Single-layer materials represent a new materials class with properties that are potentially transformative for applications in nanoelectronics and solar energy harvesting. With the goal of discovering novel two-dimensional (2D) materials with unusual compositions and structures, we have developed a grand canonical evolutionary algorithm that searches the structure and composition space while constraining the thickness of the structures. Coupling the algorithm to first principles total energy methods, we show that this approach can successfully identify known 2D materials and find novel low-energy ones. We present the details of the algorithm, including suitable objective functions, and illustrate its potential with a study of the Sn-S and C-Si binary materials systems. The algorithm identifies several new 2D structures of InP, recovers known 2D structures in the binary Sn-S and C-Si systems, and finds two new 1D Si defects in graphene with formation energies below that of isolated substitutional Si atoms.