CQSGA: A Chaotic and Quantum-Enhanced Snow Geese Algorithm for Complex Optimisation Problems

Abstract

This paper presents CQSGA, an enhanced Snow Geese Algorithm that fundamentally differs from existing chaos-enhanced or quantum-inspired methods by synergistically embedding an Exponential Discrete Memristor chaotic map and a quantum rotation gate into SGA's innate dual-phase structure. Unlike approaches that merely inject chaotic perturbations or adopt simplistic qubit encoding, CQSGA leverages the EDM system's superior ergodicity and Lyapunov properties for global exploration, while the quantum rotation gate utilises superposition-driven rotational updates to enable intelligent directional local exploitation. Both 
mechanisms execute in alternating periodic phases to achieve dynamic exploration-exploitation balance. Rigorous statistical validation via Friedman test (p < 0.001) and Nemenyi post-hoc analysis (α = 0.05) across 30 independent runs confirms that CQSGA achieves statistically significant improvements over the 14 compared algorithms on the majority of test functions, with competitive performance observed on the remaining cases. CQSGA is further applied to Physics-Informed Neural Network architecture search for solving Burgers equation, achieving sub-millesimal loss (9.9873e-4) and demonstrating superior practical efficacy