A method for generating discrete optimal sequences of base locations for mobile manipulators is presented that considers the task capability of the workspace in a cluttered environment. In implementation, the obstacles and task trajectories are represented by 2(n) trees, so that a series of set operations are performed to characterize the manipulator's configuration space into topological subspaces. By incorporating trajectory-motion-capable subspaces into the enumeration of the cost function, an optimum search technique is made applicable to the determination of a task feasible location. The method is then extended to a multiple positioning problem by concatenating the single optimization processes into a serial multistage decision making system, for which an optimal set of decisions can be found through a computationally efficient dynamic programming process. The computational paradigm of the present method is coherent with topological workspace analysis, and thus applicable to task trajectories of arbitrary dimensions and shapes. The effectiveness of the presented method is demonstrated through simulation studies performed for a 3-d.o.f. regional manipulator operating under various task conditions.