Nitride-based semiconductor materials are promising candidates for the manufacturing of very high efficiency solar cells. The Indium Gallium Nitride (InGaN) ternary alloy has a particular interest, because its energy gap can be varied in a wide spectral range just by changing the indium composition. This can lead to bandgap engineering, which would ease the design of multi-junction solar cells. Within this context, the performance of a double junction solar cell based on InGaN was simulated. In this work, we simulated globally the solar cell structure using realistic physics models and InGaN parameters obtained with experimental measurements. The modeled solar cell is composed of two p-n junctions vertically stacked having decreasing Bandgaps and connected by a specifically designed tunnel junction. This allows the conversion of different parts of the solar spectrum, thus enhancing the solar light absorption efficiency and the photocarriers transport. The device is simulated in the framework of a drift-diffusion model using the ATLAS device simulation framework from the Silvaco company. The optimization is achieved by coupling ATLAS with multivariate mathematical optimization methods based on state-of-the-art optimization algorithms. For that, we used a Python package that we developed in the SAGE software interface. The objective is to optimize the conversion efficiency of the solar cell by simultaneously optimizing several physical and geometrical parameters of the solar cell. It is an unprecedented multivariate optimization for solar cells which takes into account the correlation between these parameters. We have optimized eleven parameters simultaneously and the optimum conversion efficiency obtained is 24:4% with a short-circuit current (JSC) of 12,9 mA/cm2, an open-circuit voltage (VOC) of 2,29 V and a fill factor (FF) of 82,5 %.However, InGaN grown on available substrates have high densities of structural defects. It also has spontaneous and piezoelectric polarization fields which lead to the presence of high densities of electrostatic charges in the interfaces of the InGaN epitaxially grown layer. We thus highlight and discuss the effects of this polarization and the effects of structural defects on the photovoltaic characteristics of the solar cell.