New frontiers for CLA: efficient methods for optimization problems in finance and genetics
Joshua Fogg · ERA · 2026
Critical line algorithm is a well established method for exploring the Pareto frontier of bi-objective portfolio optimization problems. This is typically in the context of managing financial investments, but recently a connection was made to optimal contribution selection, a problem with similar structure in population genetics. In this thesis we explore how new optimization methods for optimal contribution selection can be developed using this connection. Our first key contribution is a modified description of critical line algorithm focused on improved efficiency and accuracy. A key differentiator of the genetics context is the far larger dimension of interest, several orders of magnitude higher than in finance. The treatment in this thesis addresses issues that only become apparent at this scale and, through more efficient numerical linear algebra, demonstrates that the algorithm may be stated free of matrix multiplication and matrix inversion. We also share a small five asset problem that provides better testing coverage than the ten asset problem typically used in the literature. This leads on to our novel algorithm for exploring the Pareto frontier of optimal contribution selection problems as they occur in the context of managing cattle breeding programmes. This is structurally similar to critical line algorithm, and as a result improves on the contemporary method from population genetics of solving a semi-definite optimization problem over a discretized parameter. An implementation of the algorithm with examples is provided. Finally, we provide models and methods for carrying out optimal contribution selection under uncertainty. Drawing on the literature from population genetics, we show how the uncertainty in the relationship matrix can be eliminated, leaving only the estimated breeding values to address. We then draw on the optimization literature to demonstrate how this problem can be solved using either conic optimization or sequential quadratic optimization. These are both implemented in an open-source software package for use in further research.