DE uses a population of agents. Let  denote the position of an agent being updated and which has been picked at random from the entire population. Let  be its new potential position computed as follows (this is the so-called DE/rand/1/bin variant):

Here, the vectors , , and  are the positions of distinct and randomly-picked agents from the population. The index  is randomly-picked and  is also picked randomly for each dimension, . A move is made to the new position  if it improves on the fitness of . The user-defined parameters consist of the differential weight , the crossover probability , and the population-size .