Most plant breeding programs must contend with achieving multiple breeding objectives while subject to time and resource constraints. Breeding objectives may include, but are not limited to, yield, standability, adaptation to mechanical harvesting, resistance to abiotic and biotic stressors, flavor and texture quality attributes, environmental adaptation, and genetic diversity. Many times, breeding objectives are conflicting in nature and a balance must be achieved between objectives. Both single- and multi-objective optimization techniques can be used to assist breeders in identifying trade-offs between conflicting objectives and determine a single, optimal solution which satisfies the goals of a breeding program. In this dissertation, we address and tackle several of the challenges faced when balancing multiple breeding objectives. Most of our efforts in addressing these challenges revolve around selection or mate-pairing methodologies. First, we begin by reviewing many of the selection strategies which have been proposed over the years, offer insights into the mathematical nature of several of these selection strategies, and observe attributes of successful selection strategies. Next, we introduce the software package PyBrOpS, a Python package capable of performing single- and multi-objective optimizations and single- and multi-trait simulations for breeding programs. PyBrOpS is unique among other simulation software packages in that it emphasizes multi-objective optimizations for multi-trait breeding scenarios and allows breeders to identify and visualize optimal trade-offs. Next, we introduce two new multi-objective selection strategies that seek to balance genetic gain and genetic diversity. While not the best tested selection strategies, we find that these two new selection strategies are performant, robust, and offer high long-term genetic gain while maintaining a high level of genetic diversity. Next, we introduce two new, multi-trait selection strategies which are customizable variations of marker effect upweighting-based selection strategies. One of these selection strategies dynamically adjusts its upweighting parameter based on the time to a final generation. We find that these upweighting-based selection strategies offer improvements in genetic gain and genetic diversity in ideal scenarios but fail in realistic scenarios unless a low degree of upweighting is specified. Finally, we empirically test the ability to predict the mean and variance of progenies from a diverse set of crosses. Predicting progeny mean and variance is important because it can be used to inform selections and mate-pairings. We developed genomic prediction models using information from a diversity panel, crossed several members of the diversity panel together to create progeny families, and compared predictions of progeny mean and variance using our genomic prediction models to what we observed. We were successful in predicting progeny mean, but largely unable to predict progeny variance.
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