Particle swarm optimization algorithm has recently gained much attention in the global optimization research community.
As a result, a few variants of the algorithm have been suggested. In this paper, we study the efficiency and robustness
of a number of particle swarm optimization algorithms and identify the cause for their slow convergence. We then propose
some modifications in the position update rule of particle swarm optimization algorithm in order to make the convergence
faster. These modifications result in two new versions of the particle swarm optimization algorithm. A numerical study is
carried out using a set of 54 test problems some of which are inspired by practical applications. Results show that the new
algorithms are much more robust and efficient than some existing particle swarm optimization algorithms. A comparison
of the new algorithms with the differential evolution algorithm is also made.