A Review of 315 Benchmark and Test Functions for Machine Learning Optimization Algorithms and Metaheuristics with Mathematical and Visual Descriptions

In the rapidly evolving optimization and metaheuristics domains, the efficacy of algorithms is crucially determined by the benchmark (test) functions. While several functions have been developed and derived over the past decades, little information is available on the mathematical and visual description, range of suitability, and applications of many such functions. To bridge this knowledge gap, this review provides an exhaustive survey of more than 300 benchmark functions used in the evaluation of optimization and metaheuristics algorithms. This review first catalogs benchmark and test functions based on their characteristics, complexity, properties, visuals, and domain implications to offer a wide view that aids in selecting appropriate benchmarks for various algorithmic challenges. This review also lists the 25 most commonly used functions in the open literature and proposes two new, highly dimensional, dynamic and challenging functions that could be used for testing new algorithms. Finally, this review identifies gaps in current benchmarking practices and suggests directions for future research.