Stochastic Risk-Aware Time–Cost Optimization of Construction Schedules Using a Hybrid GA–GWO Algorithm with Integer Crash-Day Decisions

Construction schedule compression requires balancing project-duration reduction against direct, indirect, and risk-related cost increases under uncertain activity performance. Many construction time–cost trade-off models still rely on deterministic durations or predefined execution modes, which limits their ability to represent practical activity-level crashing decisions under uncertainty. This study develops a stochastic risk-aware time–cost optimization framework for construction scheduling using bounded integer crash-day decision variables. Activity durations are represented using triangular distributions based on optimistic, most-likely, and pessimistic estimates, while Monte Carlo simulation is used to propagate uncertainty through the precedence network. Expected and Conditional Value-at-Risk-oriented indicators are integrated into risk-adjusted duration and cost measures, which are then combined through a nonlinear normalized objective function. A Hybrid Genetic Algorithm–Gray Wolf Optimizer is implemented to solve the resulting discrete stochastic optimization problem and is benchmarked against seven metaheuristic algorithms under identical evaluation conditions. The framework is demonstrated using a 30-activity construction project reconstructed from Microsoft Project data. The proposed Hybrid GA–GWO reduced the deterministic project duration from 895 to 699 working days and achieved the best descriptive objective performance across 30 independent runs. However, after Bonferroni correction, its differences from the Genetic Algorithm and MPGWO-DLL were not statistically significant, indicating that these methods remain competitive alternatives. Additional Monte Carlo convergence, tornado sensitivity, correlated-duration sensitivity, and computational-time analyses were added to evaluate the stability, parameter dependence, and practical applicability of the framework. The findings show that the proposed framework can support risk-aware construction schedule-crashing decisions by identifying activity-level acceleration plans while explicitly accounting for downside schedule and cost risk. Broader validation in larger and more diverse real-world projects remains necessary.