restartOpt: Restart an Optimisation Algorithm

In NMOF: Numerical Methods and Optimization in Finance

Description

The function provides a simple wrapper for the optimisation algorithms in the package.

Usage

restartOpt(fun, n, OF, algo, ...,
           method = c("loop", "multicore", "snow"),
           mc.control = list(), cl = NULL,
           best.only = FALSE)

Arguments

fun	the optimisation function: DEopt, GAopt, LSopt, TAopt or PSopt
n	the number of restarts
OF	the objective function
algo	the list algo that is passed to the particular optimisation function
...	additional data that is passed to the particular optimisation function
method	can be loop (the default), multicore or snow. See Details.
mc.control	a list containing settings that will be passed to mclapply if method is multicore. Must be a list of named elements. See the documentation of mclapply.
cl	default is NULL. If method snow is used, this must be a cluster object or an integer (the number of cores).
best.only	if TRUE, only the best run is reported. Default is FALSE.

Details

The function returns a list of lists. If a specific starting solution is passed, all runs will start from this solution. If this is not desired, initial solutions can be created randomly. This is done per default in DEopt, GAopt and PSopt, but LSopt and TAopt require to specify a starting solution.

In case of LSopt and TAopt, the passed initial solution algo$x0 is checked with is.function: if TRUE, the function is evaluated in each single run. For DEopt, GAopt and PSopt, the initial solution (which also can be a function) is specified with algo$initP.

The argument method determines how fun is evaluated. Default is loop. If method is "multicore", function mclapply from package parallel is used. Further settings for mclapply can be passed through the list mc.control. If multicore is chosen but the functionality is not available, then method will be set to loop and a warning is issued. If method == "snow", function clusterApply from package snow is used. In this case, the argument cl must either be a cluster object (see the documentation of clusterApply) or an integer. If an integer, a cluster will be set up via makeCluster(c(rep("localhost", cl)), type = "SOCK"), and stopCluster is called when the function is exited. If snow is chosen but the package is not available or cl is not specified, then method will be set to loop and a warning is issued. In case that cl is an cluster object, stopCluster will not be called automatically.

Value

If best.only is FALSE (the default), the function returns a list of n lists. Each of the n lists stores the output of one of the runs.

If best.only is TRUE, only the best restart is reported. The returned list has the structure specific to the used method.

Author(s)

Enrico Schumann

References

Gilli, M., Maringer, D. and Schumann, E. (2011) Numerical Methods and Optimization in Finance. Elsevier. http://www.elsevierdirect.com/product.jsp?isbn=9780123756626

Schumann, E. (2012) The NMOF Manual. http://enricoschumann.net/NMOF.htm

See Also

DEopt, GAopt, LSopt, PSopt, TAopt

Examples

## see example(DEopt)
algo <- list(nP = 50L,
              F = 0.5,
             CR = 0.9,
            min = c(-10, -10),
            max = c( 10,  10),
    printDetail = FALSE,
       printBar = FALSE)

## choose a larger 'n' when you can afford it
algo$nG <- 100L
res100 <- restartOpt(DEopt, n = 5L, OF = tfTrefethen, algo = algo)
res100F <- sapply(res100, `[[`, "OFvalue")

algo$nG <- 200L
res200 <- restartOpt(DEopt, n = 5L, OF = tfTrefethen, algo = algo)
res200F <- sapply(res200, `[[`, "OFvalue")

xx <- pretty(c(res100F, res200F, -3.31))
plot(ecdf(res100F), main = "optimum is -3.306",
     xlim = c(xx[1L], tail(xx, 1L)))
abline(v = -3.3069, col = "red")  ## optimum
lines(ecdf(res200F), col = "blue")
legend(x = "right", box.lty = 0, , lty = 1,
      legend = c("optimum", "100 generations", "200 generations"),
      pch = c(NA, 19, 19), col = c("red", "black", "blue"))

## a 'best-of-N' strategy: given a sample x of objective
## function values, compute the probability that, after N draws,
## we have at least one realisation not worse than X
x <- c(0.1,.3,.5,.5,.6)
bestofN <- function(x, N) {
    nx <- length(x)
    function(X)
        1 - (sum(x > X)/nx)^N
}
bestof2 <- bestofN(x, 2)
bestof5 <- bestofN(x, 5)
bestof2(0.15)
bestof5(0.15)


## Not run: 
## with R >= 2.13.0 and the compiler package
algo$nG <- 100L
system.time(res100 <- restartOpt(DEopt, n = 10L, OF = tfTrefethen, algo = algo))

require("compiler")
enableJIT(3)
system.time(res100 <- restartOpt(DEopt, n = 10L, OF = tfTrefethen, algo = algo))

## End(Not run)

NMOF documentation built on May 2, 2019, 6:39 p.m.