Concomitant reduction of cost and duration is recognized as one of the main aspects of construction planning. Expedition of project schedule naturally incurs extra costs due to implementation of more productive and/or high-price construction techniques. Meanwhile, a reduction in time is usually plausible only down to a certain limit, below which renders expeditions either technically or financially unviable. Thus, striking a reasonable balance between project cost and duration remains a desirable yet challenging task for which there has been a myriad of advancements and literature. Despite the many studies associated with this problemreferred to as time-cost trade-off problem (TCTP)it is observed that only a few exercise TCT problems with the generalized logical relationships. This observation holds despite the fact that generalized precedence relationships are imperative to introduce parallelism and to secure a realistic overlap among the activities. In this regard, a Simulated Annealing-based Genetic Algorithm (GA) as proposed herein, is specifically designed to provide the capability of exerting TCTPs with properly overlapped activities. Efficiency of this algorithm is tested over a range of problems and its performance is validated over a large-scale real-case construction project. Results of the hybridized GA indicate fast and robust convergence to high-quality solutions.