The design of inertial confinement fusion experiments, alongside improving the development of energy density physics theory and experimental methods, is one of the key challenges in the quest for nuclear fusion as a viable energy source. Recent challenges in achieving a high-yield implosion at the National Ignition Facility (NIF) have led to new interest in considering a much wider design parameter space than normally studied. Here we report an algorithmic approach that can produce reasonable ICF designs with minimal assumptions. In particular we use the genetic algorithm metaheuristic, in which `populations' of implosions are simulated, the design of capsule is described by a `genome', natural selection removes poor designs, high quality designs are `mated' with each other based on their yield, and designs undergo `mutations' to introduce new ideas. We show that it takes ~5x10^4 simulations for the algorithm to find an original NIF design. We also link this method to other parts of the design process and look towards a completely automated ICF experiment design process - changing ICF from an experiment design problem to an algorithm design problem.