In physics gravitation is the tendency of agent with object to accelerate towards each other. In the Newtonian law each object attracts every other object by a gravitational force. Gravitational search algorithm is one of the newest stochastic population based meta heuristic that has been inspired by newtanion laws of gravity and motion. The algorithm is consisted of collection of searcher agents that interact with each other through the gravity force. The agents are deliberated as objects and their execution is measured by their masses. The gravity force induces a global motion where all objects proceed towards other objects with heavier masses. The slow motion of heavier masses guarantees the victimization step of the algorithm and corresponds to good solutions. The masses are actually obeying the law of gravity as shown in Equation (3.1) and the law of motion in Equation (3.2).
F = G (M1M2 / R2) (3.1) a = F/M (2) (3.2)
Based on Equation (3.1), F represents the magnitude of the gravitational force, G is gravitational constant, M1 and M2 are the mass of the first and second objects and R is the distance between the two objects. Equation (3.1) shows that in the Newton law of gravity, the gravitational force between two objects is