During the execution of the search process, the whole populations are classified into subgroups by sufficiently analyzed the individuals' state. Each individual in a different subset is assigned to the appropriate attribute (probabilities of crossover and mutation, pc,

pm). Self-adaptive update the subgroups and adjust the control parameters, which are considered to be an optimal balance between exploration and exploitation. The empirical values and negative feedback technique are also used in parameters selection, which relieve the burden of specifying the parameters values. The new method is tested on a set of well-known benchmark test functions.

1. Randomly select an initial population.

2. Dynamically classify the population into subgroups. The individuals will be divided into three categories good, moderate and bad according to their fitness value.

3. Adaptively adjust the parameters. The probability of crossover and mutation are also classified in three ranks according to the categories of individuals. To different subgroups, different values of pc and pm are assigned to the relative elements. The pc and pm of an individual classified as "bad" is randomly chosen at a relative high level. The pc and pm of an individual classified as "good" is randomly chosen at a relative low level. The medium subgroup keeps the balance between exploration and exploitation so the parameters of crossover and mutation are distributed at a moderate range.

4.  The parameters should be adjusted using the negative feedback technique.

pm,g+1 =

pm,g + rand (0, 1) · (pm,max - pm,g)

ifmeanfitg ≥ meanfitg-1

pm,min + rand (0, 1) · (pm,g - pm,min)

otherwise

pc,g+1 =

pc,g + rand (0, 1) · (pc,max - pc,g)

ifmeanfitg ≥ meanfitg-1

pc,min + rand (0, 1) · (pc,g - pc,min)

otherwise

Calculate the difference of the mean value of the successive generation, if the difference greater than or equal to zero that means the searching result deteriorated, new probabilities of crossover and mutation should be increased, otherwise the probabilities should be decreased. Update the population by the adaptive adjust parameters until the termination criteria satisfy.

5.Framework of the Simple Adaptive GA

Initialize population randomly

Classify into 3 subgroups according to the fitness

For 3 groups of individuals, randomly choose pc, pm from relative range of crossover and mutation probabilities to be applied

Evaluate fitness

Do

Sort population by fitness and classify

Renew the operating factors

Evaluate fitness in changed genotypes

Until termination criteria

6. Simulation using bench mark functions

Function Names: Sphere, Schwefel 1.2, Schwefel 2.21, Rosenbrock, Griewank, Ackley, Penalty 1 and Penalty 2

Function Name  Unimodal /Multimodal   Separable/Nonseparable     Regular/irregular

Sphere                         unimodal                     separable                              regular

Schwefel 1.2               unimodal                     nonseparable                           regular

Schwefel 2.21             unimodal                     nonseparable                           irregular

Rosenbrock                 unimodal                     nonseparable                           regular

Griewank                    multimodal                  nonseparable                           regular

Ackley                         multimodal                  nonseparable                           regular

Penalty 1                     multimodal                  nonseparable                           regular

Penalty 2                     multimodal                  nonseparable                           regular