With the development of economy, all world countries are entering the ranks of competitive sports. The Olympic Games or large-scale gymnastics performances are of great significance to the publicity and implementation of the national health plan. This paper aims to study the computer simulation algorithm of group gymnastics formation change path under artificial intelligence and network big data, so as to find out the path change algorithm of each team member, so that members in group gymnastics can clearly see their own moving route, and finally achieve the purpose of reducing the difficulty and cost of rehearsal. In this paper, the ellipse search algorithm and the traditional
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algorithm, the rectangle search algorithm, and the traditional
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algorithm are deeply compared and analyzed, and then, the experimental comparison between the ellipse search algorithm and the rectangle search algorithm is carried out. It is concluded that when finding the shortest path and when the straight-line distance between two nodes is 4.0 km, the time used by the rectangle search algorithm is 2.1 s, while the ellipse search algorithm needs 3.98 s. This shows that the rectangle search algorithm greatly saves the operation time and has superior performance.