deoptimr

Description

This package is part of the R Optimization Infrastructure ROI

References

Babu, B. V. and Angira, R. (2006) Modified differential evolution (MDE) for optimization of non-linear chemical processes. Computers and Chemical Engineering 30, 989–1002.

Brest, J., Greiner, S., Boskovic, B., Mernik, M. and Zumer, V. (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Transactions on Evolutionary Computation 10, 646–657.

Lampinen, J. and Zelinka, I. (1999). Mechanical engineering design optimization by differential evolution; in Corne, D., Dorigo, M. and Glover, F., Eds., New Ideas in Optimization. McGraw-Hill, pp. 127–146.

Price, K. V., Storn, R. M. and Lampinen, J. A. (2005) Differential Evolution: A practical approach to global optimization. Springer, Berlin, pp. 117–118.

Storn, R. (2008) Differential evolution research — trends and open questions; in Chakraborty, U. K., Ed., Advances in differential evolution. SCI 143, Springer-Verlag, Berlin, pp. 11–12.

Storn, R. and Price, K. (1997) Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11, 341–359.

Wu, G., Pedrycz, W., Suganthan, P. N. and Mallipeddi, R. (2015) A variable reduction strategy for evolutionary algorithms handling equality constraints. Applied Soft Computing 37, 774–786.

Zhang, H. and Rangaiah, G. P. (2012) An efficient constraint handling method with integrated differential evolution for numerical and engineering optimization. Computers and Chemical Engineering 37, 74–88.

Zielinski, K. and Laur, R. (2008) Stopping criteria for differential evolution in constrained single-objective optimization; in Chakraborty, U. K., Ed., Advances in differential evolution. SCI 143, Springer-Verlag, Berlin, pp. 111–138.

See Also

Function JDEoptim() in the DEoptimR package.

Banana

Description

The following example is also known as Rosenbrock's banana function (https://en.wikipedia.org/wiki/Rosenbrock_function).

minimize \ f(x) = 100 (x_2 - x_1^2)^2 + (1 - x_1)^2

Solution: c(1, 1)

Examples

Sys.setenv(ROI_LOAD_PLUGINS = FALSE)
library(ROI)
library(ROI.plugin.deoptim)


f <- function(x) {
    return( 100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2 )
}

x <- OP( objective = F_objective(f, n=2L, names=c("x_1", "x_2")), 
         bounds = V_bound(li=1:2, ui=1:2, lb=c(-3, -3), ub=c(3,  3)) )

nlp <- ROI_solve(x, solver = "deoptim")
nlp
## Optimal solution found.
## The objective value is: 3.828383e-22
solution(nlp)
## x_1 x_2 
##   1   1 

Hock-Schittkowski-Collection Problem 16

Description

The following example solves problem 16 from the Hock-Schittkowski-Collection.

minimize \ f(x) = 100 (x_2 - x_1^2)^2 + (1 - x_1)^2

subject \ to: \ \ x_1 + x_2^2 \geq 0 \ \ \ x_1^2 + x_2 \geq 0

-2 \geq x_1 \geq 0.5 \ \ \ x_2 \geq 1

Solution: c(0.5, 0.25)

Examples

Sys.setenv(ROI_LOAD_PLUGINS = FALSE)
library(ROI)
library(ROI.plugin.deoptim)

f <- function(x) {
    return( 100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2 )
}

f.gradient <- function(x) {
    return( c( -400 * x[1] * (x[2] - x[1] * x[1]) - 2 * (1 - x[1]),
               200 * (x[2] - x[1] * x[1])) )
}

x <- OP( objective = F_objective(f, n=2L, G=f.gradient), 
         constraints = c(F_constraint(F=function(x) x[1] + x[2]^2, ">=", 0,
                                      J=function(x) c(1, 2*x[2])),
                         F_constraint(F=function(x) x[1]^2 + x[2], ">=", 0,
                                      J=function(x) c(2*x[1], x[2]))),
         bounds = V_bound(li=1:2, ui=1:2, lb=c(-2, -Inf), ub=c(0.5,  1)) )

nlp <- ROI_solve(x, solver="deoptimr", start=c(0.4, 0.3))
nlp
## Optimal solution found.
## The objective value is: 2.499999e-01
solution(nlp)
## [1] 0.5000001 0.2499994

Hock-Schittkowski-Collection Problem 36

Description

The following example solves exmaple 36 from the Hock-Schittkowski-Collection.

minimize \ -x_1 x_2 x_3

subject \ to: \ x_1 + 2 x_2 + x_3 \leq 72

0 \leq x_1 \leq 20, \ 0 \leq x_2 \leq 11, \ 0 \leq x_3 \leq 42

Examples

Sys.setenv(ROI_LOAD_PLUGINS = FALSE)
library(ROI)
library(ROI.plugin.deoptim)

hs036_obj <- function(x) {
    -x[1] * x[2] * x[3]
}

hs036_con <- function(x) {
    x[1] + 2 * x[2] + 2 * x[3]
}


x <- OP( objective = F_objective(hs036_obj, n = 3L), 
         constraints = F_constraint(hs036_con, "<=", 72),
         bounds = V_bound(ub = c(20, 11, 42)) )

nlp <- ROI_solve(x, solver = "deoptimr", start = c(10, 10, 10), 
                 max_iter = 2000)
nlp
## Optimal solution found.
## The objective value is: -3.300000e+03
solution(nlp, "objval")
## [1] -3300
solution(nlp)
## [1] 20 11 15