<p>Traditional construction project management has long emphasized the equilibrium between time and cost, acknowledging their indispensable role in achieving favorable project outcomes. Stochastic optimization algorithms have become increasingly valuable in addressing this challenge. The moth-flame optimization (MFO) algorithm is distinguished by its ability to solve challenging problems with constrained and unknown solution spaces. When integrated with the roulette wheel selection strategy, which prioritizes diversity preservation and convergence regulation by allocating probabilities based on fitness, the MFO algorithm exhibits considerable potential and effectiveness in solving intricate, especially discrete, problems. This study presents an upgraded MFO model, termed rMFO, as a novel framework for addressing time–cost trade-off problems (TCTPs) in construction projects. The performance evaluation of rMFO entailed the utilization of three benchmark test problems, involving a single case study comprising 18 activities and two additional studies featuring 63 activities. The findings indicate that rMFO surpasses other methods in managing TCTPs, highlighting its effectiveness and applicability. These results underscore the importance of the rMFO within construction project management, indicating its value as an essential tool for project managers.</p>