Allow the user to set some characteristics of the
Differential Evolution optimization algorithm implemented
in DEoptim.
DEoptim.control(VTR = -Inf, strategy = 2, bs = FALSE, NP = NA,
itermax = 200, CR = 0.5, F = 0.8, trace = TRUE, initialpop = NULL,
storepopfrom = itermax + 1, storepopfreq = 1, p = 0.2, c = 0, reltol,
steptol, parallelType = c("none", "auto", "parallel", "foreach"),
cluster = NULL, packages = c(), parVar = c(),
foreachArgs = list(), parallelArgs = NULL)The default value of control is the return value of
DEoptim.control(), which is a list (and a member of the
S3 class
DEoptim.control) with the above elements.
the value to be reached. The optimization process
will stop if either the maximum number of iterations itermax
is reached or the best parameter vector bestmem has found a value
fn(bestmem) <= VTR. Default to -Inf.
defines the Differential Evolution
strategy used in the optimization procedure:
1: DE / rand / 1 / bin (classical strategy)
2: DE / local-to-best / 1 / bin (default)
3: DE / best / 1 / bin with jitter
4: DE / rand / 1 / bin with per-vector-dither
5: DE / rand / 1 / bin with per-generation-dither
6: DE / current-to-p-best / 1
any value not above: variation to DE / rand / 1 / bin: either-or-algorithm. Default
strategy is currently 2. See *Details*.
if FALSE then every mutant will be tested against a
member in the previous generation, and the best value will proceed
into the next generation (this is standard trial vs. target
selection). If TRUE then the old generation and NP
mutants will be sorted by their associated objective function
values, and the best NP vectors will proceed into the next
generation (best of parent and child selection). Default is
FALSE.
number of population members. Defaults to NA; if
the user does not change the value of NP from NA or
specifies a value less than 4 it
is reset when DEoptim is called as 10*length(lower). For
many problems it is best to set
NP to be at least 10 times the length
of the parameter vector.
the maximum iteration (population generation) allowed.
Default is 200.
crossover probability from interval [0,1]. Default
to 0.5.
differential weighting factor from interval [0,2]. Default
to 0.8.
Positive integer or logical value indicating whether
printing of progress occurs at each iteration. The default value is
TRUE. If a positive integer is specified, printing occurs every
trace iterations.
an initial population used as a starting
population in the optimization procedure. May be useful to speed up
the convergence. Default to NULL. If given, each member of
the initial population should be given as a row of a numeric matrix, so that
initialpop is a matrix with NP rows and a number of
columns equal to the length of the parameter vector to be optimized.
from which generation should the following
intermediate populations be stored in memory. Default to
itermax + 1, i.e., no intermediate population is stored.
the frequency with which populations are stored.
Default to 1, i.e., every intermediate population
is stored.
when strategy = 6, the top (100 * p)% best
solutions are used in the mutation. p must be defined in (0,1].
c controls the speed of the
crossover adaptation. Higher values of c give more weight to the
current successful mutations. c must be defined in (0,1].
relative convergence tolerance. The algorithm stops if
it is unable to reduce the value by a factor of reltol * (abs(val) +
reltol) after steptol steps. Defaults to
sqrt(.Machine$double.eps), typically about 1e-8.
see reltol. Defaults to itermax.
Defines the type of parallelization to employ, if
any.
none: The default, this uses DEoptim on only one core.
auto: will attempt to auto-detect foreach, or parallel.
parallel: This uses all available cores, via the parallel
package, to run DEoptim.
foreach: This uses the foreach package for parallelism; see
the sandbox directory in the source code for examples.
Existing parallel cluster object. If provided, overrides
+ specified parallelType. Using cluster allows fine-grained control
+ over the number of used cores and exported data.
Used if parallelType='parallel'; a list of
package names (as strings) that need to be loaded for use by the objective
function.
Used if parallelType='parallel'; a list of variable names
(as strings) that need to exist in the environment for use by the
objective function or are used as arguments by the objective
function.
A list of named arguments for the foreach
function from the
package foreach. The arguments i, .combine and
.export are not possible to set here; they are set
internally.
A list of named arguments for the parallel engine.
For package foreach, the argument i is not possible to
set here; it is set internally.
David Ardia, Katharine Mullen mullenkate@gmail.com, Brian Peterson and Joshua Ulrich.
This defines the Differential Evolution strategy used in the optimization procedure, described below in the terms used by Price et al. (2006); see also Mullen et al. (2009) for details.
strategy = 1: DE / rand / 1 / bin.
This strategy is the classical approach for DE, and is described in DEoptim.
strategy = 2: DE / local-to-best / 1 / bin.
In place of the classical DE mutation the expression
$$
v_{i,g} = old_{i,g} + (best_{g} - old_{i,g}) + x_{r0,g} + F \cdot (x_{r1,g} - x_{r2,g})
$$
is used, where \(old_{i,g}\) and \(best_{g}\) are the
\(i\)-th member and best member, respectively, of the previous population.
This strategy is currently used by default.
strategy = 3: DE / best / 1 / bin with jitter.
In place of the classical DE mutation the expression
$$
v_{i,g} = best_{g} + jitter + F \cdot (x_{r1,g} - x_{r2,g})
$$
is used, where \(jitter\) is defined as 0.0001 * rand + F.
strategy = 4: DE / rand / 1 / bin with per vector dither.
In place of the classical DE mutation the expression
$$
v_{i,g} = x_{r0,g} + dither \cdot (x_{r1,g} - x_{r2,g})
$$
is used, where \(dither\) is calculated as \(F + \code{rand} * (1 - F)\).
strategy = 5: DE / rand / 1 / bin with per generation dither.
The strategy described for 4 is used, but \(dither\)
is only determined once per-generation.
strategy = 6: DE / current-to-p-best / 1.
The top \((100*p)\) percent best solutions are used in the mutation,
where \(p\) is defined in \((0,1]\).
any value not above: variation to DE / rand / 1 / bin: either-or algorithm.
In the case that rand < 0.5, the classical strategy strategy = 1 is used.
Otherwise, the expression
$$
v_{i,g} = x_{r0,g} + 0.5 \cdot (F + 1) \cdot (x_{r1,g} + x_{r2,g} - 2 \cdot x_{r0,g})
$$
is used.
Several conditions can cause the optimization process to stop:
if the best parameter vector (bestmem) produces a value
less than or equal to VTR (i.e. fn(bestmem) <= VTR), or
if the maximum number of iterations is reached (itermax), or
if a number (steptol) of consecutive iterations are unable
to reduce the best function value by a certain amount (reltol *
(abs(val) + reltol)). 100*reltol is approximately the percent
change of the objective value required to consider the parameter set
an improvement over the current best member.
Zhang and Sanderson (2009) define several extensions to the DE algorithm,
including strategy 6, DE/current-to-p-best/1. They also define a self-adaptive
mechanism for the other control parameters. This self-adaptation will speed
convergence on many problems, and is defined by the control parameter c.
If c is non-zero, crossover and mutation will be adapted by the algorithm.
Values in the range of c=.05 to c=.5 appear to work best for most
problems, though the adaptive algorithm is robust to a wide range of c.
Ardia, D., Boudt, K., Carl, P., Mullen, K.M., Peterson, B.G. (2011) Differential Evolution with DEoptim. An Application to Non-Convex Portfolio Optimization. R Journal, 3(1), 27-34. tools:::Rd_expr_doi("10.32614/RJ-2011-005")
Ardia, D., Ospina Arango, J.D., Giraldo Gomez, N.D. (2011) Jump-Diffusion Calibration using Differential Evolution. Wilmott Magazine, 55 (September), 76-79. tools:::Rd_expr_doi("10.1002/wilm.10034")
Mullen, K.M, Ardia, D., Gil, D., Windover, D., Cline,J. (2011). DEoptim: An R Package for Global Optimization by Differential Evolution. Journal of Statistical Software, 40(6), 1-26. tools:::Rd_expr_doi("10.18637/jss.v040.i06")
Price, K.V., Storn, R.M., Lampinen J.A. (2006) Differential Evolution - A Practical Approach to Global Optimization. Berlin Heidelberg: Springer-Verlag. ISBN 3540209506.
Zhang, J. and Sanderson, A. (2009) Adaptive Differential Evolution Springer-Verlag. ISBN 978-3-642-01526-7
DEoptim and DEoptim-methods.
## set the population size to 20
DEoptim.control(NP = 20)
## set the population size, the number of iterations and don't
## display the iterations during optimization
DEoptim.control(NP = 20, itermax = 100, trace = FALSE)
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