WOA: Optimization using Whale Optimization Algorithm
In metaheuristicOpt: Metaheuristic for Optimization

Description Usage Arguments Details Value References See Also Examples

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

1 2	WOA(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, 2016), which mimics the social behavior of humpback whales. The algorithm is inspired by the bubble-net hunting strategy.

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

Initialization: Initialize the first population of whale randomly, calculate the fitness of whale and find the best whale position as the best position obtained so far.
Update Whale Position: Update the whale position using bubble-net hunting strategy. The whale position will depend on the best whale position obtained so far. Otherwise random whale choosen if the specific condition meet.
Update the best position if there are new whale that have better fitness
Check termination criteria, if termination criterion is satisfied, return the best position as the optimal solution for given problem. Otherwise, back to Update Whale Position steps.

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

Seyedali Mirjalili, Andrew Lewis, The Whale Optimization Algorithm, Advances in Engineering Software, Volume 95, 2016, Pages 51-67, ISSN 0965-9978, https://doi.org/10.1016/j.advengsoft.2016.01.008

metaOpt

##################################
## Optimizing the sphere function

# define sphere function as objective function
sphere <- function(x){
    return(sum(x^2))
}

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

## calculate the optimum solution using Ant Lion Optimizer
resultWOA <- WOA(sphere, optimType="MIN", numVar, numPopulation=20,
                 maxIter=100, rangeVar)

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