Optimization of breeding program design through stochastic simulation with kernel regression

In recent years, breeding programs have increased significantly in size and complexity, with various highly interdependent parameters and many contrasting breeding goals. As a result, resource allocation in these programs has become more complex, and deriving an optimal breeding strategy has become increasingly challenging. To address this, a common practice is to reduce the optimization problem to a set of scenarios that differ only in a few parameters and can therefore be analyzed in detail. The goal of this article is to provide a framework for the numerical optimization of breeding programs that goes beyond the simple comparison of scenarios. For this, we first determine the space of potential breeding programs only limited by basic constraints like the budget and housing capacities. Subsequently, the goal is to identify the optimal breeding program by finding the parametrization that maximizes the target function by combining different breeding goals. To assess the value of the target function for a parametrization, we propose using stochastic simulations and the subsequent use of a kernel regression method to cope with the stochasticity of simulation outcomes. This procedure is performed iteratively to narrow down the most promising areas of the search space and perform more and more simulations in these areas of interest. In a simplified example applied to a dairy cattle program, our proposed framework has shown its ability to identify an optimal breeding strategy that aligns with a target function aiming at genetic gain and genetic diversity conservation limited by budget constraints.