Luminescent Solar Concentrators (LSCs) use fluorescent materials and light guides to convert direct and diffuse sunlight into concentrated wavelength-shifted light that produces electrical power in small photovoltaic (PV) cells with the goal of significantly reducing the cost of solar energy utilization. In this paper we present an optimization analysis based on the implementation of a genetic algorithm (GA) subroutine to a numerical ray-tracing Monte Carlo model of an LSC, SIMSOLAR-P. The initial use of the GA implementation in SIMSOLAR-P is to find the optimal parameters of a hypothetical “perfect luminescent material” that obeys the Kennard Stepanov (K-S) thermodynamic relationship between emission and absorption. The optimization balances the efficiency losses in the wavelength shift and PV conversion with the efficiency losses due to re-scattering of light out of the collector. The theoretical limits of efficiency are provided for one, two and three layer configurations; the results show that a single layer configuration is far from optimal and adding a second layer in the LSC with wavelength shifted material in the near infrared region significantly increases the power output, while the gain in power by adding a third layer is relatively small. The results of this study provide a theoretical upper limit to the performance of an LSC and give guidance for the properties required for luminescent materials, such as quantum nanocrystals, to operate efficiently in planar LSC configurations.