Efficient test case generation is essential for ensuring software quality. Genetic algorithms offer a faster alternative to manual methods for creating test cases. However, traditional genetic algorithms can be slow due to crossover and mutation probabilities. This paper presents an improved genetic algorithm framework to address these limitations and accelerate test case generation. An elite genetic algorithm with an elitist retention strategy is proposed. A pseudocode is provided to illustrate the algorithm's steps. Experimental results show that the improved algorithm outperforms traditional and random methods in terms of speed and iteration count, offering valuable insights for future software testing research. The demonstrated superiority of elite genetic algorithms in this new approach, combined with the shared knowledge of automation tools and scripting languages, has the potential to significantly advance software testing methodologies and contribute to overall enhancements in software quality.