Digital filters play a key role in the field of digital signal processing. This paper presents a linear phase digital low pass finite impulse response (FIR) filter design using particle swarm optimization and its two new variants, dynamic and adjustable particle swarm optimization (DAPSO) and particle swarm optimization with variable acceleration factor (PSO-VAF) and illustrates the superiority of the PSO-VAF method over PSO based methods. Two fitness functions are considered. The fitness1 is used to find the possible minimum ripples in pass band and stop band in case of PSO, DAPSO and PSO-VAF. Fitness2 is able to control the ripples in both bands separately. A comparison of simulation results demonstrates the performance of PSO and its methods in designing digital low pass FIR filters.