PS uses one agent or position in the search-space that is being moved around. Let the position be denoted as , which is initially picked at random from the entire search-space. The initial sampling range is the entire search-space: . The potential new position is denoted as  and is sampled as follows.

First, pick an index () at random and let  and  for all . If  improves on the fitness of  then move to . Otherwise, halve and reverse the sampling range for the  dimension with . Repeat this several times.