gena.mutation {gena}

Mutation

Description

Mutation method (algorithm) to be used in the genetic algorithm.

Usage

gena.mutation(
  children,
  lower,
  upper,
  prob = 0.2,
  prob.genes = 1/nrow(children),
  method = "constant",
  par = 1,
  iter = NULL
)

Arguments

children

numeric matrix which rows are children i.e. vectors of parameters values.

lower

lower bound of the search space.

upper

upper bound of the search space.

prob

probability of mutation for a child.

prob.genes

numeric vector or numeric value representing the probability of mutation of a child's gene. See 'Details'.

method

mutation method to be used for transforming genes of children.

par

additional parameters to be passed depending on the method.

iter

iteration number of the genetic algorithm.

Details

Denote children by C^{child} which i-th row children[i, ] is a chromosome c_{i}^{child} i.e. the vector of parameter values of the function being optimized f(.) that is provided via fn argument of gena. The elements of chromosome c_{ij}^{child} are genes representing parameters values.

Mutation algorithm determines random transformation of children's genes. Each child may be selected for mutation with probability prob. If i-th child is selected for mutation and prob.genes is a vector then j-th gene of this child is transformed with probability prob.genes[j]. If prob.genes is a constant then this probability is the same for all genes.

Argument method determines particular mutation algorithm to be applied. Denote by \tau the vector of parameters used by the algorithm. Note that \tau corresponds to par. Also let's denote by c_{ij}^{mutant} the value of gene c_{ij}^{child} after mutation.

If method = "constant" then c_{ij}^{mutant} is a uniform random variable between lower[j] and upper[j].

If method = "normal" then c_{ij}^{mutant} equals to the sum of c_{ij}^{child} and normal random variable with zero mean and standard deviation par[j]. By default par is identity vector of length ncol(children) so par[j] = 1 for all j.

If method = "percent" then c_{ij}^{mutant} is generated from c_{ij}^{child} by equiprobably increasing or decreasing it by q percent, where q is a uniform random variable between 0 and par[j]. Note that par may also be a constant then all genes have the same maximum possible percentage change. By default par = 20.

For more information on mutation algorithms please see Patil, Bhende (2014).

Value

The function returns a matrix which rows are children (after mutation has been applied to some of them).

References

S. Patil, M. Bhende. (2014). Comparison and Analysis of Different Mutation Strategies to improve the Performance of Genetic Algorithm. International Journal of Computer Science and Information Technologies, 5 (3), 4669-4673.

Examples

# Randomly initialize some children
set.seed(123)
children.n <- 10
children <- gena.population(pop.n = children.n,
                            lower = c(-5, -5), 
                            upper = c(5, 5))
                           
# Perform the mutation
mutants <- gena.mutation(children = children,
                         prob = 0.6,
                         prob.genes = c(0.7, 0.8),
                         par = 30,
                         method = "percent")
print(mutants)