This paper presents the design and optimization of a permanent magnet array for gravity compensation in rotational motion. Unlike traditional designs that require customized magnets, this approach uses standard cubic magnets of identical size and magnetization, offering a cost-effective solution for gravity compensation. The design task involves determining the optimal positions and orientations of a set of stationary magnets that interact with a magnet attached to a rotatable link, to balance the gravitational torque about the link's pivot. To achieve this, a genetic algorithm is combined with a method for calculating magnetic forces based on Monte Carlo integration. In the given example, the design demonstrated significant gravity reduction on the link, and the result was validated through finite element simulation. Additionally, several case studies were conducted to explore optimal parameters such as the number of stator magnets and the installation position of the mover magnet, and the weight capacity of the system.