Quadratic Interpolation Optimization (QIO): A new optimization algorithm based on generalized quadratic interpolation and its applications to real-world engineering problems

Abstract

An original math-inspired meta-heuristic algorithm, named quadratic interpolation optimization (QIO), is proposed to address numerical optimization and engineering issues. The main inspiration behind QIO is derived from mathematics, specifically the newly proposed generalized quadratic interpolation (GQI) method. This method overcomes the limitations of the traditional quadratic interpolation method to better find the minimizer of the quadratic function formed by any three points. The QIO utilizes the GQI method as a promising searching mechanism for tackling various types of optimization problems. This searching mechanism delivers exploration and exploitation strategies, in which the minimizer provided by the GQI method assists the QIO algorithm in exploring a promising region in unexplored areas and exploit the optimal solutions in promising regions. To evaluate QIO’s effectiveness, it is comprehensively compared with 12 other commonly used optimizers on 23 benchmark test functions and the CEC-2014 test suite. Ten engineering problems are also tested to assess QIO’s practicality. Eventually, a real-world application of QIO is presented in the operation management of a microgrid with an energy storage system. The results demonstrate that QIO is a promising alternative for addressing practical challenges. The source code of QIO is publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/135627-quadratic-interpolation-optimization-qio.