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Differential Evolution (DE), proposed by Storn and Price (1995, 1999), is a simple yet powerful evolutionary algorithm (EA) for global optimization in the continuous search domain (Price, 1999). DE has shown superior performance in both widely used benchmark functions and real-world problems (Price et al., 2005; Vesterstrom & Thomsen, 2004). Like other EAs, DE is a population-based stochastic global optimizer employing mutation, recombination and selection operators and is capable of solving reliably nonlinear and multimodal problems. However, it has some unique characteristics that make it different from other members of the EA family. DE uses a differential mutation operation based on the distribution of parent solutions in the current population, coupled with recombination with a predetermined parent to generate a trial vector (offspring) followed by a one-to-one greedy selection scheme between the trial vector and the parent. The algorithmic description of a classical DE is depicted in Figure 1.
Depending on the way the parent solutions are perturbed to generate a trial vector, there exist many trial vector generation strategies and consequently many DE variants. With seven commonly used differential mutation strategies (Montes et al., 2006), as listed in Table 1, and two crossover schemes (binomial and exponential), we get fourteen possible variants of DE viz. rand/1/bin, rand/1/exp, best/1/bin, best/1/exp, rand/2/bin, rand/2/exp, best/2/bin, best/2/exp, current-to-rand/1/bin, current-to-rand/1/exp, current-to-best/1/bin, current-to-best/1/exp, rand-to-best/1/bin and rand-to-best/1/exp. So far, no single DE variant has turned out to be best for all problems which is quiet understandable with regard to the No Free Lunch Theorem (David et al., 1997).
Table 1. Differential mutation strategies
| Nomenclature | Variant |
| rand/1 |  |
| best/1 |  |
| rand/2 |  |
| best/2 |  |
| current-to-rand/1 |  |
| current-to-best/1 |  |
| rand-to-best/1 |  |