Abstract
In structural optimization design, obtaining the optimal solution of the objective function is the key to optimal design, and one-dimensional search is one of the important methods for function optimization. The Golden Section method is the main method of one-dimensional search, which has better convergence and stability. Based on the solution of the Golden Section method, this paper proposes an efficient one-dimensional search algorithm, which has the advantages of fast convergence and good stability. An objective function calculation formula is introduced to compare and analyse this method with the Golden Section method, Newton method, and Fibonacci method. It is concluded that when the accuracy is set to 0.1, the new algorithm needs 3 iterations to obtain the target value. The Golden Section method takes 11 iterations, and the Fibonacci method requires 11 iterations. The Newton method cannot obtain the target value. When the accuracy is set to 0.01, the number of iterations of the new method is still the least. The optimized design of the T-section beam is introduced for engineering application research. When the accuracy is set to 0.1, the new method needs 3 iterations to obtain the target value and the Golden Section method requires 13 iterations. When the accuracy is set to 0.01, the new method requires 4 iterations and the Golden Section method requires 18 iterations. The new method has significant advantages in the one-dimensional search optimization problem.
Highlights
Optimization problems often appear in the fields of engineering and scientific research
Abbasi et al [2] designed an improved Harris hawks (HHO) optimization algorithm to optimize the design of tapered roller bearings (TRB)
A method of boarding gate allocation based on IPOQEA is proposed, and the effectiveness of the proposed method is verified by the actual operation data of Baiyun Airport [6]
Summary
Optimization problems often appear in the fields of engineering and scientific research. Liu [12] used the method of structural optimization to determine the section height of reinforced concrete beams and changed the traditional iterative calculation method of determining the beam height,so that the beam height was optimized to simplify the design and reduce the project cost. Shi et al [19] applied the Golden Section one-dimensional search method to unconstrained multivariate optimization problem solving, compared it with Newton’s method and damped Newton’s method, and proved that the Golden Section algorithm is effective and practical. Zhang and Chen [22] believe that the Golden Section method is represented by the division method This type of method has global convergence, it does not use the properties of the function. Erefore, a midpoint method was proposed to increase the shortening rate to 51%. is paper proposes a new onedimensional search algorithm based on the iterative algorithm of the Golden Section method (Algorithm 1)
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