In the recent years, several results in combinatorics and discrete mathematics have been obtained and advanced through effective computations involving computer algebra and numerical methods, such as kissing numbers and optimal sphere packings, independence ratios and Lovasz numbers, and graph homomorphisms. Frequently, new progress relies on the exploitation of algebraic structure. In our workshop, we want to focus on computational methods which use algebra and exploit symmetries to solve problems in graph theory. Emphasize lies on sums of squares-based optimization hierarchies which make use of lattice-based symmetry exploitation, group actions or sparsity. We aim to connect experts who are working on the intersections of combinatorics, optimization and algebra. This is foreseen to enable synergies and open opportunities for future work.