Uncovering structural bias in population-based optimization algorithms: A theoretical and simulation-based analysis of the Generalized Signature Test

Abstract

Population-based optimization algorithms are popular tools for optimization, influenced by two interactive factors: landscape bias, which guides the population toward better objective function values, and structural bias, which directs the population to a specific location in the search domain. Structural bias can impede the exploration of algorithms, compelling the population to revisit a particular area of the search domain, which leads to increased computing costs without yielding any new information. In this study, we present a comprehensive survey of structural bias. Identifying this bias in a general algorithm is challenging. We propose the ‘Generalized Signature Test’ as a methodology to detect and analyze the structural bias in population-based optimization algorithms. Numerical simulations are performed using six well-known metaheuristic algorithms: Genetic Algorithm, Differential Evolution, Particle Swarm Optimization, Grey Wolf Optimizer, Whale Optimization Algorithm, and Harris Hawks Optimization. Experimental results suggest that Differential Evolution displays the least bias toward the center of the search domain, whereas the Harris Hawks Optimization exhibits a significant axial-diagonal bias toward the origin. Our findings indicate that the proposed method is both efficient and straightforward for assessing algorithmic structural bias. The Generalized Signature Test provides an in-depth analysis and understanding of biases, tailor-made for thorough bias behavior investigations. The Generalized Signature Test can identify bias in established algorithms and evaluate bias in emerging algorithms at their early development stages.