Aerospace Instrument-Making Annotation << Back Enhanced Genetic Algorithm with GuaranteedGlobal Convergence: Theoretical Foundationand Experimental Verification He Bin, Neusypin K.A., Wang Zhong, Chen Hao The issue of premature convergence in a simple genetic algorithm (SGA) when optimizing multimodal functions is associated with its tendency to become trapped in local minima and its low search efficiency. To address these shortcomings, an improved genetic algorithm (IGA) is proposed, combining dynamic parental similarity control, adaptive mutation, and elitist preservation. First, crossover parents are selected using a dynamic similarity threshold to avoid excessive gene homogenization and enhance population diversity. Second, an adaptive mutation probability model is developed based on the population diversity index and the number of generations of evolutionary stagnation to balance global exploration and local exploitation capabilities. Finally, an optimal individual preservation mechanism is introduced to ensure algorithm convergence. At the theoretical level, a Markov chain model is used to prove that the enhanced algorithm converges to the global optimal solution with probability 1, and the mechanism for improving its efficiency is explained through dynamic equations of expected fi rst-passage time algebra and population information entropy. Experiments on the 10-dimensional Rastrigin function confirm that the standard deviation of IGA results (7.15) is 98.73 % lower than that of SGA (561.35). Keywords: Genetic algorithm, adaptive mutation, convergence, population diversity. DOI: 10.25791/aviakosmos.8.2025.1499 Pp. 37-48.