This paper presents a modification of the particle swarm optimization algorithm (PSO) intended to combat the problem of premature convergence observed in many applications of PSO. The proposed new algorithm moves particles towards nearby particles of higher fitness, instead of attracting each particle towards just the best position discovered so far by any particle. This is accomplished by using the ratio of the relative fitness and the distance of other particles to determine the direction in which each component of the particle position needs to be changed. The resulting algorithm (FDR-PSO) is shown to perform significantly better than the original PSO algorithm and some of its variants, on many different benchmark optimization problems. Empirical examination of the evolution of the particles demonstrates that the convergence of the algorithm does not occur at an early phase of particle evolution, unlike PSO. Avoiding premature convergence allows FDR-PSO to continue search for global optima in difficult multimodal optimization problems.