We have presented Grid Method, a systematic and efficient problem formulation method for task-oriented design of robot kinematics and confirmed its efficiency through various design examples. Despite of its efficient problem formulation, however, our previous research has the following limitations: (i) it gives a local optimum only due to its use of a local optimization technique (ii) it uses constatn weights for a cost function chosen by a manual weights tuning algorithm, thereby showing low efficiency in finding an optimum solution. To solve these problem, therefore, this paper presents systematic, efficient algorithms of Grid Method with a global optimization technique and an adaptive weights tuning algorithm.