In this paper, four new adaptive weight formulations are developed to enhance the performance of traditional Modified Adaptive Weight Approach (MAWA), which is the simplest way for solving the multi-objective optimization of discrete time-cost trade-off problem (DTCTP). Several numerical experiments are conducted to validate the newly proposed formulations. In addition, three meta-heuristic-based optimization algorithms are utilized to examine the variations within the results of the test instances. The proposed model provides several ways to solve DTCTP, as it includes different formulations and optimization algorithms. So, this model performs well for the medium and large-scale time-cost optimization problems on contrary to the traditional MAWA.