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The multimode resource-constrained project-scheduling problem with discounted cash flows (MRCPSPDCF) is important and challenging for project management. As the problem is strongly nondeterministic polynomial-time hard, only a few algorithms exist and the performance is still not satisfying. To design an effective algorithm for the MRCPSPDCF, this paper proposes an ant colony optimization (ACO) approach. ACO is promising for the MRCPSPDCF due to the following three reasons. First, MRCPSPDCF can be formulated as a graph-based search problem, which ACO has been found to be good at solving. Second, the mechanism of ACO enables the use of domain-based heuristics to accelerate the search. Furthermore, ACO has found good results for the classical single-mode scheduling problems. But the utility of ACO for the much more difficult MRCPSPDCF is still unexplored. In this paper, we first convert the precedence network of the MRCPSPDCF into a mode-on-node (MoN) graph, which becomes the construction graph for ACO. Eight domain-based heuristics are designed to consider the factors of time, cost, resources, and precedence relations. Among these heuristics, the hybrid heuristic that combines different factors together performs well. The proposed algorithm is compared with two different genetic algorithms (GAs), a simulated annealing (SA) algorithm, and a tabu search (TS) algorithm on 55 random instances with at least 13 and up to 98 activities. Experimental results show that the proposed ACO algorithm outperforms the GA, SA, and TS approaches on most cases.