The L-shaped selection algorithm for multitrait genomic selection.

Selecting for multiple traits as opposed to a single trait has become increasingly important in genomic selection. As one of the most popular approaches to multitrait genomic selection, index selection uses a weighted average of all traits as a single breeding objective. Although intuitive and effective, index selection is not only numerically sensitive but also structurally incapable of finding certain optimal breeding parents. This paper proposes a new selection method for multitrait genomic selection, the L-shaped selection, which addresses the limitations of index selection by normalizing the trait values and using an L-shaped objective function to find optimal breeding parents. This algorithm has been proven to be able to find any Pareto optimal solution with appropriate weights. Two performance metrics have also been defined to quantify multitrait genomic selection algorithms with respect to their ability to accelerate genetic gain and preserve genetic diversity. Computational experiments were conducted to demonstrate the improved performance of L-shaped selection over-index selection.