DEoptim: Differential Evolution Optimization
In RcppDE: Global optimization by differential evolution in C++
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
Performs evolutionary global optimization via the Differential Evolution algorithm.
Usage
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DEoptim(fn, lower, upper, control = DEoptim.control(), ...)
Arguments
fn
the function to be optimized (minimized). The function should have as its first
argument the vector of real-valued parameters to optimize, and return a scalar real result. NA
and NaN values are not allowed. Note that fn can also
be an external pointer object encapsulating a C/C++-level function pointer
to a compiled functions which may offer considerable speed improvements.
lower, upper
two vectors specifying scalar real lower and upper bounds on each parameter to be optimized, so that the i-th element
of lower and upper applied to the i-th parameter. The implementation searches
between lower and upper for the global optimum (minimum) of fn.
control
a list of control parameters; see DEoptim.control.
...
further arguments to be passed to fn.
Details
DEoptim performs optimization (minimization) of fn.
The control argument is a list; see the help file for
DEoptim.control for details.
The R implementation of Differential Evolution (DE), DEoptim, was first published on the Comprehensive R Archive
Network (CRAN) in 2005 by David Ardia. Early versions were written in
pure R. Since version 2.0-0 (published to CRAN in 2009) the package has relied on an
interface to a C implementation of DE, which is significantly
faster on most problems as compared to the implementation in
pure R. The C interface is in many respects similar to the MS
Visual C++ v5.0 implementation of the Differential Evolution algorithm
distributed with the book Differential Evolution – A Practical
Approach to Global Optimization by Price, K.V., Storn, R.M., Lampinen
J.A, Springer-Verlag, 2006, and found on-line at
http://www.icsi.berkeley.edu/~storn/. Since version 2.0-3 the C
implementation dynamically allocates the memory required to store the population, removing limitations on the
number of members in the population and length of the parameter vectors that may be optimized.
Since becoming publicly available, the package DEoptim has been used by several authors to solve optimization
problems arising in diverse domains; see Mullen et al. (2009) for a review.
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 (than box constraints) on the parameters x of
fn(x), for instance x[1] + x[2]^2 < 2, integrate the
constraint within the function to optimize, for instance:
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This simplistic strategy usually does not work all that well for gradient-based or Newton-type
methods. It is likely to be alright when the solution is in the interior of the feasible region, but when
the solution is on the boundary, optimization algorithm would have a difficult time converging. Furthermore, when
the solution is on the boundary, this strategy would make the algorithm converge to an inferior solution in the interior.
However, for methods such as DE which are not gradient based, this strategy might not be that bad.
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).
It is important to emphasize that the result of DEoptim is a random variable,
i.e., different results will obtain when the algorithm is run repeatedly with the same
settings. Hence, the user should set the random seed if they want to reproduce the results, e.g., by
setting set.seed(1234) before the call of DEoptim.
DEoptim relies on repeated evaluation of the objective function
in order to move the population toward a global minimum. Users
interested in making DEoptim run as fast as possible should
ensure that evaluation of the objective function is as efficient as
possible. Using pure R code, this may often be accomplished
using vectorization. Writing parts of the objective function in a
lower-level language like C or Fortran may also increase speed.
Further details and examples of the R package DEoptim can be found
in Mullen et al. (2009) and Ardia et al. (2010).
Please cite the package in publications.
Value
The output of the function DEoptim is a member of the S3 class DEoptim. More precisely,
this is a list (of length 2) containing the following elements:
optim, a list containing the following elements:
-
bestmem: the best set of parameters found.
-
bestval: the value of fn corresponding to bestmem.
-
nfeval: number of function evaluations.
-
iter: number of procedure iterations.
member, a list containing the following elements:
-
lower: the lower boundary.
-
upper: the upper boundary.
-
bestvalit: the best value of fn 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.
Members of the class DEoptim have a plot method that
accepts the argument plot.type. plot.type = "bestmemit" results
in a plot of the parameter values that represent the lowest value of the objective function
each generation. plot.type = "bestvalit" plots the best value of
the objective function each generation. Finally, plot.type = "storepop" results in a plot of
stored populations (which are only available if these have been saved by
setting the control argument of DEoptim appropriately). Storing intermediate populations
allows us to examine the progress of the optimization in detail.
A summary method also exists and returns the best parameter vector, the best value of the objective function,
the number of generations optimization ran, and the number of times the
objective function was evaluated.
Note
Differential Evolution (DE) is a search heuristic introduced by Storn and Price (1997).
Its remarkable performance as a global optimization algorithm on continuous numerical minimization
problems has been extensively explored; see Price et al. (2006). DE belongs to the class of genetic
algorithms which use biology-inspired operations of
crossover, mutation, and selection on a population in order to minimize an objective
function over the course of successive generations (see Mitchell, 1998). As with other evolutionary algorithms,
DE solves optimization problems by evolving a population of candidate solutions using alteration and selection
operators. DE uses floating-point instead of bit-string encoding of population members, and
arithmetic operations instead of logical operations in mutation. DE is particularly well-suited to find the global optimum of a
real-valued function of real-valued parameters, and does not require that the function be
either continuous or differentiable.
Let NP denote the number of parameter vectors (members) x in R^d in the population.
In order to create the initial generation, NP guesses for the optimal value
of the parameter vector are made, either using random values between lower and upper
bounds (defined by the user) or using values given by
the user. Each generation involves creation of a new population from
the current population members {x_i | i=1,...,NP},
where i indexes the vectors that make up the population.
This is accomplished using differential mutation of the
population members. An initial mutant parameter vector v_i is
created by choosing three members of the population, x_{r_0},
x_{r_1} and x_{r_2}, at random. Then v_i is
generated as
v_i := x_{r_0} + F * (x_{r_1} - x_{r_2})
where F is a positive scale factor, effective values for which are
typically less than one. After the first mutation operation, mutation is
continued until d mutations have been made, with a crossover probability
CR in [0,1].
The crossover probability CR controls the fraction of the parameter
values that are copied from the mutant. If an element of the trial parameter vector is found to violate the
bounds after mutation and crossover, it is reset in such a way that the bounds are respected (with the
specific protocol depending on the implementation).
Then, the objective function values associated with the children are determined. If a trial
vector has equal or lower objective function value than the previous
vector it replaces the previous vector in the population;
otherwise the previous vector remains. Variations of this scheme have also
been proposed; see Price et al. (2006) and DEoptim.control.
Intuitively, the effect of the scheme is that the shape of the distribution of the population in the
search space is converging with respect to size and direction towards areas with high
fitness. The closer the population gets to the global optimum, the more the distribution
will shrink and therefore reinforce the generation of smaller difference vectors.
As a general advice regarding the choice of NP, F and CR,
Storn et al. (2006) state the following: Set the number
of parents NP to 10 times the number of parameters, select weighting factor
F = 0.8 and crossover constant CR = 0.9. Make sure that you initialize your parameter vectors
by exploiting their full numerical range, i.e., if a parameter is allowed to exhibit
values in the range [-100, 100] it is a good idea to pick the initial values from this
range instead of unnecessarily restricting diversity. 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., DE is getting
more robust (there is always a convergence speed/robustness trade-off).
DE 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 DE robust enough for a particular problem. For more details on the DE strategy, we refer
the reader to Storn and Price (1997) and Price et al. (2006).
Author(s)
For RcppDE: Dirk Eddelbuettel.
For DEoptim:
David Ardia, Katharine Mullen katharine.mullen@nist.gov,
Brian Peterson and Joshua Ulrich.
References
Differential Evolution homepage:
URL http://www.icsi.berkeley.edu/~storn/code.html
Storn, R. and Price, K. (1997)
Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces,
Journal of Global Optimization, 11:4, 341–359.
Price, K.V., Storn, R.M., Lampinen J.A. (2006)
Differential Evolution - A Practical Approach to Global Optimization.
Berlin Heidelberg: Springer-Verlag. ISBN 3540209506.
Mitchell, M. (1998)
An Introduction to Genetic Algorithms.
The MIT Press. ISBN 0262631857.
Mullen, K.M., Ardia, D., Gil, D.L, Windover, D., Cline, J. (2009)
DEoptim: An R Package for Global Optimization by Differential Evolution.
URL http://ssrn.com/abstract=1526466
Ardia, D., Boudt, K., Carl, P., Mullen, K.M., Peterson, B.G. (2010)
Differential Evolution (DEoptim) for Non-Convex Portfolio Optimization.
URL http://ssrn.com/abstract=1584905
See Also
DEoptim.control for control arguments,
DEoptim-methods for methods on DEoptim objects,
including some examples in plotting the results;
optim or constrOptim
for alternative optimization algorithms.
Examples
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## Rosenbrock Banana function
## The function has a global minimum f(x) = 0 at the point (0,0).
## Note that the vector of parameters to be optimized must be the first
## argument of the objective function passed to DEoptim.
Rosenbrock <- function(x){
x1 <- x[1]
x2 <- x[2]
100 * (x2 - x1 * x1)^2 + (1 - x1)^2
}
## DEoptim searches for minima of the objective function between
## lower and upper bounds on each parameter to be optimized. Therefore
## in the call to DEoptim we specify vectors that comprise the
## lower and upper bounds; these vectors are the same length as the
## parameter vector.
lower <- c(-10,-10)
upper <- -lower
## run DEoptim and set a seed first for replicability
set.seed(1234)
DEoptim(Rosenbrock, lower, upper)
## increase the population size
DEoptim(Rosenbrock, lower, upper, DEoptim.control(NP = 100))
## change other settings and store the output
outDEoptim <- DEoptim(Rosenbrock, lower, upper, DEoptim.control(NP = 80,
itermax = 400, F = 1.2, CR = 0.7))
## plot the output
plot(outDEoptim)
## '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 = "'Wild function'")
outDEoptim <- DEoptim(Wild, lower = -50, upper = 50,
control = DEoptim.control(trace = FALSE))
plot(outDEoptim)
DEoptim(Wild, lower = -50, upper = 50,
control = DEoptim.control(NP = 50))
Example output
Now loading:
RcppDE: C++ Implementation of Differential Evolution Optimisation
Author: Dirk Eddelbuettel
Based on:
DEoptim (version 2.0-7): Differential Evolution algorithm in R
Authors: David Ardia, Katharine Mullen, Brian Peterson and Joshua Ulrich
Iteration: 1 bestvalit: 6.346930 bestmemit: -1.516509 2.311679
Iteration: 2 bestvalit: 5.620014 bestmemit: 0.435505 0.419911
Iteration: 3 bestvalit: 2.735287 bestmemit: 1.069276 1.308593
Iteration: 4 bestvalit: 0.425506 bestmemit: 0.347692 0.120983
Iteration: 5 bestvalit: 0.425506 bestmemit: 0.347692 0.120983
Iteration: 6 bestvalit: 0.372295 bestmemit: 0.447835 0.174593
Iteration: 7 bestvalit: 0.372295 bestmemit: 0.447835 0.174593
Iteration: 8 bestvalit: 0.372295 bestmemit: 0.447835 0.174593
Iteration: 9 bestvalit: 0.372295 bestmemit: 0.447835 0.174593
Iteration: 10 bestvalit: 0.372295 bestmemit: 0.447835 0.174593
Iteration: 11 bestvalit: 0.372295 bestmemit: 0.447835 0.174593
Iteration: 12 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 13 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 14 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 15 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 16 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 17 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 18 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 19 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 20 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 21 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 22 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 23 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 24 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 25 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 26 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 27 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 28 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 29 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 30 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 31 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 32 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 33 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 34 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 35 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 36 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 37 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 38 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 39 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 40 bestvalit: 0.001137 bestmemit: 0.966398 0.934214
Iteration: 41 bestvalit: 0.001137 bestmemit: 0.966398 0.934214
Iteration: 42 bestvalit: 0.001137 bestmemit: 0.966398 0.934214
Iteration: 43 bestvalit: 0.001137 bestmemit: 0.966398 0.934214
Iteration: 44 bestvalit: 0.001137 bestmemit: 0.966398 0.934214
Iteration: 45 bestvalit: 0.001137 bestmemit: 0.966398 0.934214
Iteration: 46 bestvalit: 0.000225 bestmemit: 0.986703 0.972892
Iteration: 47 bestvalit: 0.000225 bestmemit: 0.986703 0.972892
Iteration: 48 bestvalit: 0.000225 bestmemit: 0.986703 0.972892
Iteration: 49 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 50 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 51 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 52 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 53 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 54 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 55 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 56 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 57 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 58 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 59 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 60 bestvalit: 0.000050 bestmemit: 1.000960 1.002619
Iteration: 61 bestvalit: 0.000050 bestmemit: 1.000960 1.002619
Iteration: 62 bestvalit: 0.000050 bestmemit: 1.000960 1.002619
Iteration: 63 bestvalit: 0.000023 bestmemit: 1.004405 1.008635
Iteration: 64 bestvalit: 0.000023 bestmemit: 1.004405 1.008635
Iteration: 65 bestvalit: 0.000005 bestmemit: 1.002342 1.004696
Iteration: 66 bestvalit: 0.000005 bestmemit: 1.002342 1.004696
Iteration: 67 bestvalit: 0.000005 bestmemit: 1.002342 1.004696
Iteration: 68 bestvalit: 0.000003 bestmemit: 0.999158 0.998169
Iteration: 69 bestvalit: 0.000001 bestmemit: 1.000746 1.001415
Iteration: 70 bestvalit: 0.000001 bestmemit: 1.000746 1.001415
Iteration: 71 bestvalit: 0.000001 bestmemit: 1.000746 1.001415
Iteration: 72 bestvalit: 0.000001 bestmemit: 1.000746 1.001415
Iteration: 73 bestvalit: 0.000001 bestmemit: 1.000514 1.001100
Iteration: 74 bestvalit: 0.000000 bestmemit: 0.999758 0.999565
Iteration: 75 bestvalit: 0.000000 bestmemit: 0.999758 0.999565
Iteration: 76 bestvalit: 0.000000 bestmemit: 0.999758 0.999565
Iteration: 77 bestvalit: 0.000000 bestmemit: 0.999758 0.999565
Iteration: 78 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 79 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 80 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 81 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 82 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 83 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 84 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 85 bestvalit: 0.000000 bestmemit: 0.999802 0.999621
Iteration: 86 bestvalit: 0.000000 bestmemit: 0.999802 0.999621
Iteration: 87 bestvalit: 0.000000 bestmemit: 0.999802 0.999621
Iteration: 88 bestvalit: 0.000000 bestmemit: 0.999802 0.999621
Iteration: 89 bestvalit: 0.000000 bestmemit: 0.999873 0.999752
Iteration: 90 bestvalit: 0.000000 bestmemit: 0.999873 0.999752
Iteration: 91 bestvalit: 0.000000 bestmemit: 0.999873 0.999752
Iteration: 92 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 93 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 94 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 95 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 96 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 97 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 98 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 99 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 100 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 101 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 102 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 103 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 104 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 105 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 106 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 107 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 108 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 109 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 110 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 111 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 112 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 113 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 114 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 115 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 116 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 117 bestvalit: 0.000000 bestmemit: 0.999996 0.999991
Iteration: 118 bestvalit: 0.000000 bestmemit: 0.999996 0.999991
Iteration: 119 bestvalit: 0.000000 bestmemit: 0.999996 0.999991
Iteration: 120 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 121 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 122 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 123 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 124 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 125 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 126 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 127 bestvalit: 0.000000 bestmemit: 1.000001 1.000002
Iteration: 128 bestvalit: 0.000000 bestmemit: 1.000001 1.000002
Iteration: 129 bestvalit: 0.000000 bestmemit: 1.000001 1.000002
Iteration: 130 bestvalit: 0.000000 bestmemit: 1.000001 1.000003
Iteration: 131 bestvalit: 0.000000 bestmemit: 1.000000 0.999999
Iteration: 132 bestvalit: 0.000000 bestmemit: 1.000000 0.999999
Iteration: 133 bestvalit: 0.000000 bestmemit: 1.000000 0.999999
Iteration: 134 bestvalit: 0.000000 bestmemit: 1.000000 0.999999
Iteration: 135 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 136 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 137 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
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Iteration: 151 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 152 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
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Iteration: 154 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 155 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 156 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 157 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 158 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 159 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 160 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 161 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
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Iteration: 178 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 179 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 180 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 181 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 182 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 183 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 184 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 185 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 186 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 187 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 188 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 189 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 190 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 191 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 192 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 193 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 194 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 195 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 196 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 197 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 198 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 199 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 200 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
$optim
$optim$bestmem
par1 par2
1 1
$optim$bestval
[1] 2.54782e-21
$optim$nfeval
[1] 10050
$optim$iter
[1] 200
$member
$member$lower
par1 par2
-10 -10
$member$upper
par1 par2
10 10
$member$bestmemit
par1 par2
1 1.0666718 2.9281219
2 -1.5165089 2.3116791
3 0.4355051 0.4199115
4 1.0692761 1.3085932
5 0.3476923 0.1209829
6 0.3476923 0.1209829
7 0.4478347 0.1745927
8 0.4478347 0.1745927
9 0.4478347 0.1745927
10 0.4478347 0.1745927
11 0.4478347 0.1745927
12 0.4478347 0.1745927
13 0.7955400 0.6478828
14 0.7955400 0.6478828
15 0.7955400 0.6478828
16 0.7955400 0.6478828
17 0.7955400 0.6478828
18 0.7955400 0.6478828
19 0.7955400 0.6478828
20 0.7955400 0.6478828
21 0.7955400 0.6478828
22 0.7955400 0.6478828
23 0.7955400 0.6478828
24 0.7955400 0.6478828
25 0.7955400 0.6478828
26 1.0229105 1.0414949
27 1.0229105 1.0414949
28 1.0229105 1.0414949
29 1.0229105 1.0414949
30 1.0229105 1.0414949
31 1.0229105 1.0414949
32 1.0229105 1.0414949
33 1.0229105 1.0414949
34 1.0229105 1.0414949
35 1.0229105 1.0414949
36 1.0229105 1.0414949
37 1.0229105 1.0414949
38 1.0229105 1.0414949
39 1.0229105 1.0414949
40 1.0229105 1.0414949
41 0.9663977 0.9342136
42 0.9663977 0.9342136
43 0.9663977 0.9342136
44 0.9663977 0.9342136
45 0.9663977 0.9342136
46 0.9663977 0.9342136
47 0.9867034 0.9728923
48 0.9867034 0.9728923
49 0.9867034 0.9728923
50 0.9920263 0.9846341
51 0.9920263 0.9846341
52 0.9920263 0.9846341
53 0.9920263 0.9846341
54 0.9920263 0.9846341
55 0.9920263 0.9846341
56 0.9920263 0.9846341
57 0.9920263 0.9846341
58 0.9920263 0.9846341
59 0.9920263 0.9846341
60 0.9920263 0.9846341
61 1.0009596 1.0026186
62 1.0009596 1.0026186
63 1.0009596 1.0026186
64 1.0044055 1.0086351
65 1.0044055 1.0086351
66 1.0023415 1.0046965
67 1.0023415 1.0046965
68 1.0023415 1.0046965
69 0.9991581 0.9981689
70 1.0007455 1.0014146
71 1.0007455 1.0014146
72 1.0007455 1.0014146
73 1.0007455 1.0014146
74 1.0005139 1.0010997
75 0.9997581 0.9995646
76 0.9997581 0.9995646
77 0.9997581 0.9995646
78 0.9997581 0.9995646
79 1.0003362 1.0006548
80 1.0003362 1.0006548
81 1.0003362 1.0006548
82 1.0003362 1.0006548
83 1.0003362 1.0006548
84 1.0003362 1.0006548
85 1.0003362 1.0006548
86 0.9998024 0.9996206
87 0.9998024 0.9996206
88 0.9998024 0.9996206
89 0.9998024 0.9996206
90 0.9998735 0.9997522
91 0.9998735 0.9997522
92 0.9998735 0.9997522
93 1.0000290 1.0000624
94 1.0000290 1.0000624
95 1.0000290 1.0000624
96 1.0000290 1.0000624
97 1.0000290 1.0000624
98 1.0000290 1.0000624
99 1.0000290 1.0000624
100 1.0000290 1.0000624
101 1.0000290 1.0000624
102 1.0000290 1.0000624
103 1.0000290 1.0000624
104 1.0000038 1.0000084
105 1.0000038 1.0000084
106 1.0000038 1.0000084
107 1.0000038 1.0000084
108 1.0000038 1.0000084
109 1.0000038 1.0000084
110 1.0000038 1.0000084
111 1.0000038 1.0000084
112 1.0000038 1.0000084
113 1.0000038 1.0000084
114 1.0000038 1.0000084
115 1.0000038 1.0000084
116 1.0000038 1.0000084
117 1.0000038 1.0000084
118 0.9999957 0.9999906
119 0.9999957 0.9999906
120 0.9999957 0.9999906
121 1.0000028 1.0000054
122 1.0000028 1.0000054
123 1.0000028 1.0000054
124 1.0000028 1.0000054
125 1.0000028 1.0000054
126 1.0000028 1.0000054
127 1.0000028 1.0000054
128 1.0000007 1.0000015
129 1.0000007 1.0000015
130 1.0000007 1.0000015
131 1.0000013 1.0000027
132 0.9999996 0.9999991
133 0.9999996 0.9999991
134 0.9999996 0.9999991
135 0.9999996 0.9999991
136 1.0000002 1.0000005
137 1.0000002 1.0000005
138 1.0000002 1.0000005
139 1.0000002 1.0000005
140 1.0000002 1.0000005
141 1.0000002 1.0000005
142 1.0000002 1.0000005
143 1.0000002 1.0000005
144 1.0000000 0.9999999
145 1.0000000 0.9999999
146 1.0000000 0.9999999
147 1.0000000 0.9999999
148 1.0000000 0.9999999
149 1.0000000 0.9999999
150 1.0000000 0.9999999
151 1.0000000 0.9999999
152 1.0000000 0.9999999
153 1.0000000 0.9999999
154 1.0000000 1.0000000
155 1.0000000 1.0000000
156 1.0000000 1.0000000
157 1.0000000 1.0000000
158 1.0000000 1.0000000
159 1.0000000 0.9999999
160 1.0000000 0.9999999
161 1.0000000 0.9999999
162 1.0000000 0.9999999
163 1.0000000 1.0000000
164 1.0000000 1.0000000
165 1.0000000 1.0000000
166 1.0000000 1.0000000
167 1.0000000 1.0000000
168 1.0000000 1.0000000
169 1.0000000 1.0000000
170 1.0000000 1.0000000
171 1.0000000 1.0000000
172 1.0000000 1.0000000
173 1.0000000 1.0000000
174 1.0000000 1.0000000
175 1.0000000 1.0000000
176 1.0000000 1.0000000
177 1.0000000 1.0000000
178 1.0000000 1.0000000
179 1.0000000 1.0000000
180 1.0000000 1.0000000
181 1.0000000 1.0000000
182 1.0000000 1.0000000
183 1.0000000 1.0000000
184 1.0000000 1.0000000
185 1.0000000 1.0000000
186 1.0000000 1.0000000
187 1.0000000 1.0000000
188 1.0000000 1.0000000
189 1.0000000 1.0000000
190 1.0000000 1.0000000
191 1.0000000 1.0000000
192 1.0000000 1.0000000
193 1.0000000 1.0000000
194 1.0000000 1.0000000
195 1.0000000 1.0000000
196 1.0000000 1.0000000
197 1.0000000 1.0000000
198 1.0000000 1.0000000
199 1.0000000 1.0000000
200 1.0000000 1.0000000
$member$bestvalit
[1] 3.205337e+02 6.346930e+00 5.620014e+00 2.735287e+00 4.255061e-01
[6] 4.255061e-01 3.722953e-01 3.722953e-01 3.722953e-01 3.722953e-01
[11] 3.722953e-01 3.722953e-01 6.430063e-02 6.430063e-02 6.430063e-02
[16] 6.430063e-02 6.430063e-02 6.430063e-02 6.430063e-02 6.430063e-02
[21] 6.430063e-02 6.430063e-02 6.430063e-02 6.430063e-02 6.430063e-02
[26] 2.878081e-03 2.878081e-03 2.878081e-03 2.878081e-03 2.878081e-03
[31] 2.878081e-03 2.878081e-03 2.878081e-03 2.878081e-03 2.878081e-03
[36] 2.878081e-03 2.878081e-03 2.878081e-03 2.878081e-03 2.878081e-03
[41] 1.137470e-03 1.137470e-03 1.137470e-03 1.137470e-03 1.137470e-03
[46] 1.137470e-03 2.245852e-04 2.245852e-04 2.245852e-04 9.038870e-05
[51] 9.038870e-05 9.038870e-05 9.038870e-05 9.038870e-05 9.038870e-05
[56] 9.038870e-05 9.038870e-05 9.038870e-05 9.038870e-05 9.038870e-05
[61] 4.970519e-05 4.970519e-05 4.970519e-05 2.321945e-05 2.321945e-05
[66] 5.489089e-06 5.489089e-06 5.489089e-06 2.895931e-06 1.148947e-06
[71] 1.148947e-06 1.148947e-06 1.148947e-06 7.769532e-07 2.921012e-07
[76] 2.921012e-07 2.921012e-07 2.921012e-07 1.443103e-07 1.443103e-07
[81] 1.443103e-07 1.443103e-07 1.443103e-07 1.443103e-07 1.443103e-07
[86] 6.395584e-08 6.395584e-08 6.395584e-08 6.395584e-08 1.884063e-08
[91] 1.884063e-08 1.884063e-08 2.777032e-09 2.777032e-09 2.777032e-09
[96] 2.777032e-09 2.777032e-09 2.777032e-09 2.777032e-09 2.777032e-09
[101] 2.777032e-09 2.777032e-09 2.777032e-09 8.818867e-11 8.818867e-11
[106] 8.818867e-11 8.818867e-11 8.818867e-11 8.818867e-11 8.818867e-11
[111] 8.818867e-11 8.818867e-11 8.818867e-11 8.818867e-11 8.818867e-11
[116] 8.818867e-11 8.818867e-11 6.742806e-11 6.742806e-11 6.742806e-11
[121] 9.732897e-12 9.732897e-12 9.732897e-12 9.732897e-12 9.732897e-12
[126] 9.732897e-12 9.732897e-12 5.345352e-12 5.345352e-12 5.345352e-12
[131] 3.783477e-12 8.869835e-13 8.869835e-13 8.869835e-13 8.869835e-13
[136] 7.104047e-14 7.104047e-14 7.104047e-14 7.104047e-14 7.104047e-14
[141] 7.104047e-14 7.104047e-14 7.104047e-14 3.419765e-15 3.419765e-15
[146] 3.419765e-15 3.419765e-15 3.419765e-15 3.419765e-15 3.419765e-15
[151] 3.419765e-15 3.419765e-15 3.419765e-15 1.411010e-15 1.411010e-15
[156] 1.411010e-15 1.411010e-15 1.411010e-15 1.283663e-15 1.283663e-15
[161] 1.283663e-15 1.283663e-15 2.242708e-16 1.478263e-16 1.478263e-16
[166] 1.478263e-16 1.478263e-16 1.478263e-16 1.478263e-16 1.672408e-17
[171] 1.672408e-17 1.672408e-17 5.477594e-18 5.477594e-18 5.477594e-18
[176] 5.477594e-18 5.477594e-18 5.477594e-18 5.477594e-18 2.521403e-18
[181] 2.521403e-18 2.521403e-18 2.521403e-18 7.061309e-19 7.061309e-19
[186] 7.061309e-19 7.061309e-19 7.061309e-19 7.061309e-19 3.270615e-19
[191] 1.059362e-20 1.059362e-20 1.059362e-20 1.059362e-20 1.059362e-20
[196] 1.059362e-20 1.059362e-20 1.059362e-20 2.547820e-21 2.547820e-21
$member$pop
[,1] [,2]
[1,] 1.00000000 1.00000000
[2,] 1.00000000 1.00000000
[3,] 1.00000000 1.00000000
[4,] 1.00000000 1.00000000
[5,] 1.00000000 1.00000000
[6,] 1.00000000 1.00000000
[7,] 1.00000000 1.00000000
[8,] 1.00000000 1.00000000
[9,] 1.00000000 1.00000000
[10,] 1.00000000 1.00000000
[11,] 1.00000000 1.00000000
[12,] 1.00000000 1.00000000
[13,] 1.00000000 1.00000000
[14,] 1.00000000 0.99999999
[15,] -0.12760425 0.05061860
[16,] 1.00000000 1.00000000
[17,] 1.00000000 1.00000000
[18,] 1.00000000 1.00000000
[19,] 1.00000000 1.00000000
[20,] 1.00000000 1.00000000
[21,] -0.07208765 -0.01764878
[22,] 1.00000000 1.00000000
[23,] 1.00000000 1.00000000
[24,] 1.00000000 1.00000000
[25,] 1.00000000 1.00000000
[26,] 1.00000000 1.00000000
[27,] -1.83316974 3.39594294
[28,] 1.00000000 1.00000000
[29,] 1.00000000 1.00000000
[30,] 1.00000000 1.00000000
[31,] -1.83171918 3.38799793
[32,] 1.00000000 1.00000000
[33,] 1.00000000 1.00000000
[34,] 1.00000000 1.00000000
[35,] 1.00000000 1.00000000
[36,] 1.00000000 1.00000000
[37,] 1.00000000 1.00000000
[38,] 1.00000000 1.00000000
[39,] 1.00000000 1.00000000
[40,] 1.00000000 1.00000000
[41,] 1.00000000 1.00000000
[42,] 1.00000000 1.00000000
[43,] 1.00000000 1.00000000
[44,] 1.00000000 1.00000000
[45,] 1.00000000 1.00000000
[46,] 1.00000000 0.99999999
[47,] 1.00000000 1.00000000
[48,] 1.00000000 0.99999999
[49,] 1.00000000 1.00000000
[50,] 1.00000000 1.00000000
$member$storepop
list()
attr(,"class")
[1] "DEoptim"
Iteration: 1 bestvalit: 2.182569 bestmemit: 0.295523 -0.042523
Iteration: 2 bestvalit: 1.630486 bestmemit: 0.065188 0.091233
Iteration: 3 bestvalit: 1.630486 bestmemit: 0.065188 0.091233
Iteration: 4 bestvalit: 1.303092 bestmemit: 1.605471 2.480763
Iteration: 5 bestvalit: 1.303092 bestmemit: 1.605471 2.480763
Iteration: 6 bestvalit: 1.303092 bestmemit: 1.605471 2.480763
Iteration: 7 bestvalit: 1.132293 bestmemit: 0.976363 0.846901
Iteration: 8 bestvalit: 1.132293 bestmemit: 0.976363 0.846901
Iteration: 9 bestvalit: 0.608228 bestmemit: 1.429628 1.978748
Iteration: 10 bestvalit: 0.608228 bestmemit: 1.429628 1.978748
Iteration: 11 bestvalit: 0.138446 bestmemit: 1.260788 1.616127
Iteration: 12 bestvalit: 0.138446 bestmemit: 1.260788 1.616127
Iteration: 13 bestvalit: 0.057014 bestmemit: 1.238480 1.535023
Iteration: 14 bestvalit: 0.057014 bestmemit: 1.238480 1.535023
Iteration: 15 bestvalit: 0.057014 bestmemit: 1.238480 1.535023
Iteration: 16 bestvalit: 0.057014 bestmemit: 1.238480 1.535023
Iteration: 17 bestvalit: 0.027340 bestmemit: 1.164781 1.355347
Iteration: 18 bestvalit: 0.027340 bestmemit: 1.164781 1.355347
Iteration: 19 bestvalit: 0.007054 bestmemit: 1.041878 1.078229
Iteration: 20 bestvalit: 0.007054 bestmemit: 1.041878 1.078229
Iteration: 21 bestvalit: 0.007054 bestmemit: 1.041878 1.078229
Iteration: 22 bestvalit: 0.007054 bestmemit: 1.041878 1.078229
Iteration: 23 bestvalit: 0.001762 bestmemit: 1.037466 1.078229
Iteration: 24 bestvalit: 0.001762 bestmemit: 1.037466 1.078229
Iteration: 25 bestvalit: 0.001762 bestmemit: 1.037466 1.078229
Iteration: 26 bestvalit: 0.001762 bestmemit: 1.037466 1.078229
Iteration: 27 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 28 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 29 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 30 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 31 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 32 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 33 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 34 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 35 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 36 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 37 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 38 bestvalit: 0.000223 bestmemit: 1.009944 1.021101
Iteration: 39 bestvalit: 0.000223 bestmemit: 1.009944 1.021101
Iteration: 40 bestvalit: 0.000223 bestmemit: 1.009944 1.021101
Iteration: 41 bestvalit: 0.000045 bestmemit: 0.993643 0.987109
Iteration: 42 bestvalit: 0.000045 bestmemit: 0.993643 0.987109
Iteration: 43 bestvalit: 0.000045 bestmemit: 0.993643 0.987109
Iteration: 44 bestvalit: 0.000026 bestmemit: 1.000745 1.000990
Iteration: 45 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 46 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 47 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 48 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 49 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 50 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 51 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 52 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 53 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 54 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 55 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 56 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 57 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 58 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 59 bestvalit: 0.000000 bestmemit: 1.000376 1.000705
Iteration: 60 bestvalit: 0.000000 bestmemit: 1.000376 1.000705
Iteration: 61 bestvalit: 0.000000 bestmemit: 1.000206 1.000462
Iteration: 62 bestvalit: 0.000000 bestmemit: 1.000206 1.000462
Iteration: 63 bestvalit: 0.000000 bestmemit: 1.000006 1.000018
Iteration: 64 bestvalit: 0.000000 bestmemit: 1.000006 1.000018
Iteration: 65 bestvalit: 0.000000 bestmemit: 1.000006 1.000018
Iteration: 66 bestvalit: 0.000000 bestmemit: 1.000006 1.000018
Iteration: 67 bestvalit: 0.000000 bestmemit: 1.000006 1.000018
Iteration: 68 bestvalit: 0.000000 bestmemit: 1.000006 1.000018
Iteration: 69 bestvalit: 0.000000 bestmemit: 1.000006 1.000018
Iteration: 70 bestvalit: 0.000000 bestmemit: 1.000006 1.000018
Iteration: 71 bestvalit: 0.000000 bestmemit: 0.999964 0.999930
Iteration: 72 bestvalit: 0.000000 bestmemit: 1.000009 1.000022
Iteration: 73 bestvalit: 0.000000 bestmemit: 1.000009 1.000022
Iteration: 74 bestvalit: 0.000000 bestmemit: 1.000009 1.000022
Iteration: 75 bestvalit: 0.000000 bestmemit: 1.000009 1.000022
Iteration: 76 bestvalit: 0.000000 bestmemit: 1.000009 1.000022
Iteration: 77 bestvalit: 0.000000 bestmemit: 0.999965 0.999929
Iteration: 78 bestvalit: 0.000000 bestmemit: 0.999965 0.999929
Iteration: 79 bestvalit: 0.000000 bestmemit: 0.999979 0.999959
Iteration: 80 bestvalit: 0.000000 bestmemit: 0.999979 0.999959
Iteration: 81 bestvalit: 0.000000 bestmemit: 0.999979 0.999959
Iteration: 82 bestvalit: 0.000000 bestmemit: 0.999979 0.999959
Iteration: 83 bestvalit: 0.000000 bestmemit: 1.000004 1.000010
Iteration: 84 bestvalit: 0.000000 bestmemit: 1.000004 1.000010
Iteration: 85 bestvalit: 0.000000 bestmemit: 1.000004 1.000010
Iteration: 86 bestvalit: 0.000000 bestmemit: 1.000004 1.000010
Iteration: 87 bestvalit: 0.000000 bestmemit: 1.000004 1.000010
Iteration: 88 bestvalit: 0.000000 bestmemit: 1.000004 1.000010
Iteration: 89 bestvalit: 0.000000 bestmemit: 1.000004 1.000010
Iteration: 90 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 91 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 92 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 93 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 94 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 95 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 96 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 97 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 98 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 99 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 100 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 101 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 102 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 103 bestvalit: 0.000000 bestmemit: 0.999999 0.999997
Iteration: 104 bestvalit: 0.000000 bestmemit: 0.999999 0.999999
Iteration: 105 bestvalit: 0.000000 bestmemit: 0.999999 0.999999
Iteration: 106 bestvalit: 0.000000 bestmemit: 1.000000 1.000001
Iteration: 107 bestvalit: 0.000000 bestmemit: 1.000000 1.000001
Iteration: 108 bestvalit: 0.000000 bestmemit: 1.000000 1.000001
Iteration: 109 bestvalit: 0.000000 bestmemit: 1.000000 1.000001
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Iteration: 199 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 200 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
$optim
$optim$bestmem
par1 par2
1 1
$optim$bestval
[1] 4.030849e-24
$optim$nfeval
[1] 20100
$optim$iter
[1] 200
$member
$member$lower
par1 par2
-10 -10
$member$upper
par1 par2
10 10
$member$bestmemit
par1 par2
1 1.16143741 1.60714750
2 0.29552328 -0.04252291
3 0.06518848 0.09123304
4 0.06518848 0.09123304
5 1.60547071 2.48076341
6 1.60547071 2.48076341
7 1.60547071 2.48076341
8 0.97636272 0.84690117
9 0.97636272 0.84690117
10 1.42962793 1.97874775
11 1.42962793 1.97874775
12 1.26078836 1.61612696
13 1.26078836 1.61612696
14 1.23848008 1.53502323
15 1.23848008 1.53502323
16 1.23848008 1.53502323
17 1.23848008 1.53502323
18 1.16478086 1.35534671
19 1.16478086 1.35534671
20 1.04187768 1.07822897
21 1.04187768 1.07822897
22 1.04187768 1.07822897
23 1.04187768 1.07822897
24 1.03746607 1.07822897
25 1.03746607 1.07822897
26 1.03746607 1.07822897
27 1.03746607 1.07822897
28 0.98496001 0.96915585
29 0.98496001 0.96915585
30 0.98496001 0.96915585
31 0.98496001 0.96915585
32 0.98496001 0.96915585
33 0.98496001 0.96915585
34 0.98496001 0.96915585
35 0.98496001 0.96915585
36 0.98496001 0.96915585
37 0.98496001 0.96915585
38 0.98496001 0.96915585
39 1.00994439 1.02110059
40 1.00994439 1.02110059
41 1.00994439 1.02110059
42 0.99364297 0.98710932
43 0.99364297 0.98710932
44 0.99364297 0.98710932
45 1.00074550 1.00098973
46 1.00190873 1.00387442
47 1.00190873 1.00387442
48 1.00190873 1.00387442
49 1.00190873 1.00387442
50 1.00190873 1.00387442
51 1.00190873 1.00387442
52 1.00190873 1.00387442
53 1.00190873 1.00387442
54 1.00190873 1.00387442
55 1.00190873 1.00387442
56 1.00190873 1.00387442
57 1.00190873 1.00387442
58 1.00190873 1.00387442
59 1.00190873 1.00387442
60 1.00037577 1.00070515
61 1.00037577 1.00070515
62 1.00020582 1.00046233
63 1.00020582 1.00046233
64 1.00000630 1.00001836
65 1.00000630 1.00001836
66 1.00000630 1.00001836
67 1.00000630 1.00001836
68 1.00000630 1.00001836
69 1.00000630 1.00001836
70 1.00000630 1.00001836
71 1.00000630 1.00001836
72 0.99996424 0.99992980
73 1.00000894 1.00002156
74 1.00000894 1.00002156
75 1.00000894 1.00002156
76 1.00000894 1.00002156
77 1.00000894 1.00002156
78 0.99996496 0.99992878
79 0.99996496 0.99992878
80 0.99997861 0.99995917
81 0.99997861 0.99995917
82 0.99997861 0.99995917
83 0.99997861 0.99995917
84 1.00000440 1.00000986
85 1.00000440 1.00000986
86 1.00000440 1.00000986
87 1.00000440 1.00000986
88 1.00000440 1.00000986
89 1.00000440 1.00000986
90 1.00000440 1.00000986
91 0.99999854 0.99999703
92 0.99999854 0.99999703
93 0.99999854 0.99999703
94 0.99999854 0.99999703
95 0.99999854 0.99999703
96 0.99999854 0.99999703
97 0.99999854 0.99999703
98 0.99999854 0.99999703
99 0.99999854 0.99999703
100 0.99999854 0.99999703
101 0.99999854 0.99999703
102 0.99999854 0.99999703
103 0.99999866 0.99999731
104 0.99999866 0.99999731
105 0.99999939 0.99999883
106 0.99999939 0.99999883
107 1.00000027 1.00000052
108 1.00000027 1.00000052
109 1.00000027 1.00000052
110 1.00000027 1.00000052
111 1.00000027 1.00000052
112 1.00000027 1.00000052
113 1.00000027 1.00000052
114 1.00000027 1.00000052
115 1.00000027 1.00000052
116 1.00000027 1.00000052
117 1.00000027 1.00000052
118 1.00000027 1.00000052
119 1.00000021 1.00000042
120 0.99999989 0.99999978
121 0.99999989 0.99999978
122 0.99999997 0.99999995
123 0.99999997 0.99999995
124 0.99999997 0.99999995
125 0.99999997 0.99999995
126 0.99999999 0.99999998
127 0.99999999 0.99999998
128 0.99999999 0.99999998
129 0.99999999 0.99999998
130 0.99999999 0.99999998
131 0.99999999 0.99999997
132 0.99999999 0.99999997
133 0.99999999 0.99999997
134 0.99999999 0.99999997
135 0.99999999 0.99999997
136 0.99999999 0.99999997
137 0.99999999 0.99999997
138 0.99999999 0.99999997
139 0.99999999 0.99999997
140 1.00000001 1.00000003
141 1.00000001 1.00000003
142 1.00000001 1.00000003
143 0.99999999 0.99999998
144 0.99999999 0.99999998
145 0.99999999 0.99999998
146 0.99999999 0.99999998
147 1.00000000 1.00000001
148 1.00000000 1.00000001
149 1.00000000 1.00000001
150 1.00000000 1.00000001
151 1.00000000 1.00000001
152 1.00000000 1.00000001
153 1.00000000 1.00000001
154 1.00000000 1.00000000
155 1.00000000 1.00000000
156 1.00000000 1.00000000
157 1.00000000 1.00000000
158 1.00000000 1.00000000
159 1.00000000 1.00000000
160 1.00000000 1.00000000
161 1.00000000 1.00000000
162 1.00000000 1.00000000
163 1.00000000 1.00000000
164 1.00000000 1.00000000
165 1.00000000 1.00000000
166 1.00000000 1.00000000
167 1.00000000 1.00000000
168 1.00000000 1.00000000
169 1.00000000 1.00000000
170 1.00000000 1.00000000
171 1.00000000 1.00000000
172 1.00000000 1.00000000
173 1.00000000 1.00000000
174 1.00000000 1.00000000
175 1.00000000 1.00000000
176 1.00000000 1.00000000
177 1.00000000 1.00000000
178 1.00000000 1.00000000
179 1.00000000 1.00000000
180 1.00000000 1.00000000
181 1.00000000 1.00000000
182 1.00000000 1.00000000
183 1.00000000 1.00000000
184 1.00000000 1.00000000
185 1.00000000 1.00000000
186 1.00000000 1.00000000
187 1.00000000 1.00000000
188 1.00000000 1.00000000
189 1.00000000 1.00000000
190 1.00000000 1.00000000
191 1.00000000 1.00000000
192 1.00000000 1.00000000
193 1.00000000 1.00000000
194 1.00000000 1.00000000
195 1.00000000 1.00000000
196 1.00000000 1.00000000
197 1.00000000 1.00000000
198 1.00000000 1.00000000
199 1.00000000 1.00000000
200 1.00000000 1.00000000
$member$bestvalit
[1] 6.693336e+00 2.182569e+00 1.630486e+00 1.630486e+00 1.303092e+00
[6] 1.303092e+00 1.303092e+00 1.132293e+00 1.132293e+00 6.082283e-01
[11] 6.082283e-01 1.384460e-01 1.384460e-01 5.701444e-02 5.701444e-02
[16] 5.701444e-02 5.701444e-02 2.733980e-02 2.733980e-02 7.053775e-03
[21] 7.053775e-03 7.053775e-03 7.053775e-03 1.762095e-03 1.762095e-03
[26] 1.762095e-03 1.762095e-03 3.242833e-04 3.242833e-04 3.242833e-04
[31] 3.242833e-04 3.242833e-04 3.242833e-04 3.242833e-04 3.242833e-04
[36] 3.242833e-04 3.242833e-04 3.242833e-04 2.227490e-04 2.227490e-04
[41] 2.227490e-04 4.512182e-05 4.512182e-05 4.512182e-05 2.573794e-05
[46] 3.927422e-06 3.927422e-06 3.927422e-06 3.927422e-06 3.927422e-06
[51] 3.927422e-06 3.927422e-06 3.927422e-06 3.927422e-06 3.927422e-06
[56] 3.927422e-06 3.927422e-06 3.927422e-06 3.927422e-06 3.577770e-07
[61] 3.577770e-07 2.989021e-07 2.989021e-07 3.359826e-09 3.359826e-09
[66] 3.359826e-09 3.359826e-09 3.359826e-09 3.359826e-09 3.359826e-09
[71] 3.359826e-09 1.452960e-09 1.438511e-09 1.438511e-09 1.438511e-09
[76] 1.438511e-09 1.438511e-09 1.357719e-09 1.357719e-09 8.368029e-10
[81] 8.368029e-10 8.368029e-10 8.368029e-10 1.307656e-10 1.307656e-10
[86] 1.307656e-10 1.307656e-10 1.307656e-10 1.307656e-10 1.307656e-10
[91] 2.457301e-12 2.457301e-12 2.457301e-12 2.457301e-12 2.457301e-12
[96] 2.457301e-12 2.457301e-12 2.457301e-12 2.457301e-12 2.457301e-12
[101] 2.457301e-12 2.457301e-12 1.836514e-12 1.836514e-12 7.405935e-13
[106] 7.405935e-13 9.555996e-14 9.555996e-14 9.555996e-14 9.555996e-14
[111] 9.555996e-14 9.555996e-14 9.555996e-14 9.555996e-14 9.555996e-14
[116] 9.555996e-14 9.555996e-14 9.555996e-14 4.488064e-14 2.591881e-14
[121] 2.591881e-14 7.651104e-16 7.651104e-16 7.651104e-16 7.651104e-16
[126] 6.282602e-16 6.282602e-16 6.282602e-16 6.282602e-16 6.282602e-16
[131] 3.200478e-16 3.200478e-16 3.200478e-16 3.200478e-16 3.200478e-16
[136] 3.200478e-16 3.200478e-16 3.200478e-16 3.200478e-16 1.973895e-16
[141] 1.973895e-16 1.973895e-16 1.115809e-16 1.115809e-16 1.115809e-16
[146] 1.115809e-16 3.813215e-17 3.813215e-17 9.568118e-18 9.568118e-18
[151] 9.568118e-18 9.568118e-18 9.568118e-18 4.689996e-18 4.689996e-18
[156] 4.689996e-18 4.689996e-18 4.689996e-18 1.878585e-18 5.996729e-19
[161] 5.996729e-19 5.996729e-19 4.375495e-19 4.375495e-19 2.514807e-19
[166] 1.715069e-19 1.715069e-19 1.715069e-19 8.444166e-20 6.300337e-20
[171] 6.300337e-20 6.300337e-20 4.974277e-20 4.974277e-20 4.735747e-20
[176] 3.066051e-20 2.439194e-20 1.112233e-21 1.112233e-21 1.112233e-21
[181] 1.112233e-21 1.112233e-21 1.112233e-21 1.112233e-21 1.112233e-21
[186] 1.356627e-22 1.356627e-22 1.356627e-22 1.356627e-22 1.356627e-22
[191] 1.356627e-22 1.356627e-22 1.356627e-22 1.325608e-22 1.325608e-22
[196] 5.790256e-23 2.386139e-23 1.170190e-23 1.170190e-23 4.030849e-24
$member$pop
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[100,] -2.8813545 8.14896984
$member$storepop
list()
attr(,"class")
[1] "DEoptim"
Iteration: 1 bestvalit: 3.859239 bestmemit: 0.110778 0.187444
Iteration: 2 bestvalit: 1.340691 bestmemit: 1.596140 2.448400
Iteration: 3 bestvalit: 1.340691 bestmemit: 1.596140 2.448400
Iteration: 4 bestvalit: 1.340691 bestmemit: 1.596140 2.448400
Iteration: 5 bestvalit: 1.340691 bestmemit: 1.596140 2.448400
Iteration: 6 bestvalit: 1.340691 bestmemit: 1.596140 2.448400
Iteration: 7 bestvalit: 0.717934 bestmemit: 1.708236 2.871557
Iteration: 8 bestvalit: 0.717934 bestmemit: 1.708236 2.871557
Iteration: 9 bestvalit: 0.717934 bestmemit: 1.708236 2.871557
Iteration: 10 bestvalit: 0.717934 bestmemit: 1.708236 2.871557
Iteration: 11 bestvalit: 0.717934 bestmemit: 1.708236 2.871557
Iteration: 12 bestvalit: 0.717934 bestmemit: 1.708236 2.871557
Iteration: 13 bestvalit: 0.717934 bestmemit: 1.708236 2.871557
Iteration: 14 bestvalit: 0.717934 bestmemit: 1.708236 2.871557
Iteration: 15 bestvalit: 0.717934 bestmemit: 1.708236 2.871557
Iteration: 16 bestvalit: 0.513273 bestmemit: 1.281960 1.577559
Iteration: 17 bestvalit: 0.513273 bestmemit: 1.281960 1.577559
Iteration: 18 bestvalit: 0.513273 bestmemit: 1.281960 1.577559
Iteration: 19 bestvalit: 0.513273 bestmemit: 1.281960 1.577559
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$member$bestvalit
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[9] 68.29034 68.29034 67.92941 67.92941 67.92941 67.78611 67.62835 67.62835
[17] 67.62835 67.62835 67.62835 67.62835 67.62835 67.62835 67.62835 67.62835
[25] 67.62835 67.62835 67.62835 67.62835 67.58510 67.52985 67.48126 67.48126
[33] 67.48126 67.48126 67.48126 67.48126 67.47092 67.47092 67.47092 67.47092
[41] 67.47092 67.47092 67.47092 67.47092 67.47092 67.47092 67.47092 67.47092
[49] 67.47092 67.47092 67.47092 67.47092 67.47092 67.47092 67.47092 67.47092
[57] 67.47092 67.47092 67.47092 67.47092 67.47092 67.47092 67.47033 67.46800
[65] 67.46800 67.46800 67.46800 67.46800 67.46800 67.46800 67.46776 67.46776
[73] 67.46776 67.46776 67.46776 67.46776 67.46776 67.46776 67.46776 67.46776
[81] 67.46776 67.46776 67.46776 67.46776 67.46776 67.46776 67.46776 67.46776
[89] 67.46776 67.46774 67.46774 67.46774 67.46774 67.46774 67.46774 67.46774
[97] 67.46774 67.46774 67.46774 67.46774 67.46774 67.46774 67.46774 67.46774
[105] 67.46774 67.46774 67.46774 67.46774 67.46774 67.46774 67.46774 67.46774
[113] 67.46774 67.46774 67.46774 67.46774 67.46774 67.46773 67.46773 67.46773
[121] 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773
[129] 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773
[137] 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773
[145] 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773
[153] 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773
[161] 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773
[169] 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773
[177] 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773
[185] 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773
[193] 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773 67.46773
$member$pop
[,1]
[1,] -15.66160
[2,] -15.81515
[3,] -15.66161
[4,] -15.50654
[5,] -15.96722
[6,] -15.66161
[7,] -15.96724
[8,] -15.81515
[9,] -15.50699
[10,] -15.50651
[11,] -15.96720
[12,] -15.96733
[13,] -15.81515
[14,] -15.96724
[15,] -15.66161
[16,] -15.96723
[17,] -15.50655
[18,] -15.66160
[19,] -15.96721
[20,] -15.66160
[21,] -15.96725
[22,] -15.66163
[23,] -15.50661
[24,] -15.96721
[25,] -15.96719
[26,] -15.50652
[27,] -15.66160
[28,] -14.20047
[29,] -15.96722
[30,] -15.66161
[31,] -15.81515
[32,] -15.66161
[33,] -15.66161
[34,] -15.81515
[35,] -15.66160
[36,] -15.50652
[37,] -15.66158
[38,] -15.81515
[39,] -15.66160
[40,] -15.50653
[41,] -15.81515
[42,] -15.81515
[43,] -15.81516
[44,] -15.96720
[45,] -15.50655
[46,] -15.81515
[47,] -15.50656
[48,] -15.96720
[49,] -15.96721
[50,] -15.50656
$member$storepop
list()
attr(,"class")
[1] "DEoptim"
RcppDE documentation built on May 2, 2019, 5 p.m.
R Package Documentation
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
Performs evolutionary global optimization via the Differential Evolution algorithm.
Usage
1 | DEoptim(fn, lower, upper, control = DEoptim.control(), ...)
|
Arguments
fn |
the function to be optimized (minimized). The function should have as its first
argument the vector of real-valued parameters to optimize, and return a scalar real result. |
lower, upper |
two vectors specifying scalar real lower and upper bounds on each parameter to be optimized, so that the i-th element
of |
control |
a list of control parameters; see |
... |
further arguments to be passed to |
Details
DEoptim performs optimization (minimization) of fn.
The control argument is a list; see the help file for
DEoptim.control for details.
The R implementation of Differential Evolution (DE), DEoptim, was first published on the Comprehensive R Archive Network (CRAN) in 2005 by David Ardia. Early versions were written in pure R. Since version 2.0-0 (published to CRAN in 2009) the package has relied on an interface to a C implementation of DE, which is significantly faster on most problems as compared to the implementation in pure R. The C interface is in many respects similar to the MS Visual C++ v5.0 implementation of the Differential Evolution algorithm distributed with the book Differential Evolution – A Practical Approach to Global Optimization by Price, K.V., Storn, R.M., Lampinen J.A, Springer-Verlag, 2006, and found on-line at http://www.icsi.berkeley.edu/~storn/. Since version 2.0-3 the C implementation dynamically allocates the memory required to store the population, removing limitations on the number of members in the population and length of the parameter vectors that may be optimized. Since becoming publicly available, the package DEoptim has been used by several authors to solve optimization problems arising in diverse domains; see Mullen et al. (2009) for a review.
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 (than box constraints) on the parameters x of
fn(x), for instance x[1] + x[2]^2 < 2, integrate the
constraint within the function to optimize, for instance:
1 2 3 4 5 6 7 8 9 |
This simplistic strategy usually does not work all that well for gradient-based or Newton-type methods. It is likely to be alright when the solution is in the interior of the feasible region, but when the solution is on the boundary, optimization algorithm would have a difficult time converging. Furthermore, when the solution is on the boundary, this strategy would make the algorithm converge to an inferior solution in the interior. However, for methods such as DE which are not gradient based, this strategy might not be that bad.
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).
It is important to emphasize that the result of DEoptim is a random variable,
i.e., different results will obtain when the algorithm is run repeatedly with the same
settings. Hence, the user should set the random seed if they want to reproduce the results, e.g., by
setting set.seed(1234) before the call of DEoptim.
DEoptim relies on repeated evaluation of the objective function
in order to move the population toward a global minimum. Users
interested in making DEoptim run as fast as possible should
ensure that evaluation of the objective function is as efficient as
possible. Using pure R code, this may often be accomplished
using vectorization. Writing parts of the objective function in a
lower-level language like C or Fortran may also increase speed.
Further details and examples of the R package DEoptim can be found in Mullen et al. (2009) and Ardia et al. (2010).
Please cite the package in publications.
Value
The output of the function DEoptim is a member of the S3 class DEoptim. More precisely,
this is a list (of length 2) containing the following elements:
optim, a list containing the following elements:
-
bestmem: the best set of parameters found. -
bestval: the value offncorresponding tobestmem. -
nfeval: number of function evaluations. -
iter: number of procedure iterations.
member, a list containing the following elements:
-
lower: the lower boundary. -
upper: the upper boundary. -
bestvalit: the best value offnat each iteration. -
bestmemit: the best member at each iteration. -
pop: the population generated at the last iteration. -
storepop: a list containing the intermediate populations.
Members of the class DEoptim have a plot method that
accepts the argument plot.type. plot.type = "bestmemit" results
in a plot of the parameter values that represent the lowest value of the objective function
each generation. plot.type = "bestvalit" plots the best value of
the objective function each generation. Finally, plot.type = "storepop" results in a plot of
stored populations (which are only available if these have been saved by
setting the control argument of DEoptim appropriately). Storing intermediate populations
allows us to examine the progress of the optimization in detail.
A summary method also exists and returns the best parameter vector, the best value of the objective function,
the number of generations optimization ran, and the number of times the
objective function was evaluated.
Note
Differential Evolution (DE) is a search heuristic introduced by Storn and Price (1997). Its remarkable performance as a global optimization algorithm on continuous numerical minimization problems has been extensively explored; see Price et al. (2006). DE belongs to the class of genetic algorithms which use biology-inspired operations of crossover, mutation, and selection on a population in order to minimize an objective function over the course of successive generations (see Mitchell, 1998). As with other evolutionary algorithms, DE solves optimization problems by evolving a population of candidate solutions using alteration and selection operators. DE uses floating-point instead of bit-string encoding of population members, and arithmetic operations instead of logical operations in mutation. DE is particularly well-suited to find the global optimum of a real-valued function of real-valued parameters, and does not require that the function be either continuous or differentiable.
Let NP denote the number of parameter vectors (members) x in R^d in the population. In order to create the initial generation, NP guesses for the optimal value of the parameter vector are made, either using random values between lower and upper bounds (defined by the user) or using values given by the user. Each generation involves creation of a new population from the current population members {x_i | i=1,...,NP}, where i indexes the vectors that make up the population. This is accomplished using differential mutation of the population members. An initial mutant parameter vector v_i is created by choosing three members of the population, x_{r_0}, x_{r_1} and x_{r_2}, at random. Then v_i is generated as
v_i := x_{r_0} + F * (x_{r_1} - x_{r_2})
where F is a positive scale factor, effective values for which are
typically less than one. After the first mutation operation, mutation is
continued until d mutations have been made, with a crossover probability
CR in [0,1].
The crossover probability CR controls the fraction of the parameter
values that are copied from the mutant. If an element of the trial parameter vector is found to violate the
bounds after mutation and crossover, it is reset in such a way that the bounds are respected (with the
specific protocol depending on the implementation).
Then, the objective function values associated with the children are determined. If a trial
vector has equal or lower objective function value than the previous
vector it replaces the previous vector in the population;
otherwise the previous vector remains. Variations of this scheme have also
been proposed; see Price et al. (2006) and DEoptim.control.
Intuitively, the effect of the scheme is that the shape of the distribution of the population in the search space is converging with respect to size and direction towards areas with high fitness. The closer the population gets to the global optimum, the more the distribution will shrink and therefore reinforce the generation of smaller difference vectors.
As a general advice regarding the choice of NP, F and CR, Storn et al. (2006) state the following: Set the number of parents NP to 10 times the number of parameters, select weighting factor F = 0.8 and crossover constant CR = 0.9. Make sure that you initialize your parameter vectors by exploiting their full numerical range, i.e., if a parameter is allowed to exhibit values in the range [-100, 100] it is a good idea to pick the initial values from this range instead of unnecessarily restricting diversity. 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., DE is getting more robust (there is always a convergence speed/robustness trade-off).
DE 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 DE robust enough for a particular problem. For more details on the DE strategy, we refer the reader to Storn and Price (1997) and Price et al. (2006).
Author(s)
For RcppDE: Dirk Eddelbuettel.
For DEoptim: David Ardia, Katharine Mullen katharine.mullen@nist.gov, Brian Peterson and Joshua Ulrich.
References
Differential Evolution homepage: URL http://www.icsi.berkeley.edu/~storn/code.html
Storn, R. and Price, K. (1997) Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces, Journal of Global Optimization, 11:4, 341–359.
Price, K.V., Storn, R.M., Lampinen J.A. (2006) Differential Evolution - A Practical Approach to Global Optimization. Berlin Heidelberg: Springer-Verlag. ISBN 3540209506.
Mitchell, M. (1998) An Introduction to Genetic Algorithms. The MIT Press. ISBN 0262631857.
Mullen, K.M., Ardia, D., Gil, D.L, Windover, D., Cline, J. (2009) DEoptim: An R Package for Global Optimization by Differential Evolution. URL http://ssrn.com/abstract=1526466
Ardia, D., Boudt, K., Carl, P., Mullen, K.M., Peterson, B.G. (2010) Differential Evolution (DEoptim) for Non-Convex Portfolio Optimization. URL http://ssrn.com/abstract=1584905
See Also
DEoptim.control for control arguments,
DEoptim-methods for methods on DEoptim objects,
including some examples in plotting the results;
optim or constrOptim
for alternative optimization algorithms.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | ## Rosenbrock Banana function
## The function has a global minimum f(x) = 0 at the point (0,0).
## Note that the vector of parameters to be optimized must be the first
## argument of the objective function passed to DEoptim.
Rosenbrock <- function(x){
x1 <- x[1]
x2 <- x[2]
100 * (x2 - x1 * x1)^2 + (1 - x1)^2
}
## DEoptim searches for minima of the objective function between
## lower and upper bounds on each parameter to be optimized. Therefore
## in the call to DEoptim we specify vectors that comprise the
## lower and upper bounds; these vectors are the same length as the
## parameter vector.
lower <- c(-10,-10)
upper <- -lower
## run DEoptim and set a seed first for replicability
set.seed(1234)
DEoptim(Rosenbrock, lower, upper)
## increase the population size
DEoptim(Rosenbrock, lower, upper, DEoptim.control(NP = 100))
## change other settings and store the output
outDEoptim <- DEoptim(Rosenbrock, lower, upper, DEoptim.control(NP = 80,
itermax = 400, F = 1.2, CR = 0.7))
## plot the output
plot(outDEoptim)
## '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 = "'Wild function'")
outDEoptim <- DEoptim(Wild, lower = -50, upper = 50,
control = DEoptim.control(trace = FALSE))
plot(outDEoptim)
DEoptim(Wild, lower = -50, upper = 50,
control = DEoptim.control(NP = 50))
|
Example output
Now loading:
RcppDE: C++ Implementation of Differential Evolution Optimisation
Author: Dirk Eddelbuettel
Based on:
DEoptim (version 2.0-7): Differential Evolution algorithm in R
Authors: David Ardia, Katharine Mullen, Brian Peterson and Joshua Ulrich
Iteration: 1 bestvalit: 6.346930 bestmemit: -1.516509 2.311679
Iteration: 2 bestvalit: 5.620014 bestmemit: 0.435505 0.419911
Iteration: 3 bestvalit: 2.735287 bestmemit: 1.069276 1.308593
Iteration: 4 bestvalit: 0.425506 bestmemit: 0.347692 0.120983
Iteration: 5 bestvalit: 0.425506 bestmemit: 0.347692 0.120983
Iteration: 6 bestvalit: 0.372295 bestmemit: 0.447835 0.174593
Iteration: 7 bestvalit: 0.372295 bestmemit: 0.447835 0.174593
Iteration: 8 bestvalit: 0.372295 bestmemit: 0.447835 0.174593
Iteration: 9 bestvalit: 0.372295 bestmemit: 0.447835 0.174593
Iteration: 10 bestvalit: 0.372295 bestmemit: 0.447835 0.174593
Iteration: 11 bestvalit: 0.372295 bestmemit: 0.447835 0.174593
Iteration: 12 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 13 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 14 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 15 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 16 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 17 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 18 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 19 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 20 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 21 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 22 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 23 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 24 bestvalit: 0.064301 bestmemit: 0.795540 0.647883
Iteration: 25 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 26 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 27 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 28 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 29 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 30 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 31 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 32 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 33 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 34 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 35 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 36 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 37 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 38 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 39 bestvalit: 0.002878 bestmemit: 1.022910 1.041495
Iteration: 40 bestvalit: 0.001137 bestmemit: 0.966398 0.934214
Iteration: 41 bestvalit: 0.001137 bestmemit: 0.966398 0.934214
Iteration: 42 bestvalit: 0.001137 bestmemit: 0.966398 0.934214
Iteration: 43 bestvalit: 0.001137 bestmemit: 0.966398 0.934214
Iteration: 44 bestvalit: 0.001137 bestmemit: 0.966398 0.934214
Iteration: 45 bestvalit: 0.001137 bestmemit: 0.966398 0.934214
Iteration: 46 bestvalit: 0.000225 bestmemit: 0.986703 0.972892
Iteration: 47 bestvalit: 0.000225 bestmemit: 0.986703 0.972892
Iteration: 48 bestvalit: 0.000225 bestmemit: 0.986703 0.972892
Iteration: 49 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 50 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 51 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 52 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 53 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 54 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 55 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 56 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 57 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 58 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 59 bestvalit: 0.000090 bestmemit: 0.992026 0.984634
Iteration: 60 bestvalit: 0.000050 bestmemit: 1.000960 1.002619
Iteration: 61 bestvalit: 0.000050 bestmemit: 1.000960 1.002619
Iteration: 62 bestvalit: 0.000050 bestmemit: 1.000960 1.002619
Iteration: 63 bestvalit: 0.000023 bestmemit: 1.004405 1.008635
Iteration: 64 bestvalit: 0.000023 bestmemit: 1.004405 1.008635
Iteration: 65 bestvalit: 0.000005 bestmemit: 1.002342 1.004696
Iteration: 66 bestvalit: 0.000005 bestmemit: 1.002342 1.004696
Iteration: 67 bestvalit: 0.000005 bestmemit: 1.002342 1.004696
Iteration: 68 bestvalit: 0.000003 bestmemit: 0.999158 0.998169
Iteration: 69 bestvalit: 0.000001 bestmemit: 1.000746 1.001415
Iteration: 70 bestvalit: 0.000001 bestmemit: 1.000746 1.001415
Iteration: 71 bestvalit: 0.000001 bestmemit: 1.000746 1.001415
Iteration: 72 bestvalit: 0.000001 bestmemit: 1.000746 1.001415
Iteration: 73 bestvalit: 0.000001 bestmemit: 1.000514 1.001100
Iteration: 74 bestvalit: 0.000000 bestmemit: 0.999758 0.999565
Iteration: 75 bestvalit: 0.000000 bestmemit: 0.999758 0.999565
Iteration: 76 bestvalit: 0.000000 bestmemit: 0.999758 0.999565
Iteration: 77 bestvalit: 0.000000 bestmemit: 0.999758 0.999565
Iteration: 78 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 79 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 80 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 81 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 82 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 83 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 84 bestvalit: 0.000000 bestmemit: 1.000336 1.000655
Iteration: 85 bestvalit: 0.000000 bestmemit: 0.999802 0.999621
Iteration: 86 bestvalit: 0.000000 bestmemit: 0.999802 0.999621
Iteration: 87 bestvalit: 0.000000 bestmemit: 0.999802 0.999621
Iteration: 88 bestvalit: 0.000000 bestmemit: 0.999802 0.999621
Iteration: 89 bestvalit: 0.000000 bestmemit: 0.999873 0.999752
Iteration: 90 bestvalit: 0.000000 bestmemit: 0.999873 0.999752
Iteration: 91 bestvalit: 0.000000 bestmemit: 0.999873 0.999752
Iteration: 92 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 93 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 94 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 95 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 96 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 97 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 98 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 99 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 100 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 101 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 102 bestvalit: 0.000000 bestmemit: 1.000029 1.000062
Iteration: 103 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 104 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 105 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 106 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 107 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 108 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 109 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 110 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 111 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 112 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 113 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 114 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 115 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 116 bestvalit: 0.000000 bestmemit: 1.000004 1.000008
Iteration: 117 bestvalit: 0.000000 bestmemit: 0.999996 0.999991
Iteration: 118 bestvalit: 0.000000 bestmemit: 0.999996 0.999991
Iteration: 119 bestvalit: 0.000000 bestmemit: 0.999996 0.999991
Iteration: 120 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 121 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 122 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 123 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 124 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 125 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 126 bestvalit: 0.000000 bestmemit: 1.000003 1.000005
Iteration: 127 bestvalit: 0.000000 bestmemit: 1.000001 1.000002
Iteration: 128 bestvalit: 0.000000 bestmemit: 1.000001 1.000002
Iteration: 129 bestvalit: 0.000000 bestmemit: 1.000001 1.000002
Iteration: 130 bestvalit: 0.000000 bestmemit: 1.000001 1.000003
Iteration: 131 bestvalit: 0.000000 bestmemit: 1.000000 0.999999
Iteration: 132 bestvalit: 0.000000 bestmemit: 1.000000 0.999999
Iteration: 133 bestvalit: 0.000000 bestmemit: 1.000000 0.999999
Iteration: 134 bestvalit: 0.000000 bestmemit: 1.000000 0.999999
Iteration: 135 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 136 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
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Iteration: 138 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 139 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 140 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 141 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 142 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 143 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 144 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 145 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 146 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 147 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 148 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 149 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 150 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 151 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 152 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 153 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 154 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 155 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 156 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 157 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 158 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 159 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 160 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 161 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 162 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 163 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 164 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 165 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 166 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 167 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 168 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 169 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 170 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 171 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 172 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 173 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 174 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 175 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 176 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 177 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 178 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 179 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 180 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 181 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 182 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 183 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 184 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 185 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 186 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 187 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 188 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 189 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 190 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 191 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 192 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 193 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 194 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 195 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 196 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 197 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 198 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 199 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
Iteration: 200 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
$optim
$optim$bestmem
par1 par2
1 1
$optim$bestval
[1] 2.54782e-21
$optim$nfeval
[1] 10050
$optim$iter
[1] 200
$member
$member$lower
par1 par2
-10 -10
$member$upper
par1 par2
10 10
$member$bestmemit
par1 par2
1 1.0666718 2.9281219
2 -1.5165089 2.3116791
3 0.4355051 0.4199115
4 1.0692761 1.3085932
5 0.3476923 0.1209829
6 0.3476923 0.1209829
7 0.4478347 0.1745927
8 0.4478347 0.1745927
9 0.4478347 0.1745927
10 0.4478347 0.1745927
11 0.4478347 0.1745927
12 0.4478347 0.1745927
13 0.7955400 0.6478828
14 0.7955400 0.6478828
15 0.7955400 0.6478828
16 0.7955400 0.6478828
17 0.7955400 0.6478828
18 0.7955400 0.6478828
19 0.7955400 0.6478828
20 0.7955400 0.6478828
21 0.7955400 0.6478828
22 0.7955400 0.6478828
23 0.7955400 0.6478828
24 0.7955400 0.6478828
25 0.7955400 0.6478828
26 1.0229105 1.0414949
27 1.0229105 1.0414949
28 1.0229105 1.0414949
29 1.0229105 1.0414949
30 1.0229105 1.0414949
31 1.0229105 1.0414949
32 1.0229105 1.0414949
33 1.0229105 1.0414949
34 1.0229105 1.0414949
35 1.0229105 1.0414949
36 1.0229105 1.0414949
37 1.0229105 1.0414949
38 1.0229105 1.0414949
39 1.0229105 1.0414949
40 1.0229105 1.0414949
41 0.9663977 0.9342136
42 0.9663977 0.9342136
43 0.9663977 0.9342136
44 0.9663977 0.9342136
45 0.9663977 0.9342136
46 0.9663977 0.9342136
47 0.9867034 0.9728923
48 0.9867034 0.9728923
49 0.9867034 0.9728923
50 0.9920263 0.9846341
51 0.9920263 0.9846341
52 0.9920263 0.9846341
53 0.9920263 0.9846341
54 0.9920263 0.9846341
55 0.9920263 0.9846341
56 0.9920263 0.9846341
57 0.9920263 0.9846341
58 0.9920263 0.9846341
59 0.9920263 0.9846341
60 0.9920263 0.9846341
61 1.0009596 1.0026186
62 1.0009596 1.0026186
63 1.0009596 1.0026186
64 1.0044055 1.0086351
65 1.0044055 1.0086351
66 1.0023415 1.0046965
67 1.0023415 1.0046965
68 1.0023415 1.0046965
69 0.9991581 0.9981689
70 1.0007455 1.0014146
71 1.0007455 1.0014146
72 1.0007455 1.0014146
73 1.0007455 1.0014146
74 1.0005139 1.0010997
75 0.9997581 0.9995646
76 0.9997581 0.9995646
77 0.9997581 0.9995646
78 0.9997581 0.9995646
79 1.0003362 1.0006548
80 1.0003362 1.0006548
81 1.0003362 1.0006548
82 1.0003362 1.0006548
83 1.0003362 1.0006548
84 1.0003362 1.0006548
85 1.0003362 1.0006548
86 0.9998024 0.9996206
87 0.9998024 0.9996206
88 0.9998024 0.9996206
89 0.9998024 0.9996206
90 0.9998735 0.9997522
91 0.9998735 0.9997522
92 0.9998735 0.9997522
93 1.0000290 1.0000624
94 1.0000290 1.0000624
95 1.0000290 1.0000624
96 1.0000290 1.0000624
97 1.0000290 1.0000624
98 1.0000290 1.0000624
99 1.0000290 1.0000624
100 1.0000290 1.0000624
101 1.0000290 1.0000624
102 1.0000290 1.0000624
103 1.0000290 1.0000624
104 1.0000038 1.0000084
105 1.0000038 1.0000084
106 1.0000038 1.0000084
107 1.0000038 1.0000084
108 1.0000038 1.0000084
109 1.0000038 1.0000084
110 1.0000038 1.0000084
111 1.0000038 1.0000084
112 1.0000038 1.0000084
113 1.0000038 1.0000084
114 1.0000038 1.0000084
115 1.0000038 1.0000084
116 1.0000038 1.0000084
117 1.0000038 1.0000084
118 0.9999957 0.9999906
119 0.9999957 0.9999906
120 0.9999957 0.9999906
121 1.0000028 1.0000054
122 1.0000028 1.0000054
123 1.0000028 1.0000054
124 1.0000028 1.0000054
125 1.0000028 1.0000054
126 1.0000028 1.0000054
127 1.0000028 1.0000054
128 1.0000007 1.0000015
129 1.0000007 1.0000015
130 1.0000007 1.0000015
131 1.0000013 1.0000027
132 0.9999996 0.9999991
133 0.9999996 0.9999991
134 0.9999996 0.9999991
135 0.9999996 0.9999991
136 1.0000002 1.0000005
137 1.0000002 1.0000005
138 1.0000002 1.0000005
139 1.0000002 1.0000005
140 1.0000002 1.0000005
141 1.0000002 1.0000005
142 1.0000002 1.0000005
143 1.0000002 1.0000005
144 1.0000000 0.9999999
145 1.0000000 0.9999999
146 1.0000000 0.9999999
147 1.0000000 0.9999999
148 1.0000000 0.9999999
149 1.0000000 0.9999999
150 1.0000000 0.9999999
151 1.0000000 0.9999999
152 1.0000000 0.9999999
153 1.0000000 0.9999999
154 1.0000000 1.0000000
155 1.0000000 1.0000000
156 1.0000000 1.0000000
157 1.0000000 1.0000000
158 1.0000000 1.0000000
159 1.0000000 0.9999999
160 1.0000000 0.9999999
161 1.0000000 0.9999999
162 1.0000000 0.9999999
163 1.0000000 1.0000000
164 1.0000000 1.0000000
165 1.0000000 1.0000000
166 1.0000000 1.0000000
167 1.0000000 1.0000000
168 1.0000000 1.0000000
169 1.0000000 1.0000000
170 1.0000000 1.0000000
171 1.0000000 1.0000000
172 1.0000000 1.0000000
173 1.0000000 1.0000000
174 1.0000000 1.0000000
175 1.0000000 1.0000000
176 1.0000000 1.0000000
177 1.0000000 1.0000000
178 1.0000000 1.0000000
179 1.0000000 1.0000000
180 1.0000000 1.0000000
181 1.0000000 1.0000000
182 1.0000000 1.0000000
183 1.0000000 1.0000000
184 1.0000000 1.0000000
185 1.0000000 1.0000000
186 1.0000000 1.0000000
187 1.0000000 1.0000000
188 1.0000000 1.0000000
189 1.0000000 1.0000000
190 1.0000000 1.0000000
191 1.0000000 1.0000000
192 1.0000000 1.0000000
193 1.0000000 1.0000000
194 1.0000000 1.0000000
195 1.0000000 1.0000000
196 1.0000000 1.0000000
197 1.0000000 1.0000000
198 1.0000000 1.0000000
199 1.0000000 1.0000000
200 1.0000000 1.0000000
$member$bestvalit
[1] 3.205337e+02 6.346930e+00 5.620014e+00 2.735287e+00 4.255061e-01
[6] 4.255061e-01 3.722953e-01 3.722953e-01 3.722953e-01 3.722953e-01
[11] 3.722953e-01 3.722953e-01 6.430063e-02 6.430063e-02 6.430063e-02
[16] 6.430063e-02 6.430063e-02 6.430063e-02 6.430063e-02 6.430063e-02
[21] 6.430063e-02 6.430063e-02 6.430063e-02 6.430063e-02 6.430063e-02
[26] 2.878081e-03 2.878081e-03 2.878081e-03 2.878081e-03 2.878081e-03
[31] 2.878081e-03 2.878081e-03 2.878081e-03 2.878081e-03 2.878081e-03
[36] 2.878081e-03 2.878081e-03 2.878081e-03 2.878081e-03 2.878081e-03
[41] 1.137470e-03 1.137470e-03 1.137470e-03 1.137470e-03 1.137470e-03
[46] 1.137470e-03 2.245852e-04 2.245852e-04 2.245852e-04 9.038870e-05
[51] 9.038870e-05 9.038870e-05 9.038870e-05 9.038870e-05 9.038870e-05
[56] 9.038870e-05 9.038870e-05 9.038870e-05 9.038870e-05 9.038870e-05
[61] 4.970519e-05 4.970519e-05 4.970519e-05 2.321945e-05 2.321945e-05
[66] 5.489089e-06 5.489089e-06 5.489089e-06 2.895931e-06 1.148947e-06
[71] 1.148947e-06 1.148947e-06 1.148947e-06 7.769532e-07 2.921012e-07
[76] 2.921012e-07 2.921012e-07 2.921012e-07 1.443103e-07 1.443103e-07
[81] 1.443103e-07 1.443103e-07 1.443103e-07 1.443103e-07 1.443103e-07
[86] 6.395584e-08 6.395584e-08 6.395584e-08 6.395584e-08 1.884063e-08
[91] 1.884063e-08 1.884063e-08 2.777032e-09 2.777032e-09 2.777032e-09
[96] 2.777032e-09 2.777032e-09 2.777032e-09 2.777032e-09 2.777032e-09
[101] 2.777032e-09 2.777032e-09 2.777032e-09 8.818867e-11 8.818867e-11
[106] 8.818867e-11 8.818867e-11 8.818867e-11 8.818867e-11 8.818867e-11
[111] 8.818867e-11 8.818867e-11 8.818867e-11 8.818867e-11 8.818867e-11
[116] 8.818867e-11 8.818867e-11 6.742806e-11 6.742806e-11 6.742806e-11
[121] 9.732897e-12 9.732897e-12 9.732897e-12 9.732897e-12 9.732897e-12
[126] 9.732897e-12 9.732897e-12 5.345352e-12 5.345352e-12 5.345352e-12
[131] 3.783477e-12 8.869835e-13 8.869835e-13 8.869835e-13 8.869835e-13
[136] 7.104047e-14 7.104047e-14 7.104047e-14 7.104047e-14 7.104047e-14
[141] 7.104047e-14 7.104047e-14 7.104047e-14 3.419765e-15 3.419765e-15
[146] 3.419765e-15 3.419765e-15 3.419765e-15 3.419765e-15 3.419765e-15
[151] 3.419765e-15 3.419765e-15 3.419765e-15 1.411010e-15 1.411010e-15
[156] 1.411010e-15 1.411010e-15 1.411010e-15 1.283663e-15 1.283663e-15
[161] 1.283663e-15 1.283663e-15 2.242708e-16 1.478263e-16 1.478263e-16
[166] 1.478263e-16 1.478263e-16 1.478263e-16 1.478263e-16 1.672408e-17
[171] 1.672408e-17 1.672408e-17 5.477594e-18 5.477594e-18 5.477594e-18
[176] 5.477594e-18 5.477594e-18 5.477594e-18 5.477594e-18 2.521403e-18
[181] 2.521403e-18 2.521403e-18 2.521403e-18 7.061309e-19 7.061309e-19
[186] 7.061309e-19 7.061309e-19 7.061309e-19 7.061309e-19 3.270615e-19
[191] 1.059362e-20 1.059362e-20 1.059362e-20 1.059362e-20 1.059362e-20
[196] 1.059362e-20 1.059362e-20 1.059362e-20 2.547820e-21 2.547820e-21
$member$pop
[,1] [,2]
[1,] 1.00000000 1.00000000
[2,] 1.00000000 1.00000000
[3,] 1.00000000 1.00000000
[4,] 1.00000000 1.00000000
[5,] 1.00000000 1.00000000
[6,] 1.00000000 1.00000000
[7,] 1.00000000 1.00000000
[8,] 1.00000000 1.00000000
[9,] 1.00000000 1.00000000
[10,] 1.00000000 1.00000000
[11,] 1.00000000 1.00000000
[12,] 1.00000000 1.00000000
[13,] 1.00000000 1.00000000
[14,] 1.00000000 0.99999999
[15,] -0.12760425 0.05061860
[16,] 1.00000000 1.00000000
[17,] 1.00000000 1.00000000
[18,] 1.00000000 1.00000000
[19,] 1.00000000 1.00000000
[20,] 1.00000000 1.00000000
[21,] -0.07208765 -0.01764878
[22,] 1.00000000 1.00000000
[23,] 1.00000000 1.00000000
[24,] 1.00000000 1.00000000
[25,] 1.00000000 1.00000000
[26,] 1.00000000 1.00000000
[27,] -1.83316974 3.39594294
[28,] 1.00000000 1.00000000
[29,] 1.00000000 1.00000000
[30,] 1.00000000 1.00000000
[31,] -1.83171918 3.38799793
[32,] 1.00000000 1.00000000
[33,] 1.00000000 1.00000000
[34,] 1.00000000 1.00000000
[35,] 1.00000000 1.00000000
[36,] 1.00000000 1.00000000
[37,] 1.00000000 1.00000000
[38,] 1.00000000 1.00000000
[39,] 1.00000000 1.00000000
[40,] 1.00000000 1.00000000
[41,] 1.00000000 1.00000000
[42,] 1.00000000 1.00000000
[43,] 1.00000000 1.00000000
[44,] 1.00000000 1.00000000
[45,] 1.00000000 1.00000000
[46,] 1.00000000 0.99999999
[47,] 1.00000000 1.00000000
[48,] 1.00000000 0.99999999
[49,] 1.00000000 1.00000000
[50,] 1.00000000 1.00000000
$member$storepop
list()
attr(,"class")
[1] "DEoptim"
Iteration: 1 bestvalit: 2.182569 bestmemit: 0.295523 -0.042523
Iteration: 2 bestvalit: 1.630486 bestmemit: 0.065188 0.091233
Iteration: 3 bestvalit: 1.630486 bestmemit: 0.065188 0.091233
Iteration: 4 bestvalit: 1.303092 bestmemit: 1.605471 2.480763
Iteration: 5 bestvalit: 1.303092 bestmemit: 1.605471 2.480763
Iteration: 6 bestvalit: 1.303092 bestmemit: 1.605471 2.480763
Iteration: 7 bestvalit: 1.132293 bestmemit: 0.976363 0.846901
Iteration: 8 bestvalit: 1.132293 bestmemit: 0.976363 0.846901
Iteration: 9 bestvalit: 0.608228 bestmemit: 1.429628 1.978748
Iteration: 10 bestvalit: 0.608228 bestmemit: 1.429628 1.978748
Iteration: 11 bestvalit: 0.138446 bestmemit: 1.260788 1.616127
Iteration: 12 bestvalit: 0.138446 bestmemit: 1.260788 1.616127
Iteration: 13 bestvalit: 0.057014 bestmemit: 1.238480 1.535023
Iteration: 14 bestvalit: 0.057014 bestmemit: 1.238480 1.535023
Iteration: 15 bestvalit: 0.057014 bestmemit: 1.238480 1.535023
Iteration: 16 bestvalit: 0.057014 bestmemit: 1.238480 1.535023
Iteration: 17 bestvalit: 0.027340 bestmemit: 1.164781 1.355347
Iteration: 18 bestvalit: 0.027340 bestmemit: 1.164781 1.355347
Iteration: 19 bestvalit: 0.007054 bestmemit: 1.041878 1.078229
Iteration: 20 bestvalit: 0.007054 bestmemit: 1.041878 1.078229
Iteration: 21 bestvalit: 0.007054 bestmemit: 1.041878 1.078229
Iteration: 22 bestvalit: 0.007054 bestmemit: 1.041878 1.078229
Iteration: 23 bestvalit: 0.001762 bestmemit: 1.037466 1.078229
Iteration: 24 bestvalit: 0.001762 bestmemit: 1.037466 1.078229
Iteration: 25 bestvalit: 0.001762 bestmemit: 1.037466 1.078229
Iteration: 26 bestvalit: 0.001762 bestmemit: 1.037466 1.078229
Iteration: 27 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 28 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 29 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 30 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 31 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 32 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 33 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 34 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 35 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 36 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 37 bestvalit: 0.000324 bestmemit: 0.984960 0.969156
Iteration: 38 bestvalit: 0.000223 bestmemit: 1.009944 1.021101
Iteration: 39 bestvalit: 0.000223 bestmemit: 1.009944 1.021101
Iteration: 40 bestvalit: 0.000223 bestmemit: 1.009944 1.021101
Iteration: 41 bestvalit: 0.000045 bestmemit: 0.993643 0.987109
Iteration: 42 bestvalit: 0.000045 bestmemit: 0.993643 0.987109
Iteration: 43 bestvalit: 0.000045 bestmemit: 0.993643 0.987109
Iteration: 44 bestvalit: 0.000026 bestmemit: 1.000745 1.000990
Iteration: 45 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 46 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 47 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 48 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 49 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 50 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 51 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 52 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 53 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 54 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 55 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 56 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 57 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 58 bestvalit: 0.000004 bestmemit: 1.001909 1.003874
Iteration: 59 bestvalit: 0.000000 bestmemit: 1.000376 1.000705
Iteration: 60 bestvalit: 0.000000 bestmemit: 1.000376 1.000705
Iteration: 61 bestvalit: 0.000000 bestmemit: 1.000206 1.000462
Iteration: 62 bestvalit: 0.000000 bestmemit: 1.000206 1.000462
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Iteration: 200 bestvalit: 0.000000 bestmemit: 1.000000 1.000000
$optim
$optim$bestmem
par1 par2
1 1
$optim$bestval
[1] 4.030849e-24
$optim$nfeval
[1] 20100
$optim$iter
[1] 200
$member
$member$lower
par1 par2
-10 -10
$member$upper
par1 par2
10 10
$member$bestmemit
par1 par2
1 1.16143741 1.60714750
2 0.29552328 -0.04252291
3 0.06518848 0.09123304
4 0.06518848 0.09123304
5 1.60547071 2.48076341
6 1.60547071 2.48076341
7 1.60547071 2.48076341
8 0.97636272 0.84690117
9 0.97636272 0.84690117
10 1.42962793 1.97874775
11 1.42962793 1.97874775
12 1.26078836 1.61612696
13 1.26078836 1.61612696
14 1.23848008 1.53502323
15 1.23848008 1.53502323
16 1.23848008 1.53502323
17 1.23848008 1.53502323
18 1.16478086 1.35534671
19 1.16478086 1.35534671
20 1.04187768 1.07822897
21 1.04187768 1.07822897
22 1.04187768 1.07822897
23 1.04187768 1.07822897
24 1.03746607 1.07822897
25 1.03746607 1.07822897
26 1.03746607 1.07822897
27 1.03746607 1.07822897
28 0.98496001 0.96915585
29 0.98496001 0.96915585
30 0.98496001 0.96915585
31 0.98496001 0.96915585
32 0.98496001 0.96915585
33 0.98496001 0.96915585
34 0.98496001 0.96915585
35 0.98496001 0.96915585
36 0.98496001 0.96915585
37 0.98496001 0.96915585
38 0.98496001 0.96915585
39 1.00994439 1.02110059
40 1.00994439 1.02110059
41 1.00994439 1.02110059
42 0.99364297 0.98710932
43 0.99364297 0.98710932
44 0.99364297 0.98710932
45 1.00074550 1.00098973
46 1.00190873 1.00387442
47 1.00190873 1.00387442
48 1.00190873 1.00387442
49 1.00190873 1.00387442
50 1.00190873 1.00387442
51 1.00190873 1.00387442
52 1.00190873 1.00387442
53 1.00190873 1.00387442
54 1.00190873 1.00387442
55 1.00190873 1.00387442
56 1.00190873 1.00387442
57 1.00190873 1.00387442
58 1.00190873 1.00387442
59 1.00190873 1.00387442
60 1.00037577 1.00070515
61 1.00037577 1.00070515
62 1.00020582 1.00046233
63 1.00020582 1.00046233
64 1.00000630 1.00001836
65 1.00000630 1.00001836
66 1.00000630 1.00001836
67 1.00000630 1.00001836
68 1.00000630 1.00001836
69 1.00000630 1.00001836
70 1.00000630 1.00001836
71 1.00000630 1.00001836
72 0.99996424 0.99992980
73 1.00000894 1.00002156
74 1.00000894 1.00002156
75 1.00000894 1.00002156
76 1.00000894 1.00002156
77 1.00000894 1.00002156
78 0.99996496 0.99992878
79 0.99996496 0.99992878
80 0.99997861 0.99995917
81 0.99997861 0.99995917
82 0.99997861 0.99995917
83 0.99997861 0.99995917
84 1.00000440 1.00000986
85 1.00000440 1.00000986
86 1.00000440 1.00000986
87 1.00000440 1.00000986
88 1.00000440 1.00000986
89 1.00000440 1.00000986
90 1.00000440 1.00000986
91 0.99999854 0.99999703
92 0.99999854 0.99999703
93 0.99999854 0.99999703
94 0.99999854 0.99999703
95 0.99999854 0.99999703
96 0.99999854 0.99999703
97 0.99999854 0.99999703
98 0.99999854 0.99999703
99 0.99999854 0.99999703
100 0.99999854 0.99999703
101 0.99999854 0.99999703
102 0.99999854 0.99999703
103 0.99999866 0.99999731
104 0.99999866 0.99999731
105 0.99999939 0.99999883
106 0.99999939 0.99999883
107 1.00000027 1.00000052
108 1.00000027 1.00000052
109 1.00000027 1.00000052
110 1.00000027 1.00000052
111 1.00000027 1.00000052
112 1.00000027 1.00000052
113 1.00000027 1.00000052
114 1.00000027 1.00000052
115 1.00000027 1.00000052
116 1.00000027 1.00000052
117 1.00000027 1.00000052
118 1.00000027 1.00000052
119 1.00000021 1.00000042
120 0.99999989 0.99999978
121 0.99999989 0.99999978
122 0.99999997 0.99999995
123 0.99999997 0.99999995
124 0.99999997 0.99999995
125 0.99999997 0.99999995
126 0.99999999 0.99999998
127 0.99999999 0.99999998
128 0.99999999 0.99999998
129 0.99999999 0.99999998
130 0.99999999 0.99999998
131 0.99999999 0.99999997
132 0.99999999 0.99999997
133 0.99999999 0.99999997
134 0.99999999 0.99999997
135 0.99999999 0.99999997
136 0.99999999 0.99999997
137 0.99999999 0.99999997
138 0.99999999 0.99999997
139 0.99999999 0.99999997
140 1.00000001 1.00000003
141 1.00000001 1.00000003
142 1.00000001 1.00000003
143 0.99999999 0.99999998
144 0.99999999 0.99999998
145 0.99999999 0.99999998
146 0.99999999 0.99999998
147 1.00000000 1.00000001
148 1.00000000 1.00000001
149 1.00000000 1.00000001
150 1.00000000 1.00000001
151 1.00000000 1.00000001
152 1.00000000 1.00000001
153 1.00000000 1.00000001
154 1.00000000 1.00000000
155 1.00000000 1.00000000
156 1.00000000 1.00000000
157 1.00000000 1.00000000
158 1.00000000 1.00000000
159 1.00000000 1.00000000
160 1.00000000 1.00000000
161 1.00000000 1.00000000
162 1.00000000 1.00000000
163 1.00000000 1.00000000
164 1.00000000 1.00000000
165 1.00000000 1.00000000
166 1.00000000 1.00000000
167 1.00000000 1.00000000
168 1.00000000 1.00000000
169 1.00000000 1.00000000
170 1.00000000 1.00000000
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174 1.00000000 1.00000000
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182 1.00000000 1.00000000
183 1.00000000 1.00000000
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187 1.00000000 1.00000000
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189 1.00000000 1.00000000
190 1.00000000 1.00000000
191 1.00000000 1.00000000
192 1.00000000 1.00000000
193 1.00000000 1.00000000
194 1.00000000 1.00000000
195 1.00000000 1.00000000
196 1.00000000 1.00000000
197 1.00000000 1.00000000
198 1.00000000 1.00000000
199 1.00000000 1.00000000
200 1.00000000 1.00000000
$member$bestvalit
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[6] 1.303092e+00 1.303092e+00 1.132293e+00 1.132293e+00 6.082283e-01
[11] 6.082283e-01 1.384460e-01 1.384460e-01 5.701444e-02 5.701444e-02
[16] 5.701444e-02 5.701444e-02 2.733980e-02 2.733980e-02 7.053775e-03
[21] 7.053775e-03 7.053775e-03 7.053775e-03 1.762095e-03 1.762095e-03
[26] 1.762095e-03 1.762095e-03 3.242833e-04 3.242833e-04 3.242833e-04
[31] 3.242833e-04 3.242833e-04 3.242833e-04 3.242833e-04 3.242833e-04
[36] 3.242833e-04 3.242833e-04 3.242833e-04 2.227490e-04 2.227490e-04
[41] 2.227490e-04 4.512182e-05 4.512182e-05 4.512182e-05 2.573794e-05
[46] 3.927422e-06 3.927422e-06 3.927422e-06 3.927422e-06 3.927422e-06
[51] 3.927422e-06 3.927422e-06 3.927422e-06 3.927422e-06 3.927422e-06
[56] 3.927422e-06 3.927422e-06 3.927422e-06 3.927422e-06 3.577770e-07
[61] 3.577770e-07 2.989021e-07 2.989021e-07 3.359826e-09 3.359826e-09
[66] 3.359826e-09 3.359826e-09 3.359826e-09 3.359826e-09 3.359826e-09
[71] 3.359826e-09 1.452960e-09 1.438511e-09 1.438511e-09 1.438511e-09
[76] 1.438511e-09 1.438511e-09 1.357719e-09 1.357719e-09 8.368029e-10
[81] 8.368029e-10 8.368029e-10 8.368029e-10 1.307656e-10 1.307656e-10
[86] 1.307656e-10 1.307656e-10 1.307656e-10 1.307656e-10 1.307656e-10
[91] 2.457301e-12 2.457301e-12 2.457301e-12 2.457301e-12 2.457301e-12
[96] 2.457301e-12 2.457301e-12 2.457301e-12 2.457301e-12 2.457301e-12
[101] 2.457301e-12 2.457301e-12 1.836514e-12 1.836514e-12 7.405935e-13
[106] 7.405935e-13 9.555996e-14 9.555996e-14 9.555996e-14 9.555996e-14
[111] 9.555996e-14 9.555996e-14 9.555996e-14 9.555996e-14 9.555996e-14
[116] 9.555996e-14 9.555996e-14 9.555996e-14 4.488064e-14 2.591881e-14
[121] 2.591881e-14 7.651104e-16 7.651104e-16 7.651104e-16 7.651104e-16
[126] 6.282602e-16 6.282602e-16 6.282602e-16 6.282602e-16 6.282602e-16
[131] 3.200478e-16 3.200478e-16 3.200478e-16 3.200478e-16 3.200478e-16
[136] 3.200478e-16 3.200478e-16 3.200478e-16 3.200478e-16 1.973895e-16
[141] 1.973895e-16 1.973895e-16 1.115809e-16 1.115809e-16 1.115809e-16
[146] 1.115809e-16 3.813215e-17 3.813215e-17 9.568118e-18 9.568118e-18
[151] 9.568118e-18 9.568118e-18 9.568118e-18 4.689996e-18 4.689996e-18
[156] 4.689996e-18 4.689996e-18 4.689996e-18 1.878585e-18 5.996729e-19
[161] 5.996729e-19 5.996729e-19 4.375495e-19 4.375495e-19 2.514807e-19
[166] 1.715069e-19 1.715069e-19 1.715069e-19 8.444166e-20 6.300337e-20
[171] 6.300337e-20 6.300337e-20 4.974277e-20 4.974277e-20 4.735747e-20
[176] 3.066051e-20 2.439194e-20 1.112233e-21 1.112233e-21 1.112233e-21
[181] 1.112233e-21 1.112233e-21 1.112233e-21 1.112233e-21 1.112233e-21
[186] 1.356627e-22 1.356627e-22 1.356627e-22 1.356627e-22 1.356627e-22
[191] 1.356627e-22 1.356627e-22 1.356627e-22 1.325608e-22 1.325608e-22
[196] 5.790256e-23 2.386139e-23 1.170190e-23 1.170190e-23 4.030849e-24
$member$pop
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$member$storepop
list()
attr(,"class")
[1] "DEoptim"
Iteration: 1 bestvalit: 3.859239 bestmemit: 0.110778 0.187444
Iteration: 2 bestvalit: 1.340691 bestmemit: 1.596140 2.448400
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Iteration: 7 bestvalit: 0.717934 bestmemit: 1.708236 2.871557
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$member$pop
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$member$storepop
list()
attr(,"class")
[1] "DEoptim"
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