Clarifying and Standardizing the Lévy Flight in Scientific Computing

The Lévy flight is a fundamental stochastic model widely utilized across various domains, including engineering optimization and biological foraging. However, the current literature reveals notable inconsistencies in its definition, parameter interpretation, and algorithmic implementation, which compromise the reliability and reproducibility of empirical findings. To address these issues, this paper proposes a unified framework derived from a systematic review and critical analysis of existing studies. The framework standardizes the core definition, clarifies the roles of key parameters, and establishes a consistent computational paradigm, thereby resolving ambiguities and enhancing the consistency, reliability, and cross-study comparability of Lévy flight applications in scientific computing. Additionally, a targeted analysis examines the influence of the Lévy index, demonstrating how its variation systematically affects both the global scale and local behavior of the flights. This analysis provides a practical guidance for selecting appropriate Lévy index values for specific application contexts. Overall, this work provides a comprehensive and actionable reference to strengthen the methodological rigor and coherence of research involving Lévy flight models.