To design the layout of LED light sources(called as LEDs) in a medium or large LED-based lighting system to optimize the system's performance in illuminance, uniformity and heat dissipation by developing a Genetic Algorithm, the searching space formed by x,y, z coordinates and rotation angles of an LED light source will be rather huge as to paralyze the evolution program. Hence, we propose the idea of representative LED sources (called as representatives), which are parts of LEDs. In this paper, we will develop some a Genetic Algorithm to search for suitable representatives to make the evolutional design of a programmable Fresnel lens for the mentioned lighting system feasible. Based on the designed programmable Fresnel lens, develop another Genetic Algorithm to arrange the layout of LEDs, including locations and orientations of LEDs, to let the lighting system's performance be further enhanced.© (2009) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.