This paper presents a conceptual design approach for high-temperature gas-cooled reactors using recirculating pebble bed cores. The method employs PEBBED, a reactor physics code specifically designed to solve for the asymptotic burnup state of pebble bed reactors in conjunction with a genetic algorithm to obtain a core with acceptable properties. The uniqueness of the asymptotic core state and the small number of independent parameters that define it suggest that core geometry and fuel cycle can be efficiently optimized toward a specified objective. A novel representation of the distribution of pebbles enables efficient coupling of the burnup and neutron diffusion solvers. Complex pebble recirculation schemes can be expressed in terms of a few parameters that are amenable to manipulation using modern optimization techniques. The user chooses the type and range of core physics parameters that represent the design space. A set of traits, each with acceptable and preferred values expressed by a simple fitness function, is used to evaluate the candidate reactor cores. The stochastic search algorithm automatically drives the generation of core parameters toward the optimal core as defined by the user. For this study, the design of two pebble bed high-temperature reactor concepts subjected to demanding physical constraints demonstrated the technique's efficacy.