DEoptim {DEoptim} | R Documentation |
Performs evolutionary optimization via the Differential Evolution algorithm.
DEoptim(FUN, lower, upper, control = list(), ...)
FUN |
A function to be minimized, with first argument the vector
of parameters over which minimization is to take place. It should
return a scalar result. NA and NaN values are not allowed. |
lower, upper |
Bounds on the variables. |
control |
A list of control parameters. See *Details*. |
... |
Further arguments to be passed to FUN . |
DEoptim
performs minimization of FUN
.
The control
argument is a list that can supply any of
the following components:
VTR
itermax
is reached or the best parameter vector bestmem
has found a value
FUN(bestmem) <= VTR
. Default to -Inf
.itermax
200
.NP
50
.F
0.8
.CR
0.5
.initial
NULL
.storepopfrom
itermax+1
, i.e., no intermediate population is stored.storepopfreq
1
, i.e. every intermediate population is memorized.strategy
1
2
3
4
5
By default strategy
is 2
. See references below for details.
refresh
10
iterations.digits
A list of lists of the class DEoptim
.
list optim
contains the followings:
bestmem
: the best set of parameters found.
bestval
: the value of FUN
corresponding to bestmem
.
nfeval
: number of function evaluations.
iter
: number of procedure iterations.
list member
contains the followings:
lower
: the lower boundary.
upper
: the upper boundary.
bestvalit
: the best value of FUN
at each iteration.
bestmemit
: the best member at each iteration.
pop
: the population generated at the last iteration.
storepop
: a list containing the intermediate populations.
DEoptim
is a R-vectorized variant of the Differential Evolution algorithm
initialy developed by Rainer Storn storn@icsi.berkeley.edu,
International Computer Science Institute (ICSI), 1947 Center Street, Suite 600,
Berkeley, CA 94704.
If you experience misconvergence in the optimization process you usually
have to increase the value for NP
, but often you only have to adjust
F
to be a little lower or higher than 0.8
. If you increase
NP
and simultaneously lower F
a little, convergence is more
likely to occur but generally takes longer, i.e. DEoptim
is getting
more robust (there is always a convergence speed/robustness tradeoff).
DEoptim
is much more sensitive to the choice of F
than it is to
the choice of CR
. CR
is more like a fine tuning element. High
values of CR
like CR=1
give faster convergence if convergence
occurs. Sometimes, however, you have to go down as much as CR=0
to
make DEoptim
robust enough for a particular problem.
The R-adaptation DEoptim
has properties which differ from the
original DE version:
DEoptim
executes fairly fast.
To perform a maximization (instead of minimization) of a given
function, simply define a new function which is the opposite of the
function to maximize and apply DEoptim
to it.
To integrate additional constraints on the parameters x
of
FUN(x)
, for instance x[1] + x[2]^2 < 2
, integrate the
constraint within the function to optimize, for instance:
FUN <- function(x){ if (x[1] + x[2]^2 < 2){ r <- Inf else{ ... } return(r) }
Note that DEoptim
stops if any NA
or NaN
value is
obtained. You have to redefine your function to handle these values
(for instance, set NA
to Inf
in your objective function).
Please cite the package in publications. Use citation("DEoptim")
.
David Ardia david.ardia@unifr.ch for the R-port; Rainer Storn storn@icsi.berkeley.edu for the Differential Evolution algorithm.
Differential Evolution homepage :
http://www.icsi.berkeley.edu/~storn/code.html
Some useful books:
Price, K. V., Storn, R. M. and Lampinen J. A. (2005) Differential Evolution - A Practical Approach to Global Optimization. Springer. ISBN 3540209506.
Nocedal, J. and Wright, S. J. (1999) Numerical Optimization. Springer. ISBN 0387987932.
DEoptim-methods
for methods on DEoptim
object;
optim
or constrOptim
for constrained optimization.
## Rosenbrock Banana function Rosenbrock <- function(x){ x1 <- x[1] x2 <- x[2] 100 * (x2 - x1 * x1)^2 + (1 - x1)^2 } lower <- c(-10,-10) upper <- -lower DEoptim(Rosenbrock, lower, upper) DEoptim(Rosenbrock, lower, upper, control = list(NP = 100, refresh = 1)) DEoptim(Rosenbrock, lower, upper, control = list(NP = 50, itermax = 200, F = 1.5, CR = 0.2, refresh = 1)) DEoptim(Rosenbrock, lower, upper, control = list(NP = 80, itermax = 400, F = 1.2, CR = 0.7, refresh = 1)) ## 'Wild' function, global minimum at about -15.81515 Wild <- function(x) 10 * sin(0.3*x) * sin(1.3*x^2) + 0.00001 * x^4 + 0.2 * x + 80 plot(Wild, -50, 50, n = 1000, main = "DEoptim minimizing 'Wild function'") DEoptim(Wild, lower = -50, upper = 50, control = list(NP = 50, refresh = 1)) DEoptim(Wild, lower = -50, upper = 50, control = list(NP = 50, refresh = 1, digits = 8))