Advances in synthetic chemistry, lithography, and microfabrication continue to expand the library of shapes and materials that can be used to synthesize new nanoparticles. By combining a hierarchy of interaction energies with complex geometries to form novel building blocks we aim to enable the self-assembly of more complicated materials and devices, but it also becomes more difficult to predict what structures these new building blocks will form. With a range of complex anisotropic interactions available to these particles, systems can become easily trapped in metastable states during Metropolis Monte Carlo (MC) simulations, making it computationally difficult if not impossible to find their energy minimizing configurations even with cluster-based MC methods. We present a new computational method - binary hierarchical assembly - that rapidly generates zero temperature, energy-minimizing configurations of sets of complex nanoparticles. Our new algorithm generates lower energy structures than can be predicted with standard cluster Monte Carlo techniques in a fraction of the time and facilitates an understanding of how small changes in nanoparticle detail can translate to large changes in macrostructure. We provide a quantitative measure to determine if a given system is a good candidate for binary hierarchical assembly. We discuss why and under what conditions our new method and other optimization techniques are more efficient than Monte Carlo methods for strongly interacting systems of particles.