Off-site construction is a modern construction method that brings many sustainability merits to the built environment. However, the sub-optimal planning decisions (e.g., resource allocation, logistics and overtime planning decisions) of off-site construction projects can easily wipe away their sustainability merits. Therefore, simulation modelling—an efficient tool to consider the complexity and uncertainty of these projects—is integrated with metaheuristics, developing a simulation-optimization model to find the best possible planning decisions. Recent swarm intelligence metaheuristics have been used to solve various complex optimization problems. However, their potential for solving the simulation-optimization problems of construction projects has not been investigated. This research contributes by investigating the status-quo of simulation-optimization models in the construction field and comparing the performance of five recent swarm intelligence metaheuristics to solve the stochastic time–cost trade-off problem with the aid of parallel computing and a variance reduction technique to reduce the computation time. These five metaheuristics include the firefly algorithm, grey wolf optimization, the whale optimization algorithm, the salp swarm algorithm, and one improved version of the well-known bat algorithm. The literature analysis of the simulation-optimization models in the construction field shows that: (1) discrete-event simulation is the most-used simulation method in these models, (2) most studies applied genetic algorithms, and (3) very few studies used computation time reduction techniques, although the simulation-optimization models are computationally expensive. The five selected swarm intelligence metaheuristics were applied to a case study of a bridge deck construction project using the off-site construction method. The results further show that grey wolf optimization and the improved bat algorithm are superior to the firefly, whale optimization, and salp swarm algorithms in terms of the obtained solutions’ quality and convergence behaviour. Finally, the use of parallel computing and a variance reduction technique reduces the average computation time of the simulation-optimization models by about 87.0%. This study is a step towards the optimum planning of off-site construction projects in order to maintain their sustainability advantages.