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+
+1. [Introduction](introduction.md)  
+2. [Fitness functions](fitness-functions.md)  
+3. [Encodings](encodings.md)  
+4. [Algorithms](algorithms.md)  
+5. **Genetic operators**  
+6. [Stop conditions](stop-conditions.md)  
+7. [Metrics](metrics.md)  
+8. [Miscellaneous](miscellaneous.md)
+
+------------------------------------------------------------------------------------------------
+
+# Genetic operators
+
+The genetic operators are used to create new candidate solutions from the existing
+ones in the population, thus providing the basic search mechanism of the genetic
+algorithms. The 2 main operators are the crossover and mutation, but the library
+also allows for specifying a repair function.
+
+The selection method is considered to be a part of the `Algorithm` in the library,
+so it will not be discussed here.
+
+The library contains implementations of several crossover and mutation methods
+that can be used. These can be found in the `gapp::crossover` and
+`gapp::mutation` namespaces respectively.
+
+As the genetic operators operate on candidate solutions, their
+implementations depend on the encoding type used for the GA. A given crossover or
+mutation method can only be used with the encoding types it is implemented for.
+Because of this, the implemented crossover and mutation methods are further broken
+up into multiple namespaces based on the encoding type they can be used with.
+For example, the crossover operators are in the following namespaces:
+
+ - `crossover::binary`
+ - `crossover::real`
+ - `crossover::perm`
+ - `crossover::integer`
+
+Crossover methods in the `binary` namespace can only be used for the `BinaryGA`,
+methods in the `real` namespace can only be used for the `RCGA`, and so on.
+The mutation methods are organized similarly.
+
+The library doesn't provide any repair functions since their use in the GAs
+is optional. These always have to be defined by the user when they are used.
+
+## Crossover
+
+The crossover operator is responsible for generating new solutions from existing
+ones. The operator takes 2 solutions selected from the population, and performs
+some operation on them with a given probability to generate 2 new solutions.
+When the operation is not performed, it returns copies of the parent solutions.
+
+The crossover operator used by the GA can be set either in the constructor or by
+using the `crossover_method` method:
+
+```cpp
+PermutationGA GA;
+GA.crossover_method(crossover::perm::Edge{});
+```
+
+The probability of performing the crossover operation is a general parameter
+of the crossovers and it can be set for all of the crossover operators either
+in their constructors or by using the `crossover_rate` method:
+
+```cpp
+PermutationGA GA;
+GA.crossover_method(crossover::perm::Edge{ /* crossover_rate = */ 0.8 });
+```
+
+The GA classes also provide a `crossover_rate` method that can be used to set
+the crossover probability for the current crossover operator used by the GA:
+
+```cpp
+PermutationGA GA;
+GA.crossover_method(crossover::perm::Edge{});
+GA.crossover_rate(0.8);
+```
+
+Some crossover operators may also have additional parameters that are specific
+to the given operator.
+
+## Mutation
+
+The mutation operator is applied to each of the solutions generated by the
+crossovers in order to promote diversity in the population. This help the GA
+with exploring more of the search space and avoiding convergence to local
+optima.
+
+The mutation operator used by the GAs can be set similar to the crossover operators,
+either in the constructor or by using the `mutation_method` method:
+
+```cpp
+RCGA GA;
+GA.mutation_method(mutation::real::NonUniform{});
+```
+
+Similar to the crossovers, the mutation operators also all have a
+mutation probability parameter, but how this probability is interpreted
+(either on a per-gene or per-solution basis) depends on the specific
+operator.
+
+The mutation probability can be set similar to the crossover probability, either
+in the constructor of the mutation operator, or by using the `mutation_rate`
+method:
+
+```cpp
+RCGA GA;
+GA.mutation_method(mutation::real::NonUniform{ /* mutation_rate = */ 0.1 });
+```
+
+The GA classes also provide a `mutation_rate` method that can be used to set
+the mutation probability for the current mutation operator of the GA:
+
+```cpp
+RCGA GA;
+GA.mutation_method(mutation::real::NonUniform{});
+GA.mutation_rate(0.1);
+```
+
+Similar to the crossovers, some mutation operators may have additional parameters
+that are specific to the particular operator.
+
+## Repair
+
+The repair function is an additional operator that will be applied to each
+solution after the mutations. Using a repair function is optional, and they are
+not used in the GAs by default.
+
+Repair functions can be specified using the `repair_function` method of the GAs:
+
+```cpp
+ga.repair_function([](const GA<RealGene>&, const Chromosome<RealGene>& chrom)
+{
+    auto new_chrom = chrom;
+    // do something with new_chrom ...
+    return new_chrom;
+});
+```
+
+If a repair function has been set previously, it can be cleared by passing
+a nullptr to the setter:
+
+```cpp
+GA.repair_function(nullptr);
+```
+
+## Custom genetic operators (crossover and mutation)
+
+In addition to the operators already implemented in the library,
+user defined crossover and mutation operators can also be used in the GAs.
+
+The simplest way to do this is to use a lambda function:
+
+```cpp
+RCGA ga;
+
+ga.crossover_method([](const GA<RealGene>&, const Candidate<RealGene>& parent1, const Candidate<RealGene>& parent2)
+{
+    auto child1 = parent1;
+    auto child2 = parent2;
+
+    // perform the crossover ...
+
+    return CandidatePair<RealGene>{ std::move(child1), std::move(child2) };
+});
+
+ga.mutation_method([](const GA<RealGene>& ga, const Candidate<RealGene>& sol, Chromosome<RealGene>& chrom)
+{
+    for (RealGene& gene : chrom)
+    {
+        if (rng::randomReal() < ga.mutation_rate())
+        {
+            // modify the gene ...
+        }
+    }
+});
+```
+
+Alternatively, crossover and mutation operators can also be implemented as
+classes derived from `crossover::Crossover<GeneType>` and
+`mutation::Mutation<GeneType>` respectively. Crossovers must implement the
+`crossover` method, while mutations must implement the `mutate` method:
+
+```cpp
+class MyCrossover : public crossover::Crossover<RealGene>
+{
+public:
+    using Crossover::Crossover;
+
+    CandidatePair<RealGene> crossover(const GA<RealGene>& ga, const Candidate<RealGene>& parent1, const Candidate<RealGene>& parent2) const override
+    {
+        // perform the crossover ...
+    }
+};
+```
+
+```cpp
+class MyMutation : public mutation::Mutation<RealGene>
+{
+public:
+    using Mutation::Mutation;
+
+    void mutate(const GA<RealGene>& ga, const Candidate<RealGene>& candidate, Chromosome<RealGene>& chromosome) const override
+    {
+        // perform the mutation on chromosome ...
+    }
+};
+```
+
+There are a few things that should be kept in mind for the implementations
+of these operators regardless of how they are defined:
+
+ - The crossover implementation shouldn't take the crossover rate into account.
+   This is done elsewhere.
+ - The mutation implementation must take the mutation rate into account, as how
+   the mutation rate is interpreted depends on the specific mutation method.
+ - The mutation modifies the `chrom` parameter, and does not return anything.
+ - The implementations should be thread-safe.
+
+------------------------------------------------------------------------------------------------