Newton Downhill Optimizer for Global Optimization

The study presents the Newton's Downhill Optimizer (NDO), a novel metaheuristic algorithm designed to address the challenges of complex, high-dimensional, and nonlinear optimization problems. Mathematical-Based Algorithms (MBAs) are a category of algorithms designed based on mathematical principles. They are widely applied in numerical computation, symbolic manipulation, geometric processing, optimization problems, and probabilistic statistics, offering efficient and precise solutions to complex problems. Inspired by Newton's Method, NDO combines its precision with a downhill strategy based on stochastic processes, specifically designed to address real-world applications and benchmark problems. NDO combines the precision of Newton's method with a downhill strategy inspired by stochastic processes, enhancing the capability of exploring the solution space and escaping local optima. In benchmark tests, NDO demonstrated exceptional performance, surpassing the majority of competing algorithms in multiple test suites of CEC 2017 and CEC 2022. We conducted a comprehensive comparison of NDO against 14 well-established optimization algorithms. These include mathematical-based approaches such as AOA, SCHO, SCA, SABO, NRBO, and RUN. We also compared it with classical algorithms like CMA-ES, ABC, DE, and PSO. Additionally, we included advanced and recently published algorithms such as WSO, EHO, FDB_AGDEand GQPSO. The results demonstrate that NDO outperforms most of these algorithms. It exhibits superior convergence speed and remarkable stability.In engineering applications, NDO outperformed other algorithms in the speed reducer design task and step-cone pulley task and delivered outstanding results in multiple disk clutch brake design tasks. A significant contribution of the study is the application of NDO to breast cancer feature selection, tested on two Breast cancer datasets. The NDO demonstrated outstanding performance in accuracy, sensitivity, specificity, and the Matthews Correlation Coefficient (MCC), achieving superior accuracy across two datasets. This underscores its potential as a viable tool for addressing complex challenges in both engineering and medical fields. The source codes of NDO algorithm will be shared at https://github.com/oykc1234/NDO.