Comprehensive Evaluation of METHoD-NO for Benchmark Optimization and Neural Network Training

Metaheuristic optimization algorithms are widely used for solving complex global optimization problems due to their flexibility, derivative-free search mechanisms, and effectiveness in nonlinear search spaces. In this study, the performance of the recently proposed METHoD-NO optimizer is comprehensively investigated on both numerical benchmark problems and artificial neural network training tasks. METHoD-NO is a robust statistics-inspired metaheuristic algorithm whose search mechanism is organized into three complementary phases to achieve a balanced exploration–exploitation process. In the central tendency phase, the search is guided by robust location measures so that the population can be directed toward promising regions while reducing sensitivity to extreme or misleading candidate solutions. In the Harrell–Davis phase, the algorithm benefits from the Harrell–Davis quantile estimator, which estimates quantiles as weighted combinations of order statistics and thereby provides a smoother and more informative characterization of the population distribution [1]. In the Navruz–Özdemir quantile estimator phase, an alternative quantile-based learning mechanism is employed to refine the search dynamics and strengthen the algorithm’s ability to adapt to the underlying distributional structure of candidate solutions [2]. By combining these three phases, METHoD-NO aims to preserve population diversity, enhance stability, and maintain effective search performance over complicated optimization landscapes. In the first part of the study, the global optimization capability of METHoD-NO is evaluated using 23 classical benchmark functions together with the CEC 2017 and CEC 2022 test suites. These benchmark sets include unimodal, multimodal, hybrid, and composition functions with varying difficulty levels and therefore provide a comprehensive basis for performance assessment. The results obtained by METHoD-NO are compared with those of well-known metaheuristic algorithms in terms of solution quality, convergence behavior, and robustness. In addition, the statistical significance of the observed differences is examined using the Wilcoxon rank-sum test, providing a more reliable basis for pairwise algorithm comparisons. In the second part of the study, the applicability of METHoD-NO to data-driven learning problems is examined through artificial neural network training. In this framework, METHoD-NO is employed to optimize the weights and biases of feed-forward neural networks, and its performance is compared with competing metaheuristic methods on both regression and classification datasets. Since neural network training often involves highly nonlinear and multimodal error surfaces, it is an appropriate test bed for evaluating the search capability of metaheuristic optimizers. The findings are expected to show that METHoD-NO provides competitive and stable performance not only for numerical global optimization problems but also for artificial neural network training tasks.

Keywords:
METHoD-NO, Metaheuristic optimization, Global optimization, Benchmark functions, Artificial neural networks, Wilcoxon test