Abstract: To precisely evaluate the form error of sphere, a modified particle swarm
optimizer (PSO) using dynamic inertia weight based on four kinds of mathematical models of
sphericity error evaluation is proposed to calculate two groups of data. The dynamic inertia weight
is changed in every iteration according to the particles’ positions and the objective function in this
optimizer. A comparison is made among this optimizer, the basic PSO, the least square method,
the genetic algorithm and an improved particle swarm optimizer. The experimental results show
that, compared with other methods, error gained by the modified PSO using dynamic inertia
weight based on the mathematical model of the sphericity error under the condition of minimum
zone is the least. For the first group it only takes about 50ms to converge and the iteration times
are just about 30. The speed of convergence of the second group is also very rapid. Repeated tests
indicate that the algorithm has high stability. Therefore, the algorithm can evaluate the sphericity
error precisely and rapidly.

Key words: sphericity error, PSO, evaluation, inertia weight