A new hybridization of the Cuckoo Search (CS) is developed and applied to optimize multi-cell solar systems; namely multi-junction and split spectrum cells. The new approach consists of combining the CS with the Nelder-Mead method. More precisely, instead of using single solutions as nests for the CS, we use the concept of a simplex which is used in the Nelder-Mead algorithm. This makes it possible to use the flip operation introduces in the Nelder-Mead algorithm instead of the Levy flight which is a standard part of the CS. In this way, the hybridized algorithm becomes more robust and less sensitive to parameter tuning which exists in CS. The goal of our work was to optimize the performance of multi-cell solar systems. Although the underlying problem consists of the minimization of a function of a relatively small number of parameters, the difficulty comes from the fact that the evaluation of the function is complex and only a small number of evaluations is possible. In our test, we show that the new method has a better performance when compared to similar but more compex hybridizations of Nelder-Mead algorithm using genetic algorithms or particle swarm optimization on standard benchmark functions. Finally, we show that the new method outperforms some standard meta-heuristics for the problem of interest.