The proper design of the multi junction solar cell (MJSC) requires the optimisation search through the vast parameter space, with parameters for the proper operation quite often being constrained, like the current matching throughout the cell. Due to high complexity number of MJSC device parameters might be huge, which makes it a demanding task for the most of the optimising strategies based on gradient algorithm. One way to overcome those difficulties is to employ the global optimisation algorithms based on the stochastic search. We present the procedure for the design of MJSC based on the heuristic method, the genetic algorithm, taking into account physical parameters of the solar cell as well as various relevant radiative and non-radiative losses. In the presented model, the number of optimising parameters is 5 M + 1 for a series constrained M-jtmctions solar cell. Diffusion dark current, radiative and Auger recombinations are taken into account with actual ASTM G173-03 Global tilted solar spectra, while the absorption properties of individual SCs were calculated using the multi band Icv Hamiltonian. We predicted the efficiencies in case of M = 4 to be 50.8% and 55.2% when all losses are taken into account and with only radiative recombination, respectively.