Cause of significant Lempel–Ziv complexity increases in Differential Evolution

Determine whether the significant increases of joint Lempel–Ziv complexity observed in some iterations of Differential Evolution during optimization of the 10-dimensional Rastrigin function are caused by the population discovering several optima of equal quality and randomly switching among them.

Background

The paper analyzes phase-like transitions in swarm optimization algorithms—Particle Swarm Optimization (PSO), Differential Evolution (DE), and Self-Organizing Migrating Algorithm (SOMA)—using recurrence quantification analysis and joint Lempel–Ziv complexity (LZC). The setting includes optimizing the 10-dimensional Rastrigin function with population sizes between 40 and 100 and algorithm-specific hyperparameters tuned via random search.

While PSO and SOMA exhibited predictable relationships between convergence and the dynamics of complexity measures, DE showed instances where LZC increased significantly during some runs. The authors explicitly state that the reason for these increases remains unclear and hypothesize that they may occur when the population identifies multiple optima of equal quality and randomly switches among them. Clarifying the mechanism would refine the interpretation of complexity indicators in DE and improve understanding of its convergence dynamics.