DE creates new candidate solutions by combining the parent individual and several other individuals of the same population. A candidate replaces the parent only if it has better fitness value.
The population of the original DE algorithm (Storn & Price, 1995) (Storn & Price, 1997) contains NP D-dimensional vectors: xi,G, i = 1, 2, …, NP. G denotes the generation. The initial population is usually selected uniform randomly between the lower and upper bounds. The bounds are specified by the user according to the nature of the problem. After initialization DE performs several vector transforms (operations): mutation, crossover, and selection.
Mutant vector vi,G can be created by using one of the mutation strategies (Price et al., 2005). The most useful strategy is ‘rand/1’: vi,G = xr1,G + F × (xr2,G - xr3,G), where F is the mutation scale factor within range [0, 2], usually less than 1. Indexes r1, r2, r3 represent the random and distinct integers generated within range [1, NP], and also different from index i.
After mutation, a ‘binary’ crossover operation forms the trial vector ui,G, according to the ith population vector and its corresponding mutant vector vi,G:if (rand ≤ CRorj = jrand) thenui,j,G = vi,j,Gelseui,j,G = xi,j,G, where i = 1, 2, …, NP and j = 1, 2, …, D. CR is the crossover parameter or factor within the range [0,1] and presents the probability of creating parameters for the trial vector from the mutant vector. Uniform random value rand is within [0, 1]. Index jrand ∈ [1, NP] is a randomly chosen index and is responsible for the trial vector containing at least one parameter from the mutant vector.
The selection operation selects, according to the objective fitness value of the population vector xi,G and its corresponding trial vector ui,G, which vector will survive to be a member of the next generation.
The original DE has more strategies and Feoktistov (Feoktistov, 2006) proposed some general extensions to DE strategies. The question is which strategy is the most suitable to solve a particular problem. Recently some researchers used various combinations of two, three or even more strategies during the evolutionary process.