DE {metaheuristicOpt}

Optimization using Differential Evolution Algorithm

Description

This is the internal function that implements Differential Evolution Algorithm. It is used to solve continuous optimization tasks. Users do not need to call it directly, but just use metaOpt.

Usage

DE(FUN, optimType = "MIN", numVar, numPopulation = 40, maxIter = 500,
  rangeVar, scalingVector = 0.8, crossOverRate = 0.5,
  strategy = "best 1")

Arguments

FUN

an objective function or cost function

optimType

a string value that represent the type of optimization. There are two option for this arguments: "MIN" and "MAX". The default value is "MIN", which the function will do minimization. Otherwise, you can use "MAX" for maximization problem. The default value is "MIN".

numVar

a positive integer to determine the number variables.

numPopulation

a positive integer to determine the number populations. The default value is 40.

maxIter

a positive integer to determine the maximum number of iterations. The default value is 500.

rangeVar

a matrix (2 \times n) containing the range of variables, where n is the number of variables, and first and second rows are the lower bound (minimum) and upper bound (maximum) values, respectively. If all variable have equal upper bound, you can define rangeVar as matrix (2 \times 1).

scalingVector

a positive numeric between 0 and 1 to determine scalingVector for mutation operator. The default value is 0.8.

crossOverRate

a positive numeric between 0 and 1 to determine crossOver probability. The default value is 0.5.

strategy

characters to determine mutation method. They are six methods to choose:

• "classical".

• "best 1"

• "target to best"

• "best 2"

• "rand 2"

• "rand 2 dir"

details of the mutation methods are on the references. The default value is "best 1".

Details

This Differential Evolution algorithm based on jurnal by (Das & Suganthan, 2011). Differential Evolution algorithm use genetic operator for optimization such as mutation, crossover and selection.

In order to find the optimal solution, the algorithm follow the following steps.

• initialize population randomly.

• create some mutation vectors as new candidate solutions (mutation operator).

• perform crossover operator.

• perform selection operator.

• If a termination criterion (a maximum number of iterations or a sufficiently good fitness) is met, exit the loop, else back to create some mutation vector.

Value

Vector [v1, v2, ..., vn] where n is number variable and vn is value of n-th variable.

References

Das, S., & Suganthan, P. N. (2011). Differential evolution: A survey of the state-of-the-art. IEEE transactions on evolutionary computation, 15(1), 4-31.

See Also

metaOpt

Examples

##################################
## Optimizing the step function

# define step function as objective function
step <- function(x){
    result <- sum(abs((x+0.5))^2)
    return(result)
}

## Define parameter
numVar <- 5
rangeVar <- matrix(c(-100,100), nrow=2)

## calculate the optimum solution using differential evolution
resultDE <- DE(step, optimType="MIN", numVar, numPopulation=20,
                 maxIter=100, rangeVar)

## calculate the optimum value using step function
optimum.value <- step(resultDE)