<p>The Modified Adaptive Weight Approach (MAWA) is a widely used and relatively straightforward method for addressing time–cost optimization problems, which are typically formulated as multi-objective optimization tasks. Metaheuristic algorithms are particularly effective for these problems since they iteratively refine a randomly generated population of candidate solutions. However, a noted drawback of the standard MAWA is its assignment of uniform weight factors to all solutions, without considering their individual fitness or distribution in the search space. To overcome this limitation, this study introduces a novel multi-objective framework that integrates the Rao-2 algorithm with MAWA, yielding a set of Pareto-optimal solutions. The performance of this hybrid MAWA–Rao-2 model was evaluated using benchmark construction project case studies from the literature, each consisting of 146 activities. The obtained results were compared with Hybrid heuristic meta-heuristic (HHMH), non-dominated sorting TLBO, non-dominated sorting Aquila optimizer, non-dominated sorting AOA reported in the literature. Findings demonstrate that the MAWA–Rao-2 algorithm serves as a robust and efficient approach for solving time–cost trade-off problems (TCTP) in construction engineering and management.</p>