Figure 1: Computational methods evaluated by their reliability, required researcher effort, and scaling of the computational effort with system size. The coloration of the left semicircle represents the complexity and expertise necessary for the researcher to perform the technique, where a blue tone signifies low effort and a red tone signifies high effort. The coloration of the right semicircle characterizes the reliability of the method on a similar coloration scale. Finally, the size of the Circle demonstrates how the computational effort scales with system size. Methods evaluated include a variety of density functional theory (DFT) techniques, including local density approximation (LDA) and generalized gradient approximation (GGA), empirical tight-binding, and many-bodied GW approaches. Reprinted from Butler, et al. [1].

Figure 2: An example of a fitness landscape. Gene 1 and Gene 2 are selected characteristics of a material, such as a processing condition, or a mechanical, electrical, chemical, optical, thermal, or magnetic property. Fitness is a measure of how well the genome at some (i,j) values for Gene 1 and Gene 2 optimize a desired property or set of properties. The red, blue, and green paths represent different optimization steps that a genetic algorithm could take to diverse maxima on the fitness landscape. Note that not all paths necessarily lead to the same maximum, as multiple local maxima may be present. Reprinted from Le, et al. [10].

Figure 3: The general process of a genetic algorithm. A population is established, and then evolutionary operators are applied to each generation. Typically, evolutionary operators include selection, reproduction (crossover/mutation), and elitism. The process is repeated on subsequent generations until a certain number of iterations have been completed or a specific fitness threshold is reached

Figure 4: (a) The fitness of simulated populations over 35 generations for three different hypothetical fitness funct ions. All three fitness functions converged to similar populations with peak fitness. Minimal variation was observed in the speed and accuracy of the optimization among the three fitness functions. (b) Top panel: The luminance as a function of generation when the genetic algorithm was applied to actual data. Inset: The resulting experimental luminance of the first and tenth generations, demonstrating the stark improvement resulting from algorithmic optimization. Bottom panel: The evolution of the ideal material composition over the course of ten generations. Reprinted from Sohn, et al. [19].