With the continuous development of computer information technology, its influence in various fields is increasing, especially in algorithmic dynamic systems, special computer algorithms can be used to improve calculation accuracy and efficiency, and improve working methods. With the rapid development of science and technology, especially the rapid development of various network technologies, the shortest path problem is increasingly used in various technologies, such as urban transportation planning, network routing, project planning, artificial intelligence games, etc. Nowadays, many new algorithms are gradually developed, the representatives of these new algorithms are genetic algorithms and recursive algorithms. In order to prove the superiority of genetic algorithms in solving the shortest path problem in dynamic weight systems, this article analyzes recursive algorithms and genetic algorithms based on dynamic systems based on computational algorithms, studies two cases of bus planning model based on multi-objective optimization and genetic algorithm and aircraft height optimization based on recursive algorithm. The research results show that the bus dispatch model based on multi-objective optimization and genetic algorithm can find the optimal bus dispatch plan through the algorithm in only 32 s; the recursive algorithm can optimize the green trajectory of aircraft high-altitude flight, reducing the total cost by 9.08%.