A new approach to the optimal design of power inverters for on-grid photovoltaic systems that uses genetic algorithms (GA) is provided in this article. The nonlinear average model is adopted to model the conversion stage in order to accurately evaluate and quickly estimate the power losses of the power devices. The hysteresis current control that guarantees a quasi-sinusoidal output current is applied to generate the inverter control signals. The design of the solar inverter must meet three contradictory objectives that need to be optimized at the same time. In fact, the aim is to maximize the efficiency of the converter while minimizing its size and price under electrical constraints. The problem variables are the output current ripple and the passive and active components available on the market (IGBTs/MOSFETs, Diodes, Inductors). NSGA-II (Elitist Nondominated Sorting Genetic Algorithm) is appropriate in the case where discrete design variables are used to search for optimal Pareto solutions. It carries out a systematic and efficient search among the developed databases for a set of components which define the optimal structures of the inverter. The introduced method makes the design task easier since the best solutions depend on the components available on the market and significantly reduces the time to market for manufacturers.