Crossover and mutation perform two different roles. Crossover (like selection) is a convergence operation which is intended to pull the population towards a local minimum/maximum. In an interesting aside, crossover is not one of the original genetic operators; Holland's original thesis used only selection and probabilistic mutation.

Mutation is a divergence operation. It is intended to occasionally break one or more members of a population out of a local minimum/maximum space and potentially discover a better minimum/maximum space.

Since the end goal is to bring the population to convergence, selection/crossover happen more frequently (typically every generation). Mutation, being a divergence operation, should happen less frequently, and typically only effects a few members of a population (if any) in any given generation.

See http://www.ai-junkie.com/ga/intro/gat1.html

http://www.obitko.com/tutorials/genetic-algorithms/

Basically, crossover and mutation is the process which enables the solution to the problem to be found. New solutions are found from old solutions by the process of crossover and mutation, much like what happens in nature with chromosomes. So, new solutions are the offspring of the old solutions or the children of the old solutions.

So how mutations or crossover is carried out depends on the how the problem is set up which determines the type of chromosome that is chosen to code the problem.

See http://bb.vu.nl/bbcswebdav/courses/FEW_X_400111_2011_110/FEW_X_400111_2011_110_ImportedContent_20110830013034/03-Genetic_Algorithms-pdf.pdf

Mutation maintains genetic diversity in the subsequent generations  which means that you avoid premature convergence on a local maximum or minimum. Too high a mutation probability means that convergence is slow or it does not occur. It is possible to set up an adaptive process for altering the crossover and mutation probabilities depending on the genetic diversity in the population.

See https://www.ee.iitb.ac.in/uma/~rajesht/genetic/gen_improv.pdf.gz

Crossover and mutation perform two different roles. Crossover (like selection) is a convergence operation which is intended to pull the population towards a local minimum/maximum. In an interesting aside, crossover is not one of the original genetic operators; Holland's original thesis used only selection and probabilistic mutation.

Mutation is a divergence operation. It is intended to occasionally break one or more members of a population out of a local minimum/maximum space and potentially discover a better minimum/maximum space.

Since the end goal is to bring the population to convergence, selection/crossover happen more frequently (typically every generation). Mutation, being a divergence operation, should happen less frequently, and typically only effects a few members of a population (if any) in any given generation.

So concerning the probability, the crossover probability is the probability of a selected individual to go through a crossover process (with another selected individual). There is, before this step, a selection process (many possibilities: roulette wheel, tournament, etc...) to select the individuals that will go through genetic operations.

The same process is applied for mutation and simple reproduction.

I'm glad to see so many good explanations about this issue. My two cents: take a look at the Prof. Pier Luca Lanzi's course notes http://www.pierlucalanzi.net/#!/genetic-algorithms/ where you could find the theory behind selectorecombinative GA's and why these operators work the way they work. Another good read is in Prof. David Goldberg's "The design of innovation" book (a bit advanced though).

these are operators that make adversity in searching the solution space . bye these operation you can both explore and exploit the search space

dear friend

Greetings.

The role of mutation and crossover are as follows:

1. To generate new offsprings that helps to find new solutions.

2. To simulate the nature's laws of origin and adaptation to the environment.

3. it is nature inspired computing.

4. It is helpful to solve problems where there is no idea of the solution of the problems.

Dear friend I hope it helps you.

Have a great day. Happy dussera.

Best regards

Dr. Indrajit Mandal

Most people above have given excellent answers to your questions. I would like to add an interesting - although contested - theory that humans may have evolved due to a random mutation in the mitochondria of jaw muscles in apes. This resulted in the shrinkage of jaw muscle size in apes which cause the ridge line (where jaw muscle connects to skull) to reduce in length. This allowed the increase in cranial size and thus in the size of the brain to make us smart! This is how sometime mutation can be helpful in giving a good solution to the GA.

Consider Crossover and mutation two genetic operators very important, but if you need more robust your algorithm is very important using a third operator named "Migration", because is technique will be move to another part of population many individuals or "solutions issues" to diversify the population. If research with Cultural Algorithms and this concept is very important.

The previous answers provide good explanations on what crossover and mutation probabilirties do in a Genetic Algorithm (GA). When you design a GA for a new/specific problem you could start using probability settings from a similar problem. The purpose always is to find a set up that converges and sufficiently diversifies to find the global optimum for a problem.

A simple way to think about  this: Crossover facilitates inheritance of "characteristics"  or "traits" by an offspring from its parents. Mutation allows the development of un-inherited characteristics --- it promoted diversity by allowing an offspring to also evolve in ways not solely determined by inherited traits. 

Crossover is used to create new solutions from population's genetic information and mutation is used to introduce new genetic information. Thus, crossover probability modules the convergence over a local optimum and mutation is used to add new genetic information (divergence) in order to perform a global search over the solution space and avoid to get stuck in local optima.

My question with respective of implementation.  If I represent chromosome as array of integers what is the use of probability.

The probability of crossover is the probability of using crossover for creating a new chromosome (if you don't use crossover you can just make a copy of an existing chromosome or use mutation only).

The probability of mutation, Pm,  is the probability of modifying an integer of the array. Then each integer has a probability Pm of being changed (for example adding a small integer or replacing it by another random integer).

thank you!

Nice contribuition there!

In fact, I could agree with most of these posts but I think that some refinements are needed. Genetic algorithms are some models of creative processes in virtual reality. In general,

“Creative Process Operator”, are C = R + S,

here

R (Rotations) – the rotational synthesis of informational structures;

S (Selection) – the selection of informational structures (based on principle of harmony and beauty).

Genetic algorithms: R – “genetic operators” (crossover, point mutation, inversion), that create new variants of the solution; the process is completely analogous to the functioning of biological genetic operators. S – automated selection of “virtual descendants” based on “cost function”, that corresponds to “natural selection” in the Nature.  The action of the operators of crossover and point mutation are different as noted in above comments. I should also mention that in terms of biology - crossover combines already had ordered genome fragments and mutations  - create  new genes. 

https://www.researchgate.net/publication/244995094_Theory_of_Creative_Processes_as_a_Scientific_Basis_of_Biocentrism_in_ECO-_And_Bioethics_%28in_RussianEnglish%29                                      

As for the genetic algorithms, I would like to recommend recursive to solving complex problems.

https://www.researchgate.net/publication/262686057_RECURSIVE_GENETIC_ALGORITHM_FOR_SOVING_THE_TRAVELING_SALESMAN_PROBLEM

Article Theory of Creative Processes as a Scientific Basis of Biocen...

Article RECURSIVE GENETIC ALGORITHM FOR SOVING THE TRAVELING SALESMAN PROBLEM

I am wondering is the input data affect the selection crossover mutation process? and how?

Any idea how can i implement the genetic algorithm in MATLAB?

https://www.mathworks.com/help/gads/how-the-genetic-algorithm-works.html?requestedDomain=www.mathworks.com

I agree with Ferran Torrent Fontbona and Ram pakath.

What does high (95%) of cross over ratio reflect ?

Based on the fitment factor, you select the most probable chromosome( which are set of points near maxima/minima in the global space). Thus good chromosome are mutated (as they have high probability to be selected) and achieve offspring which is better than their parents i.e. in a way you are converging to the local minima/maxima of the selected chromosome. Mutation(Pm) is harm full in real biology thats why in this algorithm also it is given very less probability and it is used for not getting trapped into local minima/maxima.

@vivek Saxena, Thanks a lot.

The mutation is more an inner individual perturbation looking to explore a local space of solution, instead, the crossover looks for a wider range of solution due to take more than one individual an interchange information between them.