DA: Optimization using Dragonfly Algorithm
In metaheuristicOpt: Metaheuristic for Optimization

Description Usage Arguments Details Value References See Also Examples

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

1 2	DA(FUN, optimType = "MIN", numVar, numPopulation = 40, maxIter = 500, rangeVar)

`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).

This algorithm was proposed by (Mirjalili, 2015). The main inspiration of the DA algorithm originates from the static and dynamic swarming behaviours of dragonflies in nature. Two essential phases of optimization, exploration and exploitation, are designed by modelling the social interaction of dragonflies in navigating, searching for foods, and avoiding enemies when swarming dynamically or statistically.

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

Initialization: Initialize the first population of dragonflies randomly, calculate the fitness of dragonflies and find the best dragonfly as food source and the worst dragonfly as enemy position.
Calculating Behaviour Weight that affecting fly direction and distance. First, find the neighbouring dragonflies for each dragonfly then calculate the behaviour weight. The behaviour weight consist of separation, alignment, cohesion, attracted toward food sources and distraction from enemy. The neighbouring dragonfly determined by the neighbouring radius that increasing linearly for each iteration.
Update the position each dragonfly using behaviour weight and the delta (same as velocity in PSO).
Calculate the fitness and update food and enemy position
Check termination criteria, if termination criterion is satisfied, return the food position as the optimal solution for given problem. Otherwise, back to Calculating Behaviour Weight steps.

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

Seyedali Mirjalili. 2015. Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput. Appl. 27, 4 (May 2015), 1053-1073. DOI=https://doi.org/10.1007/s00521-015-1920-1

metaOpt

##################################
## Optimizing the schewefel's problem 1.2 function

# define schewefel's problem 1.2 function as objective function
schewefels1.2 <- function(x){
  dim <- length(x)
  result <- 0
    for(i in 1:dim){
       result <- result + sum(x[1:i])^2
   }
  return(result)
}

## Define parameter
numVar <- 5
rangeVar <- matrix(c(-10,10), nrow=2)

## calculate the optimum solution using dragonfly algorithm
resultDA <- DA(schewefels1.2, optimType="MIN", numVar, numPopulation=20,
                 maxIter=100, rangeVar)

## calculate the optimum value using schewefel's problem 1.2 function
optimum.value <- schewefels1.2(resultDA)