Modified Adaptive Weight Approach (MAWA) is one of the simplest methods used for solving time-cost optimization problems. This type of optimization problem, categorized as multi-objective optimization, can be solved with metaheuristic algorithms. Here, metaheuristic algorithms evaluate a randomly generated solution set, referred to as population, within the boundary condition of a solution space. The weight factor values determined by MAWA are applied to all solutions in the population without distinguishing the solutions in that population. However, the potential solutions in the population indicate different fitness properties concerning solution space. In this paper to solve time-cost optimization problems, new adaptive weight formulations are proposed. In contrast to MAWA, the novelty of this study's formulations is to adaptively detect the weight factor value, depending on the solution's fitness in the population. The results obtained from the numerical experiments examined in this study show that the proposed formulations can improve the performance of MAWA and can find identical or slightly different Pareto results for investigated multi-objective optimization problems.