Exponential-trigonometric optimization algorithm for solving complicated engineering problems

Abstract

This article presents an innovative optimization algorithm called the Exponential-Trigonometric Optimization (ETO) algorithm, which is based on a sophisticated combination of exponential and trigonometric functions. The ETO algorithm is structured to strike a balance between two important stages: exploration and exploitation, a challenge that many other optimization algorithms have also sought to address. ETO incorporates several additional random and adaptive variables, resulting in better performance compared to existing algorithms. The algorithm's performance and potential were validated through three phases of testing. First, the ETO algorithm is evaluated against seven other meta-heuristic algorithms, including SCHO, SCA, AOA, GWO, HHO, HGS, and GJO, using 23 classical benchmark functions of varying sizes. These benchmark functions are categorized into three main groups: "unimodal" (F1 to F7), "multi-modal" (F8 to F13), and "fixed-dimension" (F14 to F23). Next, the ETO algorithm was tested on CEC2019 and CEC2020 functions and compared with 7 algorithms mentioned above to evaluate performance. In addition, the ETO algorithm is tested on the CEC2017 benchmark functions with dimensions of 10-D, 30-D, and 50-D. It is then compared and evaluated against other potential algorithms, such as SHADE, LSHADE, and JADE, using the Wilcoxon rank-sum test. Finally, the ETO algorithm is utilized to tackle five intricate engineering problems to show its robustness, including optimizing the shape of aircraft wings to increase lift. These results have demonstrated the effectiveness and potential of the ETO algorithm, yielding outstanding results and ranking first among other algorithms. Notably, the optimization of the improved aircraft wing increased the lift force from 0.797055 to 0.951817, signaling promising prospects for advancing optimization problems in the future. Source codes of ETO is publicly available at https://ceats.ou.edu.vn/us/exponential-trigonometric-optimization-algorithm-.html.