The performance of micro-LEDs (µLEDs) is crucial for micro-displays, a field of expertise at the LITE laboratory within CEA-LETI. However, simulating these components is complex and computationally expensive due to the incoherent nature of light sources and the involved geometries. This limits the ability to effectively explore multi-parameter design spaces. This thesis proposes to develop an innovative finite element method to accelerate simulations and enable the use of topological optimization. The goal is to produce non-intuitive designs that maximize performance while respecting industrial constraints. The work is divided into two phases: Develop a fast and reliable simulation method by incorporating appropriate physical approximations for incoherent sources and significantly reducing computation times. Design a robust topological optimization framework that includes fabrication constraints to generate immediately realizable designs. The expected results include optimized designs for micro-displays with enhanced performance and a methodology that can be applied to other photonic devices.