nloptr: crs2lm – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

crs2lm

Controlled Random Search

Description

The Controlled Random Search (CRS) algorithm (and in particular, the CRS2 variant) with the ‘local mutation’ modification.

Usage

crs2lm(x0, fn, lower, upper, maxeval = 10000, pop.size = 10 *
  (length(x0) + 1), ranseed = NULL, xtol_rel = 1e-06,
  nl.info = FALSE, ...)

Arguments

`x0`	initial point for searching the optimum.
`fn`	objective function that is to be minimized.
`lower, upper`	lower and upper bound constraints.
`maxeval`	maximum number of function evaluations.
`pop.size`	population size.
`ranseed`	prescribe seed for random number generator.
`xtol_rel`	stopping criterion for relative change reached.
`nl.info`	logical; shall the original NLopt info been shown.
`...`	additional arguments passed to the function.

Details

The CRS algorithms are sometimes compared to genetic algorithms, in that they start with a random population of points, and randomly evolve these points by heuristic rules. In this case, the evolution somewhat resembles a randomized Nelder-Mead algorithm.

The published results for CRS seem to be largely empirical.

Value

List with components:

`par`	the optimal solution found so far.
`value`	the function value corresponding to `par`.
`iter`	number of (outer) iterations, see `maxeval`.
`convergence`	integer code indicating successful completion (> 0) or a possible error number (< 0).
`message`	character string produced by NLopt and giving additional information.

Note

The initial population size for CRS defaults to 10x(n+1) in n dimensions, but this can be changed; the initial population must be at least n+1.

References

W. L. Price, “Global optimization by controlled random search,” J. Optim. Theory Appl. 40 (3), p. 333-348 (1983).

P. Kaelo and M. M. Ali, “Some variants of the controlled random search algorithm for global optimization,” J. Optim. Theory Appl. 130 (2), 253-264 (2006).

Examples

### Minimize the Hartmann6 function
hartmann6 <- function(x) {
    n <- length(x)
    a <- c(1.0, 1.2, 3.0, 3.2)
    A <- matrix(c(10.0,  0.05, 3.0, 17.0,
                   3.0, 10.0,  3.5,  8.0,
                  17.0, 17.0,  1.7,  0.05,
                   3.5,  0.1, 10.0, 10.0,
                   1.7,  8.0, 17.0,  0.1,
                   8.0, 14.0,  8.0, 14.0), nrow=4, ncol=6)
    B  <- matrix(c(.1312,.2329,.2348,.4047,
                   .1696,.4135,.1451,.8828,
                   .5569,.8307,.3522,.8732,
                   .0124,.3736,.2883,.5743,
                   .8283,.1004,.3047,.1091,
                   .5886,.9991,.6650,.0381), nrow=4, ncol=6)
    fun <- 0.0
    for (i in 1:4) {
        fun <- fun - a[i] * exp(-sum(A[i,]*(x-B[i,])^2))
    }
    return(fun)
}

S <- mlsl(x0 = rep(0, 6), hartmann6, lower = rep(0,6), upper = rep(1,6),
            nl.info = TRUE, control=list(xtol_rel=1e-8, maxeval=1000))
## Number of Iterations....: 4050
## Termination conditions:  maxeval: 10000	xtol_rel: 1e-06
## Number of inequality constraints:  0
## Number of equality constraints:    0
## Optimal value of objective function:  -3.32236801141328
## Optimal value of controls:
##     0.2016893 0.1500105 0.4768738 0.2753326 0.3116516 0.6573004

nloptr

R Interface to NLopt

v1.2.2.2

LGPL-3

Authors

Jelmer Ypma [aut, cre], Steven G. Johnson [aut] (author of the NLopt C library), Hans W. Borchers [ctb], Dirk Eddelbuettel [ctb], Brian Ripley [ctb] (build process on multiple OS), Kurt Hornik [ctb] (build process on multiple OS), Julien Chiquet [ctb], Avraham Adler [ctb] (removal deprecated calls from tests, <https://orcid.org/0000-0002-3039-0703>)

Initial release

2020-07-02