Interpolation Based Mutation Variants of Differential Evolution

2. The Basic De

Differential evolution algorithm a simple, powerful and iteration based search technique for global optimization. It starts with a set of solution, which is randomly generated when no preliminary knowledge about the solution space is available. This set of solution is called population. Let P^G={X_i^G, i=1,2,...NP} be the population at any generation G which contain NP individuals and an individual X_i^G can be defined as a D dimensional vector i.e., X_i^G =(x_1,i^G_,, x_2,i^G…, x_D,i^G). For basic DE (DE/rand/1/bin) mutation, crossover and selection operations are defined as:

• Mutation: For each target vector X_i,^G mutant vector V_i^G is defined by:

  
  (1)

Some other mutation variants are given as:

Where are randomly chosen integers, distinct from each other and also different from the running index i. F is a real and constant factor having value between [0, 2] and controls the amplification of differential variation (X_r2^G – X_r3^G).

• Crossover: Crossover is introduced to increase the diversity of perturbed parameter vectors V_i^G ={v_1,i^G, v_2,i^G …v_D,i^G}.