Genomic optimum contribution selection and mate allocation using JuMP.

Motivation: Artificial selection improves desired traits, but reduces genetic diversity within populations. Modern breeding programs aim to balance genetic gain with the maintenance of genetic variation to ensure long-term sustainability. Optimum contribution selection (OCS) is a widely adopted strategy that maximizes genetic gain while limiting the rate of inbreeding, traditionally relying on pedigree data. However, genomic relationship matrices offer a more accurate measure of genetic relatedness. A subsequent step to OCS involves mate allocation (MA) to optimize breeding plans, which often presents significant computational challenges for large datasets. Results: We developed a two-stage genomic OCS and mate allocation (GOCSMA) method implemented in JuMP/Julia. The OCS problem is formulated as a linear program with quadratic constraints and solved efficiently using the conic operator splitting method (COSMO). The subsequent MA problem, expressed as a mixed integer program, is solved with the SCIP framework's branch-cut-and-price algorithm. Applying GOCSMA to the simulated QTLMAS2010 dataset, we observed efficient convergence for OCS, balancing genetic gain with coancestry constraints better compared to traditional top selection. The MA stage consistently achieved very low runtimes ( < 0.01 seconds), with integer mating constraints providing lower coancestry and higher genetic gain compared to binary constraints, indicating a more optimal mating scheme.Hence, GOCSMA provides an efficient deterministic mathematical optimization framework for integrated genomic OCS and MA. Using advanced solvers within the flexible JuMP environment, our method offers a robust solution to balance genetic gain and diversity in large-scale breeding programs. Availability and implementation: Source code and documentation are available at https://github.com/patwa67/GOCSMA.