<p>Resource Constrained Project Scheduling Problem (RCPSP) is among the most well-known problems in the field of project management and the reason is twofold: First, the problem is of wide variety, and second, due to its NP-Hardness, scholars have been looking for more efficient methods to tackle it. In this paper, we present a bi-objective mathematical model for the RCPSP that incorporates both makespan and cost objectives under General Precedence Relations (GPR). Furthermore, we evaluate the performance of four meta-heuristic methods, namely Non-Dominated Sorting Genetic Algorithm III (NSGA-III), Non-dominated Ranked Genetic Algorithm (NRGA), Strength Pareto Evolutionary Algorithm II (SPEA-II), and Pareto Envelope-based Selection Algorithm II (PESA-II) algorithms, combined with three heuristic methods, on a set of benchmark problems from the Program Specification Block Library (PSBLIB). The meta-heuristic methods are further evaluated by comparing to the Augmented Epsilon Constraint (AEC) method. The results indicate AEC algorithm outperformed PESA-II algorithm regarding one of the utilized metrics. Regarding the remaining metrics, the hypothesis testing on mean equality showed that there is no significant statistical difference in the performance of the algorithms. Finally, to highlight the novelty of our study, we emphasize that our approach integrates a bi-objective optimization framework with GPR in the RCPSP, a combination that has been underexplored in existing literature. Additionally, we employ a comprehensive evaluation using multiple performance metrics and rigorous statistical analysis, providing a robust comparison between metaheuristic algorithms and exact methods. This comprehensive methodology offers valuable insights into the effectiveness of different solution strategies for complex scheduling problems.</p>