Investigating the Dynamical Behavior of Quantum Dynamics Framework Algorithm with the Rastrigin-like Test Benchmark

With the emergence of various optimization algorithms, studying the specific dynamic evolution process of algorithms is of significant importance for proposing new algorithms and optimizing classical ones. The Quantum Dynamics Framework(QDF) Optimization Algorithm is derived from the Taylor expansion of the Schrödinger equation, providing a rigorous mathematical and physical foundation. Its iterative behavior can reflect the generality of evolution in most optimization algorithms. However, the iteration process of QDF on the multi-modal Rastrigin function faces challenges in convergence, necessitating meticulous evaluation and research of test functions. Therefore, this paper constructs an adjustable, scalable, and diverse Rastrigin-like Test Benchmark (RTB) collection, extending, shifting, and rotating the Rastrigin function in multi-modal scenarios. By viewing the algorithm's iteration process from the perspective of quantum dynamics as the evolution of sampling particles over time, and utilizing RTB to delve into the dynamical behavior of QDF algorithm, this research approach effectively supports the observation and improvement of algorithmic iteration processes, providing fundamental guidance for algorithmic optimization decisions.