The paper deals with the description of the procedure of mathematical optimization of a model of stand-alone energy system based only on renewable source (solar irradiance and micro-hydro power) integrated with a system for the production of hydrogen (electrolyzer, compressed gas storage and Proton Exchange Membrane Fuel Cell), whose aim is to supply the electricity needs of a residential user during a complete year of operation. The objective of the optimization problem is to minimize the investment cost of the plant while assuring the supply of the user requests. The decision variables of the optimization problem are linked to the size of the micro-hydro turbine, of the PV array, of the electrolyzer and of the fuel cell. Because of the structure of the plant, the mathematical problem is classified as a black-box problem, and it has been solved using the Downhill Simplex Method. The structure of the optimized plant is discussed through energy considerations. Moreover, the modifications that have been introduced in the basic Downhill algorithm are explained and discussed as well. (C) 2004 Elsevier Ltd. All rights reserved.