FFA {metaheuristicOpt}

Optimization using Firefly Algorithm

Description

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

Usage

FFA(FUN, optimType = "MIN", numVar, numPopulation = 40,
  maxIter = 500, rangeVar, B0 = 1, gamma = 1, alphaFFA = 0.2)

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).

B0

a positive integer to determine the attractiveness firefly at r=0. The default value is 1.

gamma

a positive integer to determine light absorption coefficient. The default value is 1.

alphaFFA

a positive integer to determine randomization parameter. The default value is 0.2.

Details

This algorithm was proposed by (Yang, 2009). The firefly algorithm (FFA) mimics the behavior of fireflies, which use a kind of flashing light to communicate with other members of their species. Since the intensity of the light of a single firefly diminishes with increasing distance, the FFA is implicitly able to detect local solutions on its way to the best solution for a given objective function.

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

• Initialization: Initialize the first population of fireflies randomly, calculate the fitness of fireflies and assumes fitness values as Light Intensity.

• Update the firefly position based on the attractiveness. The firefly that have higher light intensity will tend to attract other fireflies. The attracted firefly will move based on the parameter that given by user.

• Calculate the fitness and update the best firefly position.

• Check termination criteria, if termination criterion is satisfied, return the best position as the optimal solution for given problem. Otherwise, back to Update firefly position steps.

Value

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

References

X.-S. Yang, Firefly algorithms for multimodal optimization, in: Stochastic Algorithms: Foundations and Applications, SAGA 2009, Lecture Notes in Computer Sciences, Vol. 5792, pp. 169-178 (2009).

See Also

metaOpt

Examples

##################################
## Optimizing the quartic with noise function
# define Quartic with noise function as objective function
quartic <- function(x){
    dim <- length(x)
    result <- sum(c(1:dim)*(x^4))+runif(1)
    return(result)
}

## Define parameter
B0 <- 1
gamma <- 1
alphaFFA <- 0.2
numVar <- 5
rangeVar <- matrix(c(-1.28,1.28), nrow=2)

## calculate the optimum solution using Firefly Algorithm
resultFFA <- FFA(quartic, optimType="MIN", numVar, numPopulation=20,
                 maxIter=100, rangeVar, B0, gamma, alphaFFA)

## calculate the optimum value using sphere function
optimum.value <- quartic(resultFFA)