In this paper, we study the base placement problem for a two-degree-freedom-robot. The feasible area for the robot base is described, and its manipulability measure is formulated. To find the optimal base location of the robot, we develop a genetic algorithm (GA) to search for the valid solution in the reachable area of the robot base. To speed up the evolutionary process, we keep the elitists from one generation to the next generation according to certain elitist rate. The genetic algorithm approach is beneficial because it can also be extended to trajectory planning for robots with more degrees-of-freedom. We demonstrate the algorithm with some examples.