Predicting the atomic structure of large systems requires simultaneous exploration of atomic positions, species, and, generally, the number of atoms. The combinatorial growth of possible arrangements can make this search difficult even for standard genetic algorithms. We introduce Hereditary Effective Atom Theory (HEAT), which integrates Effective Atom Theory into a genetic algorithm to enable efficient global search through a differentiable effective-atom representation. Central to the method is a crossover scheme that directly superimposes two parent structures and relaxes the combined structure. HEAT outperforms conventional genetic-algorithm baselines in recovering a missing 240-atom H sublattice, predicting a 364-atom edge-dislocation core, and reconstructing twisted-bilayer WSe₂ containing 1150 atoms from ptychographic constraints. These results demonstrate how continuous effective-atom relaxation improves the exploration of large combinatorial structure spaces.