Code for Exponential-Trigonometric Optimization algorithm

Exponential-Trigonometric Optimization (ETO) algorithm

The Exponential-Trigonometric Optimization (ETO) algorithm, proposed by members of the Center for Engineering Application and Technology Solutions at Ho Chi Minh City Open University, Vietnam, is a novel optimization method developed through an advanced integration of exponential and trigonometric functions. The algorithm is designed to effectively balance the two essential phases of optimization: exploration and exploitation—an ongoing challenge in the field of meta-heuristic optimization. By incorporating additional random and adaptive variables, ETO enhances search capability and overall performance compared to existing algorithms.

The effectiveness and robustness of the proposed method were validated through three phases of evaluation. In the first phase, ETO was compared with seven well-known meta-heuristic algorithms—SCHO, SCA, AOA, GWO, HHO, HGS, and GJO—using 23 classical benchmark functions of varying dimensions. These functions were categorized into three groups: unimodal functions (F1–F7), multimodal functions (F8–F13), and fixed-dimension functions (F14–F23).

In the second phase, ETO was further assessed on the CEC2019 and CEC2020 benchmark suites and compared with the same seven algorithms to evaluate its competitive performance. Finally, the algorithm was tested on the CEC2017 benchmark functions with dimensions of 10, 30, and 50, and its results were statistically compared with advanced algorithms such as SHADE, LSHADE, and JADE using the Wilcoxon rank-sum test.

Link to the published paper: https://doi.org/10.1016/j.cma.2024.117411