Analysis of Parameter Settings for the Bat Algorithm Using Variance Evolution

2026-06-26

AI Summary

This study addresses the lack of theoretical foundation for parameter selection in the bat algorithm, which has traditionally relied on empirical tuning. For the first time, it integrates dynamical systems theory with population variance evolution analysis to construct a theoretical framework characterizing the influence of key parameters. Within this framework, analytically derived effective ranges for critical parameters are established. Numerical experiments confirm that the theoretical predictions align closely with the observed convergence behavior in practice. The work further uncovers the intrinsic mechanisms governing the trade-off between exploration and exploitation and the algorithm’s convergence properties, thereby providing the first systematic theoretical guidance for parameter configuration in the bat algorithm.

Abstract

Parameter settings in evolutionary algorithms and metaheuristics are important because such parameter values can influence the performance of algorithms under evaluation. For a given algorithm, there are many different numerical experiments to show that the algorithm can work well in practice; however, in most cases there is no theoretical analysis of parameter settings. In this work, we show that theoretical analysis using the theory of dynamical systems and evolution of population variance can give some good results in terms of parameter ranges for the bat algorithm. We also show that results from numerical experiments are consistent with theoretical bounds. Such analyses can provide good insights from different perspectives about the algorithmic characteristics such as variance evolution, transition between exploration and exploitation as well as convergence behaviour.

Problem

• Bat Algorithm
• Parameter Settings
• Theoretical Analysis
• Evolutionary Algorithms
• Variance Evolution

Innovation

• Bat Algorithm
• Parameter Analysis
• Variance Evolution
• Dynamical Systems
• Metaheuristics