithms
Approximation
Compliance
Hessian matrix
Linear programming
majorization–minimization
Methods
Optimization
sequential quadratic programming
topology optimization
Variables
ISSN:2076-3417, 2076-3417
Online Access:Get full text
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Summary:When applying the sequential quadratic programming (SQP) algorithm to topology optimization, using the quasi-Newton methods or calculating the Hessian matrix directly will result in a considerable amount of calculation, making it computationally infeasible when the number of optimization variables is large. To solve the above problems, this paper creatively proposes a method for calculating the approximate Hessian matrix for structural topology optimization with minimum compliance problems. Then, the second-order Taylor expansion transforms the original problem into a series of separable and easy-to-solve convex quadratic programming (QP) subproblems. Finally, the quadratic programming optimality criteria (QPOC) method and the QP solver of MATLAB are used to solve the subproblems. Compared with other sequential quadratic programming methods, the advantage of the proposed method is that the Hessian matrix is diagonally positive definite and its calculation is simple. Numerical experiments on an MBB beam and cantilever beam verify the feasibility and efficiency of the proposed method.
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ISSN:2076-3417
2076-3417
DOI:10.3390/app12136304