Many biological processes are governed by large assemblies of protein molecules. However, it is often very difficult to determine the three-dimensional structures of these assemblies using experimental biophysical techniques. Hence there is a need to develop computational approaches to fill this gap. This article presents an ant colony optimization approach to predict the structure of large multi-component protein complexes. Starting from pair-wise docking predictions, a multi-graph consisting of vertices representing the component proteins and edges representing candidate interactions is constructed. This allows the assembly problem to be expressed in terms of searching for a minimum weight spanning tree. However, because the problem remains highly combinatorial, the search space cannot be enumerated exhaustively and therefore heuristic optimisation techniques must be used. The utility of the ant colony based approach is demonstrated by re-assembling known protein complexes from the Protein Data Bank. The algorithm is able to identify near-native solutions for five of the six cases tested. This demonstrates that the ant colony approach provides a useful way to deal with the highly combinatorial multi-component protein assembly problem.