Freeform shell structures, with their unique geometric forms and excellent structural properties, have become an important development direction in modern architecture. However, the complexity of their design and the requirements for construction accuracy make it difficult for traditional construction management models to meet actual needs. To solve this problem, this paper proposes a construction management method for freeform shell structures that combines BIM (building information modeling) technology with optimization algorithms. By constructing an integrated BIM model, the visualization design, precise construction monitoring and multi-dimensional data integration of freeform shell structures can be realized. At the same time, genetic algorithms and ant colony algorithms are introduced to make intelligent decisions on construction path optimization, resource allocation and scheduling, and construction progress control. The research results show that this method can significantly improve construction efficiency, reduce construction costs, and effectively improve construction quality and accuracy. This paper also discusses the challenges and improvement directions in the combined application of BIM technology and algorithms, providing an important reference for the digital and intelligent development of complex building construction management.