Biological processes are often governed by functional modules of large protein assemblies such as the proteasomes and the nuclear pore complex, for example. However, atomic structures can be determined experimentally only for a small fraction of these multicomponent assemblies. In this article, we present an ant colony optimization based approach to predict the structure of large multicomponent complexes. Starting with pair-wise docking predictions, a multigraph consisting of vertices representing the component proteins and edges representing scored transformations is constructed. Thus, the assembly problem corresponds to identifying minimum weighted spanning trees that yield arrangements of components with few atomic clashes. The utility of the approach is demonstrated using protein complexes taken from the Protein Data Bank. Our algorithm was able to identify near-native solutions for 5 of the 6 cases tested, including one 6-component complex. This demonstrates that the ant colony model provides a useful way to deal with highly combinatorial problems such as assembling multicomponent protein complexes.