Translocations of threatened species can reduce the risk of extinction from a catastrophic event. For plants, translocation consists of moving individuals, seeds, or cuttings from a native (source) population to a new site. Ideally a translocation population would be genetically diverse and consist of fit founding individuals. In practice, there are challenges to designing such a population, including constraints on the availability of material, and tradeoffs between different goals. We present an approach for designing a translocation population that identifies sets of founders that are optimized according to multiple criteria (e.g., genetic diversity), while also conforming to constraints on the representation of different founders (e.g., propagation success). It uses flexible inputs, including SNP genotypes, matrices of similarity between individuals, and vectors of phenotype data. We apply the approach to a critically endangered plant, Hibbertia puberula subsp. glabrescens (Dilleniaceae), which was genotyped at thousands of SNP loci. The goals of minimizing genetic similarity among the founding individuals and maximizing genetic diversity were largely complementary – populations optimized for one of these criteria were near-optimal for the other. We also performed analyses in which we minimized genetic similarity among founding individuals while imposing selection (against hypothetical deleterious alleles, and against undesirable phenotypes, respectively), and here characterized sharp tradeoffs. This is useful in allowing the benefits of selection to be weighed against ‘costs’ in terms of genetic similarity. In sum, we present an approach for designing a translocation population that allows flexible inputs, the imposition of realistic constraints, and examination of conflicting goals.