The study of Special Lagrangian three-cycles (sLAGs) in Calabi-Yau threefolds is an interesting problem in Physics and Mathematics. A three-cycle L is Lagrangian if the Kahler form of the Calabi-Yau manifold vanishes when restricted to L, and it is special if the complex phase of the holomorphic top form restricted to L is constant. SLAGs are volume-minimizing in their homology class, and they ensure that supersymmetry remains unbroken. SLAGs also feature prominently in the SYZ conjecture of mirror symmetry. Despite their importance, almost no concrete examples of sLAGs are known. We will report on work in progress where we develop an approach that combines tools from machine learning (neural networks), artificial life (genetic algorithms with quality-diversity optimization), and persistent homology (a tool from topological data analysis that assigns homological data to point clouds) to search for new sLAGs in Calabi-Yau manifolds.