crs2lm {nloptr}

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 be 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 Hartmann 6-Dimensional function
## See https://www.sfu.ca/~ssurjano/hart6.html

a <- c(1.0, 1.2, 3.0, 3.2)
A <- matrix(c(10,  0.05, 3, 17,
              3, 10, 3.5, 8,
              17, 17, 1.7, 0.05,
              3.5, 0.1, 10, 10,
              1.7, 8, 17, 0.1,
              8, 14, 8, 14), nrow = 4)

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)

hartmann6 <- function(x, a, A, B) {
  fun <- 0
  for (i in 1:4) {
    fun <- fun - a[i] * exp(-sum(A[i, ] * (x - B[i, ]) ^ 2))
  }

  fun
}

## The function has a global minimum of -3.32237 at
## (0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573)

S <- crs2lm(x0 = rep(0, 6), hartmann6, lower = rep(0, 6), upper = rep(1, 6),
            ranseed = 10L, nl.info = TRUE, xtol_rel=1e-8, maxeval = 10000,
            a = a, A = A, B = B)

S