Abstract: Back propagation algorithm (BPA) have the complexity, local minima problem so we are using Particle Swarm optimization (PSO) algorithms to reduce and optimize BPA. In this paper, two variants of Particle Swarm Optimization (PSO) PSO_Hill and PSO_A* is used as optimization algorithm. PSO_Hill and PSO_A* algorithms are analyzed and evaluated on the basis of their advantages, applied to feed forward neural network(FNN) for back propagation algorithm(BPA) which is a gredient desent technique. where BPA is used for non_linear problems. These non_linear problems are improved by a PSO_Hill and PSO_A* algorithms.