where rand is a pseudo-random value in the range of
[0,1]. The sequence number of chaos variable is i. The
dimension of the particles is j. Chaos variable i, j is in [0,
1] interval. The rate for reproduction is set to ¼ 4.
In the perturbation stage, chaos disturbance r to the
particles is added, and then the cost values are calculated.
Solutions at the initial stage should have a big
variation and explore the search space in large-scale,
then every solution gradually approaches to optimal
point with an increase in iterations, therefore, a smaller
variation is needed so that the current solution can
search in a small range. The disturbance r can be
defined by