Abstract: The aim of this project is to develop algorithmic tools for simplex packings that stem from the ball packing problem in symplectic topology. We want to formulate these packing questions as optimization problems so that recent, advanced algorithmic tools from combinatorial optimization (mixed integer non-linear programming, semidefinite optimization) can be used in this context. The insight gained from this experimental work should serve as the basis for further theoretical study. A major challenge, both computationally and theoretically, is the computation of packing widths in dimension greater than four.