The application of mathematical optimization methods provides the capacity to increase the energy efficiency and to lower the investment costs of technical systems, considerably. We present a system approach for the optimization of the design and operation of pumping systems and exemplify it by applying it to the water supply of high-rise buildings. The underlying fluid system is modeled as a Mixed-Integer Nonlinear Program as well as a Mixed-Integer Linear Program by piecewise linearization of the pumps' characteristic curves. We consider layout and control decisions for different load scenarios, which leads to a two-stage stochastic optimization program. Besides the solution of the Mixed-Integer Nonlinear or Linear Program with off-the-shelf solvers, we implemented a problem specific algorithm to improve the computation time for solving the different models. Focusing on the efficient exploration of the solution space we divide the problem into smaller subproblems, which partly can be cut off in the solution process. On the one hand, we discuss the performance and applicability of the solution approaches for real buildings. On the other hand, we analyze the technical aspects of the solutions from an engineer's point of view. Furthermore, the constructed modular pumping test rig allows us to validate the optimization models experimentally and thus confirm the methodology.