Constraint Satisfaction Problems (CSP) belong to a kind of traditional NP-hard problems with a high impact on both research and industrial domains. The goal of these problems is to find a feasible assignment for a group of variables where a set of imposed restrictions is satisfied. This family of NP-hard problems demands a huge amount of computational resources even for their simplest cases. For this reason, different heuristic methods have been studied so far in order to discover feasible solutions at an affordable complexity level. This paper elaborates on the application of Ant Colony Optimization (ACO) algorithms with a novel CSP-graph based model to solve Resource-Constrained Project Scheduling Problems (RCPSP). The main drawback of this ACO-based model is related to the high number of pheromones created in the system. To overcome this issue we propose two adaptive Oblivion Rate heuristics to control the number of pheromones: the first one, called Dynamic Oblivion Rate, takes into account the overall number of pheromones produced in the system, whereas the second one inspires from the recently contributed Coral Reef Optimization (CRO) solver. A thorough experimental analysis has been carried out using the public PSPLIB library, and the obtained results have been compared to those of the most relevant contributions from the related literature. The performed experiments reveal that the Oblivion Rate heuristic removes at least 79% of the pheromones in the system, whereas the ACO algorithm renders statistically better results than other algorithmic counterparts from the literature.