  Compared with random sampling, low-discrepancy sampling is more effective in
covering the search space. However, the existing research cannot definitely
state whether the impact of a low-discrepancy sample on particle swarm
optimization (PSO) is positive or negative. Using Niderreiter's theorem, this
study completes an error analysis of PSO, which reveals that the error bound of
PSO at each iteration depends on the dispersion of the sample set in an
expanded dimensional space. Based on this error analysis, an acceleration
technique for PSO-type algorithms is proposed with low-discrepancy sampling in
the expanded dimensional space. The acceleration technique can generate a
low-discrepancy sample set with a smaller dispersion, compared with a random
sampling, in the expanded dimensional space; it also reduces the error at each
iteration, and hence improves the convergence speed. The acceleration technique
is combined with the standard PSO and the comprehensive learning particle swarm
optimization, and the performance of the improved algorithm is compared with
the original algorithm. The experimental results show that the two improved
algorithms have significantly faster convergence speed under the same accuracy
requirement.
