Contributions to Dynamic Analysis of Differential Evolution Algorithms
针对差分进化算法，推导了在球面目标函数下个体改进概率的解析表达式，并通过数值实验验证，用于分析种群动态和参数选择的影响。
The Differential Evolution (DE) algorithm is one of the most successful evolutionary computation techniques. However, its structure is not trivially translatable in terms of mathematical transformations that describe its population dynamics. In this work, analytical expressions are developed for the probability of enhancement of individuals after each application of a mutation operator followed by a crossover operation, assuming a population distributed radially around the optimum for the sphere objective function, considering the DE/rand/1/bin and the DE/rand/1/exp algorithm versions. These expressions are validated by numerical experiments. Considering quadratic functions given by f(x)=xTDTDx and populations distributed according to the linear transformation D-1 of a radially distributed population, it is also shown that the expressions still hold in the cases when f(x) is separable (D is diagonal) and when D is any nonsingular matrix and the crossover rate is Cr=1.0. The expressions are employed for the analysis of DE population dynamics. The analysis is extended to more complex situations, reaching rather precise predictions of the effect of problem dimension and of the choice of algorithm parameters.