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The particle position and velocity update equations in the simplest form that govern the PSO are given by
* <math> v_{i,j+1} \leftarrow c_0 v_{i,j} + c_1 r_1 ( global best_j - x_{i,j} ) + c_2 r_2 ( local best_{i,j} - x_{i,j} ) + c_3 r_3 ( neighborhood best_j - x_{i,j} )</math>
* <math> x_{i,j+1} \leftarrow x_{i,j} + v_{i,j}.</math>
In Standard PSO (available on the Particle Swarm Central, see the external link below), the parameter <math> c_1 </math> is set to zero. And when <math> neighborhood best_j = local best_{i,j} </math>, then <math> r_3 </math> is also (temporarily) set to zero.
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