When applied to real-world problems, the powerful optimization tool of Evolutionary Algorithms frequently turns out to be too time-consuming due to elaborate fitness calculations that are often based on run-time-intensive simulations. Incorporating domain-specific knowledge by problem-tailored heuristics or local searchers is a commonly used solution, but turns the generally applicable Evolutionary Algorithm into a problem-specific tool. The new method of hybridization implemented in HyGLEAM is aimed at overcoming this limitation and getting the best of both algorithm classes: A fast, globally searching, and robust procedure that preserves the convergence reliability of evolutionary search. Extensive tests demonstrate the superiority of the approach, but also show a drawback: No common parameterization can be drawn from the experiments. As a solution, a new concept of a self-adapting hybrid is introduced. It is stressed that the methods presented can be applied to Evolutionary Algorith...