MDE: Modified DE

In FilippoPic/DEoptimPIC: DEoptimPIC provides some interesting tools and benchmark functions to test three different versions of the differential evolution algorithm

Description

Modified version of the DE algorithm, proposed by Zhu et al., for solving optimization problems with bound constraints, where the mutation strategy is randomly selected between DE/best/1 and DE/rand/1 with a probability that favours the first with the progress of the run of the algorithm.

Usage

MDE(funcname, lo, up, n, NP, n_gen, ...)

Arguments

funcname	function to optimize
lo	lower bound (same for each component of the vector x)
up	upper bound (same for each component of the vector x)
n	problem size
NP	population size (should be ~ four times the size of the problem)
n_gen	number of generations (~ ten times the value of NP)
...	parameters to pass at objective function to optimize

Details

This modified version selects two mutation strategies every generation:

• DE/best/1 with probability p1 = 1/(1+exp(-0.005*g))

• DE/rand/1 with probability 1-p1

Note that the probability for the strategy DE/best/1 increases as the generation counter does. This will favour this strategy with the run of the algorithm. Mutation factor F is selected from a Gaussian distribution with mean 0.6 and standard deviation 0.2. Of course negative values are not acceptable. The crossover rate is picked randomly from the range between 0.1 and 0.9.

Value

The output of the function DEbase is a list (of length 3) containing the following elements:

• f_best: the best value found by the algorithm for the last generation

• x_best: the vector which corresponds to the best overall function value

• f: the vector of the n_gen optimal values found by the algorithm at each generation

References

W. Zhu, Y. Tang, J. Fang, W. Zhang, Adaptive population tuning scheme for differential evolution. Information Sciences, vol. 223 n. 13, 2013, pp. 390–401.

S. Das, S. Mullick, P. N. Suganthan, Recent advances in differential evolution– an updated survey. Swarm and evolutionary computation, vol. 23, 2016, pp. 1–30

Examples

##implementation of the schwefel function
schwef <- function(x)
{
 if(is.vector(x))
 {
   d <- length(x)
   sum <- sum(x*sin(sqrt(abs(x))))
   y <- 418.9829*d - sum
   return(y)
 }
 if(is.matrix(x))
 {
   d <- ncol(x)
   sum <- apply(x*sin(sqrt(abs(x))),1,sum)
   y <- 418.9829*d - sum
   return(y)
 }
}
##application of DEbase function
set.seed(123)
d <- MDE(schwef,-500,500,10,40,400)

FilippoPic/DEoptimPIC documentation built on Feb. 14, 2022, 5:12 a.m.