The structure of high thermal conductivity matrices have been optimized to improve the discharge behaviour of thermal energy stores. Topology optimization and genetic algorithms were validated by verifying their ability to converge to the global optimum for small grid sizes. Genetic algorithms are prone to converge to local maxima while requiring significantly longer convergence times compared to topology optimization. This results in tree structures which consistently outperform a standard rectangular fin by a margin, which increases with grid refinement. Store discharge after ~2 hrs can be improved from 70% to 90% at a loading of 10 vol%. Topology optimization resulted in structures representing parallel sheets, which are as thin as the grid allows. These configurations can maintain the maximum surface area between the low and high conductivity materials at high refinement, resulting in the best performance. Time required for 99% store discharge is decreased by 70% using a 50x50 optimization grid at a loading of 10 vol%.