We analyze in the framework of the Quark-Gluon String Model the experimental data on the production of strange Λ s, and multistrange baryons (Ξ, Ω), and antibaryons, on nuclear targets, as well as on the ratios of multistrange to strange antibaryon production, at the energy region from SPS up to LHC. One remarkable result of this analysis is the manifest violation of the quark combinatorial rules, shown by the experimental dependence on the centrality of the collision of the Ξ + /Λ and Ω + /Λ ratios in heavy-ion collisions.