Schedulers can compress the schedule of construction projects by overlapping design and construction activities. However, overlapping may induce increased total cost with the decrease of duration. To solve the concurrency-based time-cost tradeoff problem effectively, this paper demonstrates an overlapping optimization algorithm that identifies an optimal overlapping strategy with exact overlap rates and generates the required duration at the minimum cost. The method makes use of overlapping strategy matrix (OSM) to illustrate the dependency relationships between activities. This method then optimizes the genetic algorithm (GA) to compute an overlapping strategy with exact overlap rates by means of overlapping and crashing. This paper then proposes an integrated framework of genetic algorithm and building information modeling (BIM) to prove the practice feasibility of theoretical research. The study is valuable to practitioners because the method allows establishing a compressed schedule which meets the limited budget within the contract duration. This article is also significant to researchers because it can compute the optimal scheduling strategy with exact overlap rates, crashing degree, and resources expeditiously. The usability and validity of the optimized method are verified by a test case in this paper.