crs2lm {nloptr} | R Documentation |
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 |
iter |
number of (outer) iterations, see |
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