This paper introduces a combined algorithm to particle swarm based optimization and discusses the results of experimentally comparing the performances of its three versions with the performance of the particle swarm optimizer. In the combined algorithm, each particle flies and is attracted toward a new position according to its previous best position and the point resulted from the combination of the previous global best position and the global best position. The variants of the combined algorithm and the particle swarm optimizer are tested using a set of multimodal functions commonly used as benchmark optimization problems in evolutionary computation. Results indicate that the algorithm is highly competitive and can be considered as a viable alternative to solve the optimization problems.