This study focuses on the sizing and optimization of a micro-grid with storage, which is destined to supply the load of an economic activity zone (EAZ) in Sidi Bouzid, Tunisia. To solve this problem, a genetic algorithm is established and programmed into MATLAB. The objective functions are considered by providing three minimums, namely Greenhouse Gas emissions (GHG), Life Cycle Cost (LCC) and Embodied Energy (EE), for three values of loss of power supply probability (LPSP) previously fixed. The sizing and optimization results are found and evaluated using a time series exchange of energy during a year to determine the optimal component size of a photovoltaic/wind/battery system (PV/WT/Bat). The simulation results show that the lowest ratio of LPSP values corresponds to the higher GHG, EE, LCC, photovoltaic panels area (APV), battery storage capacity (Cn), wind turbines area (AWT) and vice versa. This means that demanding higher energy reliability leads to higher energy cost and pollution. A comparative analysis was made, showing the cons and pros of each LPSP value in order to allow the owner of the plant to choose the most suitable PV/WT/Bat configuration.