To effectively distribute power to a system of multiple electrolyzer stack units, control strategies have been developed that now need to be applied to heterogeneous electrolysis systems. These are the 'segment principle', the 'slow start principle' and the 'start-stop principle'. As there are many possible combinations to the system composition of a modular heterogeneous electrolysis system together with the most suitable control strategy, a discrete multi-criteria optimisation problem can be formulated. To solve this discrete multi-criteria optimisation problem, two discrete decision variables are introduced. One is the electrolysis system composition, represented by the power ratio/configuration (C). A total of 17 different configurations were used for this, consisting of different proportions of alkaline electrolysis (AEL) and proton exchange membrane electrolysis (PEMEL). The other one are the control strategies (R). For the control strategies, the conventional strategies, mentioned above, have been adjusted to deal with the heterogeneity of the electrolysis system. Variations are made in the priorization of certain technologies for power distribution and the availability of a base load operation. The objective function was designed to be the weighted sum of the three highest ranked decision criteria in the categories 'flexibility', 'cost', and 'process engineering' from an empirical expert survey, which led to the respective decision criteria LGC, LCOH and the reciprocal of ?sys. The weights were derived from the ranking, a global grid search identified the combination of (R) and (C) which will be discussed in the paper together with a detailed analysis of the optimization problem.