The reconstruction of DNA sequences from DNA fragments is one of the most challenging problems in computational biology. In recent years the specific problem of DNA sequencing by hybridization has attracted quite a lot of interest in the optimization community. Despite the fact that well-working constructive heuristics are often the basis for well-working metaheuristics, only two constructive heuristics exist. Both approaches were proposed by Blazewicz and colleagues; the first one is a look-ahead greedy technique, and the second one is a constructive technique based on constructing reliable sub-sequences. Our motivation was twofold. First, we wanted to develop better constructive heuristics. Second, on the basis of these heuristics we wanted to develop new state-of-the-art metaheuristics for DNA sequencing by hybridization. In the first part of the paper we present our constructive heuristics. We show that the results of the best constructive heuristic are comparable to the results of existing metaheuristics, while using less computational time. In the second part of the paper we propose an ant colony optimization (ACO) approach and apply it in a so-called multi-level framework. Both, the ACO algorithm and the multi-level framework are based on our constructive heuristics. The computational results show that our algorithm is currently a state-of-the-art algorithm for DNA sequencing by hybridization.