# Mutation (genetic algorithm)

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Mutation is a genetic operator used to maintain genetic diversity from one generation of a population of genetic algorithm chromosomes to the next. It is analogous to biological mutation. Mutation alters one or more gene values in a chromosome from its initial state. In mutation, the solution may change entirely from the previous solution. Hence GA can come to a better solution by using mutation. Mutation occurs during evolution according to a user-definable mutation probability. This probability should be set low. If it is set too high, the search will turn into a primitive random search.

The classic example of a mutation operator involves a probability that an arbitrary bit in a genetic sequence will be changed from its original state. A common method of implementing the mutation operator involves generating a random variable for each bit in a sequence. This random variable tells whether or not a particular bit will be modified. This mutation procedure, based on the biological point mutation, is called single point mutation. Other types are inversion and floating point mutation. When the gene encoding is restrictive as in permutation problems, mutations are swaps, inversions, and scrambles.

The purpose of mutation in GAs is preserving and introducing diversity. Mutation should allow the algorithm to avoid local minima by preventing the population of chromosomes from becoming too similar to each other, thus slowing or even stopping evolution. This reasoning also explains the fact that most GA systems avoid only taking the fittest of the population in generating the next but rather a random (or semi-random) selection with a weighting toward those that are fitter.[1]

For different genome types, different mutation types are suitable:

• Bit string mutation
The mutation of bit strings ensue through bit flips at random positions.
Example:
 1 0 1 0 0 1 0 ↓ 1 0 1 0 1 1 0
The probability of a mutation of a bit is ${\displaystyle {\frac {1}{l}}}$, where ${\displaystyle l}$ is the length of the binary vector. Thus, a mutation rate of ${\displaystyle 1}$ per mutation and individual selected for mutation is reached.
• Flip Bit

This mutation operator takes the chosen genome and inverts the bits (i.e. if the genome bit is 1, it is changed to 0 and vice versa).

• Boundary

This mutation operator replaces the genome with either lower or upper bound randomly. This can be used for integer and float genes.

• Non-Uniform

The probability that amount of mutation will go to 0 with the next generation is increased by using non-uniform mutation operator. It keeps the population from stagnating in the early stages of the evolution. It tunes solution in later stages of evolution. This mutation operator can only be used for integer and float genes.

• Uniform

This operator replaces the value of the chosen gene with a uniform random value selected between the user-specified upper and lower bounds for that gene. This mutation operator can only be used for integer and float genes.

• Gaussian

This operator adds a unit Gaussian distributed random value to the chosen gene. If it falls outside of the user-specified lower or upper bounds for that gene, the new gene value is clipped. This mutation operator can only be used for integer and float genes.

• Shrink

This operator adds a random number taken from a Gaussian distribution with mean equal to the original value of each decision variable characterizing the entry parent vector. [2]

## References

1. ^ "XI. Crossover and Mutation". http://www.obitko.com/: Marek Obitko. Retrieved 2011-04-07.
2. ^ Claudio Comis Da Ronco, Ernesto Benini, A Simplex-Crossover-Based Multi-Objective Evolutionary Algorithm, IAENG Transactions on Engineering Technologies, Volume 247 of the series Lecture Notes in Electrical Engineering pp 583-598, 2013 https://link.springer.com/chapter/10.1007%2F978-94-007-6818-5_41