Mutation of Chromosomes

The mutation, defined as random change of chromosomes, is the most essential part of an evolutionary algorithm. If a chromosome is mutated one value of the vector 1...n of the chromosome is slightly changed. To give the overall algorithm a direction in searching for the optimum, the maximum change each generation of a value must be limited. Each generation a chromosome's value can only be changed by a value defined by its maximum change parameter defined by the interval of the -cut level of each fuzzy value. Mutation generates a random value from the interval

$[-\text{maximum change parameter},\text{maximum change parameter}]$.

Without maximum change parameter, there is a big risk that the process is not settling at all; not finding any optimum. Each value of the chromosome has its own maximum change parameter.

A mutation strength has been defined to set the effective maximum change parameter during the optimum process. The mutation strength defines the percentage of the maximum change parameter used in each generation. If the mutation strength is $80\%$ the interval for picking the random value to change the chromosome value is

$[-0.8*\text{maximum change parameter},0.8*\text{maximum change parameter}]$.

This enables the evolutionary algorithm to adapt mutation. At the beginning of the optimum process the mutation strength is high to avoid getting stuck at local optimum.

To automate the adaptation of the mutation strength Rechenberg's $\frac{1}{5}$-Rule-of-Success as stated in [7] has been applied. $\frac{1}{5}$-Rule-of-Success is defined as:

$\frac{1}{5}$ of the mutated children must be better then the parents otherwise the mutation strength must be adapted. If more than $\frac{1}{5}$ of the mutated children are better than their parents, the mutation strength is increased. If less than $\frac{1}{5}$ of the mutated children are better than their parents, the mutation strength is decreased.

Nonetheless a mutation rate is needed to state the overall number of mutations that each generation could occur.