This paper presents the application of the Ant Colony Optimization (ACO) meta-heuristic to a new NP-hard problem involving the replication of multi-quality database-driven web applications (DAs) by a large application service provider (ASP). The ASP must assign DA replicas to its network of heterogeneous servers so that user demand is satisfied at the desired quality level and replica update loads are minimized. Our ACO algorithm, AntDA, for solving the ASP's replication problem has several novel or infrequently seen features: ants traverse a bipartite graph in both directions as they construct solutions, pheromone is used for traversing from one side of the bipartite graph to the other and back again, heuristic edge values change as ants construct solutions, and ants may sometimes produce infeasible solutions. Testing shows that the best results are achieved by using pheromone and heuristics to traverse the bipartite graph in both directions. Additionally, experiments show that AntDA outperforms several other solution methods.