Numerical optimization of recursive systems of equations with an application to optimal swine genetic selection

A new dynamic programming method is developed for numerical optimization of recursive systems of equations, in which continuous choice variables determine the allowed choices in subsequent stages of the problem. The method works by dynamically creating bubbles, or subspaces, of the total search space, allowing the indexing of states visited for later use, and taking advantage of the fact that states adjacent to a visited state are likely to be visited. The method thereby allows search of spaces far larger than would traditionally be permitted by memory limitations. The search allows an infinite planning horizon, and tests at each stage to determine whether further optimization is worth the costs, reverting to a default choice when no longer profitable. The method is applied to the quantitative genetics problem of finding the optimal selection choices for quantitative traits using an identified locus, using the present discounted value of all generations. The method is then applied to the Estrogen Receptor Gene (ESR) to find the economic value of testing for this particular gene.