In this work, a set of operators for a Particle Swarm (PS) based optimization algorithm is investigated for the purpose of finding optimal values for some of the classical benchmark problems. Particle swarm algorithms are implemented as mathematical operators inspired by the social behaviors of bird flocks and fish schools. In addition, particle swarm algorithms utilize a small number of relatively uncomplicated rules in response to complex behaviors, such that they are computationally inexpensive in terms of memory requirements and processing time. In particle swarm algorithms, particles in a continuous variable space are linked with neighbors, therefore the updated velocity means of particles influences the simulation results. The paper presents a statistical investigation on the velocity update rule for continuous variable PS algorithm. In particular, the probability density function influencing the particle velocity update is investigated along with the components used to construct the updated velocity vector of each particle within a flock. The simulation results of several numerical benchmark examples indicate that small amount of negative velocity is necessary to obtain good optimal values near global optimality.

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