© The Author(s) 2025.Let C?Np be an integer cone. A C-semigroup S?C is an affine semigroup such that the set CS is finite. Such C-semigroups are central to our study. We develop new algorithms for computing C-semigroups with specified invariants, including genus, Frobenius element, and their combinations, among other invariants. To achieve this, we introduce a new class of C-semigroups, termed B-semigroups. By fixing the degree lexicographic order, we also research the embedding dimension for both ordinary and mult-embedded N2-semigroups. These results are applied to test some generalizations of Wilf’s conjecture.