We present a multi-objective integer programming model for the gene stacking problem, which is to bring desirable alleles found in multiple inbred lines to a single target genotype. Pareto optimal solutions from the model provide strategic stacking schemes to maximize the likelihood of successfully creating the target genotypes and to minimize the number of generations associated with a stacking strategy. A consideration of genetic diversity is also incorporated in the models to preserve all desirable allelic variants in the target population. Although the gene stacking problem is proved to be NP-hard, we have been able to obtain Pareto frontiers for smaller sized instances within one minute using the state-of-the-art commercial computer solvers in our computational experiments.
