Time–Cost Tradeoff Problems (TCTPs) represent a critical class of multiobjective optimization challenges in construction project management, requiring the simultaneous minimization of project duration and total cost. To address these conflicting objectives more efficiently, this study proposes a novel hybrid multiobjective optimization framework, termed Oppositional Modified Adaptive Weight Arithmetic Optimization Algorithm (Oppositional MAWA-AOA). The main novelty of the proposed approach lies in the first integration of Opposition-Based Learning (OBL) within the MAWA-AOA framework, where OBL is applied exclusively during the iteration-level updating phase to enhance exploration and maintain population diversity. The MAWA mechanism dynamically adjusts the relative importance of time and cost objectives throughout the search process, enabling adaptive traversal of different regions of the Pareto-optimal front. The performance of the proposed algorithm is evaluated using three benchmark construction project networks comprising 63, 81, and 146 activities. The results demonstrate that Oppositional MAWA-AOA consistently produces high-quality and well-distributed Pareto-optimal solutions with strong convergence characteristics. In terms of solution quality, the proposed method achieves competitive hypervolume (HV) values across all cases and attains the highest HV value of 0.650 for the medium-scale 146-activity project, highlighting its effectiveness in handling complex optimization landscapes. Furthermore, Oppositional MAWA-AOA exhibits exceptional computational efficiency, achieving a reduction of up to 99.27% in the number of function evaluations (NFE) compared with the hybrid heuristic metaheuristic (HHMH). Comparative analyses against established multiobjective algorithms, including NDSII-TLBO, NDSII-PSO, Aquila Optimizer, Hybrid Genetic Algorithm, and NDS-AOA, confirm the robustness and scalability of the proposed approach. Overall, the results indicate that integrating OBL with MAWA-AOA significantly enhances performance for medium-scale TCTPs, offering a practical and efficient decision-support tool for construction project scheduling.