The agent's current position is denoted as  and is initially picked at random from the entire search-space. The potential new position is denoted as  and is sampled from the neighborhood of  by letting , where  is a random vector picked uniformly from the range , which is initially . In other words, the full range of the entire search-space is defined by its upper boundaries, , and its lower boundaries, . LUS moves from position  to position  in the event of any improvement in the fitness. Upon each failure for  to improve on the fitness of , the sampling range is decreased by multiplication with a factor of , as follows:

Here, the decrease factor  is then defined as follows:

The preceding formula denotes  as the dimensionality of the search-space and  as a user-defined parameter used to adjust the rate of sampling-range decrease. A value of  has been found to work well for many optimization problems.