Generalized Quadratic Interpolation （GQI）

Generalized Quadratic Interpolation (GQI): a new selection method for optimization

When solving a minimization problem for a univariate function, the traditional quadratic interpolation method do not always guarantee obtaining the minimum value of the interpolation polynomial for three points. It has certain requirements for the three points that constitute the interpolation polynomial. However, the generalized quadratic interpolation (GQI) method can overcome this limitation by obtaining the minimum value of the interpolation polynomial formed by any three points. This method is simple and easy to implement, therefore, as a new operator, it can conveniently be integrated into various optimization algorithms to enhance their optimization capabilities.

The codes include: (1) a demo of the GQI method for minimization; (2) a simple example where the GQI method is integrated into WOA.

W. Zhao, L. Wang, Z. Zhang, S. Mirjalili, N. Khodadadi, Q. Ge, Quadratic Interpolation Optimization (QIO): A new optimization algorithm based on generalized quadratic interpolation and its applications to real-world engineering problems, Computer Methods in Applied Mechanics and Engineering (2023) 116446, https://doi.org/10.1016/j.cma.2023.116446.

The code of QIO can be found here: https://ww2.mathworks.cn/matlabcentral/fileexchange/135627-quadratic-interpolation-optimization-qio?s_tid=srchtitle

The free download of paper (before November 17, 2023) is available at:https://authors.elsevier.com/a/1hqpHAQEJ1Ki8