| Title: | Modular Differential Evolution for Experimenting with Operators |
|---|---|
| Description: | Modular implementation of the Differential Evolution algorithm for experimenting with different types of operators. |
| Authors: | Felipe Campelo [aut, cre], Moises Botelho [aut] |
| Maintainer: | Felipe Campelo <[email protected]> |
| License: | GPL-2 |
| Version: | 0.1.4 |
| Built: | 2024-10-29 03:30:27 UTC |
| Source: | https://github.com/fcampelo/expde |
Implements different stop criteria for the ExpDE framework
check_stop_criteria()check_stop_criteria()
logical flag indicating whether any stop condition has been reached.
This routine accesses the parent environment used in the main function
ExpDE(), which means that changes made in the variables
contained in env WILL change the original values. DO NOT change
anything unless you're absolutely sure of what you're doing.
Creates a new population for the ExpDE framework
create_population(popsize, probpars)create_population(popsize, probpars)
popsize |
population size |
probpars |
list of named problem parameters (see |
A matrix containing the population for the ExpDE
Evaluates the DE population on a given objective function.
evaluate_population(probpars, Pop)evaluate_population(probpars, Pop)
probpars |
problem parameters (see |
Pop |
population matrix (each row is a candidate solution, normalized to the [0, 1] interval,) |
numeric vector (with length nrow(Pop)) containing the function
values of each point in the population.
Modular implementation of the Differential Evolution Algorithm for the experimental investigation of the effects of different operators on the performance of the algorithm.
ExpDE(popsize, mutpars = list(name = "mutation_rand", f = 0.2), recpars = list(name = "recombination_bin", cr = 0.8, nvecs = 1), selpars = list(name = "standard"), stopcrit, probpars, seed = NULL, showpars = list(show.iters = "none"))ExpDE(popsize, mutpars = list(name = "mutation_rand", f = 0.2), recpars = list(name = "recombination_bin", cr = 0.8, nvecs = 1), selpars = list(name = "standard"), stopcrit, probpars, seed = NULL, showpars = list(show.iters = "none"))
popsize |
population size |
mutpars |
list of named mutation parameters.
See |
recpars |
list of named recombination parameters.
See |
selpars |
list of named selection parameters.
See |
stopcrit |
list of named stop criteria parameters.
See |
probpars |
list of named problem parameters.
See |
seed |
seed for the random number generator.
See |
showpars |
parameters that regulate the echoing of progress indicators
See |
This routine is used to launch a differential evolution algorithm for the minimization of a given problem instance using different variants of the recombination, mutation and selection operators. The input parameters that describe those operators receive list objects describing the operator variants to be used in a given optimization procedure.
A list object containing the final population (sorted by performance) , the performance vector, and some run statistics.
mutpars is used to inform the routine the type of differential
mutation to use, as well as any mutation-related parameter values. The
current version accepts the following options:
mutation_current_to_pbest (incl. special case
current-to-best)
mutpars receives a list object with name field mutpars$name
(containing the name of the function to be called, e.g.,
name = "mutation_rand") as well as whatever parameters that function
may require/accept (e.g., mutpars$f = 0.7, mutpars$nvecs = 2,
etc.). See the specific documentation of each function for details.
Some examples are provided in the Examples section below.
As with the mutation parameters, recpars is used to define the
desired recombination strategy. The current version accepts the following
options:
recombination_blxAlphaBeta (incl. special cases
blxAlpha and flat)
recpars receives a list object with name field recpars$name
(containing the name of the function to be called, e.g.,
name = "recombination_bin") as well as whatever parameters that
function may require/accept (e.g., recpars$cr = 0.8,
recpars$minchange = TRUE, etc.). See the specific documentation of
each function for details.
Some examples are provided in the Examples section below.
selpars follows the same idea as mutpars and recpars,
and is used to define the selection operators. Currently, only the standard
DE selection, selection_standard, is implemented.
stopcrit is similar to recpar and the other list arguments,
but with the difference that multiple stop criteria can be defined for the
algorithm. The names of the stop criteria to be used are passed in the
stopcrit$names field, which must contain a character vector. Other
parameters to be used for stopping the algorithm (e.g., the maximum number
of iterations stopcrit$maxiter) can also be included as
stopcrit fields. Currently implemented criteria are:
"stop_maxiter" (requires additional field
stopcrit$maxiter = ? with the maximum number of iterations).
"stop_maxeval" (requires additional field
stopcrit$maxevals = ? with the maximum number of function calls).
See check_stop_criteria for details.
The probpars parameter receives a list with all definitions related
to the problem instance to be optimized. There are three required fields in
this parameter:
probpars$name, the name of the function that represents the
problem to be solved.
probpars$xmin, a vector containing the lower bounds of all
optimization variables (i.e., a vector of length M, where M is the
dimension of the problem).
probpars$xmax, a vector containing the upper bounds of all
optimization variables.
This list can also contain the following optional arguments
probpars$matrixEval, indicates what kind of input is expected
by the function provided in probpars$name. Valid entries are
"vector", "colMatrix" and "rowMatrix".
Defaults to probpars$matrixEval = "rowMatrix"
Important: the objective function routine must receive either a vector or a matrix of vectors to be evaluated in the form of an input parameter named either "x" or "X" or "Pop" (any one of the three is allowed).
The seed argument receives the desired seed for the PRNG. This value
can be set for reproducibility purposes. The value of this parameter defaults
to NULL, in which case the seed is arbitrarily set using
.Random.seed.
showpars is a list containing parameters that control the printed
output of ExpDE. Parameter showpars can have the following
fields:
showpars$show.iters = c("dots", "numbers", "none"): type of
output. Defaults to "numbers".
showpars$showevery: positive integer that determines how
frequently the routine echoes something to the terminal. Defaults
to 1.
Felipe Campelo ([email protected]) and Moises Botelho ([email protected])
F. Campelo, M. Botelho, "Experimental Investigation of Recombination Operators for Differential Evolution", Genetic and Evolutionary Computation Conference, July 20-24, 2016, Denver/CO. DOI: 10.1145/2908812.2908852
# DE/rand/1/bin with population 40, F = 0.8 and CR = 0.5 popsize <- 100 mutpars <- list(name = "mutation_rand", f = 0.8) recpars <- list(name = "recombination_bin", cr = 0.5, minchange = TRUE) selpars <- list(name = "selection_standard") stopcrit <- list(names = "stop_maxiter", maxiter = 100) probpars <- list(name = "sphere", xmin = rep(-5.12,10), xmax = rep(5.12,10)) seed <- NULL showpars <- list(show.iters = "numbers", showevery = 1) ExpDE(popsize, mutpars, recpars, selpars, stopcrit, probpars, seed, showpars) # DE/wgi/1/blxAlpha recpars <- list(name = "recombination_blxAlphaBeta", alpha = 0.1, beta = 0.1) mutpars <- list(name = "mutation_wgi", f = 0.8) ExpDE(popsize, mutpars, recpars, selpars, stopcrit, probpars) # DE/best/1/sbx recpars <- list(name = "recombination_sbx", eta = 10) mutpars <- list(name = "mutation_best", f = 0.6, nvecs = 1) ExpDE(popsize, mutpars, recpars, selpars, stopcrit, probpars) # DE/best/1/eigen/bin recpars <- list(name = "recombination_eigen", othername = "recombination_bin", cr = 0.5, minchange = TRUE) showpars <- list(show.iters = "dots", showevery = 10) stopcrit <- list(names = "stop_maxeval", maxevals = 10000) ExpDE(popsize, mutpars, recpars, selpars, stopcrit, probpars, seed = 1234)# DE/rand/1/bin with population 40, F = 0.8 and CR = 0.5 popsize <- 100 mutpars <- list(name = "mutation_rand", f = 0.8) recpars <- list(name = "recombination_bin", cr = 0.5, minchange = TRUE) selpars <- list(name = "selection_standard") stopcrit <- list(names = "stop_maxiter", maxiter = 100) probpars <- list(name = "sphere", xmin = rep(-5.12,10), xmax = rep(5.12,10)) seed <- NULL showpars <- list(show.iters = "numbers", showevery = 1) ExpDE(popsize, mutpars, recpars, selpars, stopcrit, probpars, seed, showpars) # DE/wgi/1/blxAlpha recpars <- list(name = "recombination_blxAlphaBeta", alpha = 0.1, beta = 0.1) mutpars <- list(name = "mutation_wgi", f = 0.8) ExpDE(popsize, mutpars, recpars, selpars, stopcrit, probpars) # DE/best/1/sbx recpars <- list(name = "recombination_sbx", eta = 10) mutpars <- list(name = "mutation_best", f = 0.6, nvecs = 1) ExpDE(popsize, mutpars, recpars, selpars, stopcrit, probpars) # DE/best/1/eigen/bin recpars <- list(name = "recombination_eigen", othername = "recombination_bin", cr = 0.5, minchange = TRUE) showpars <- list(show.iters = "dots", showevery = 10) stopcrit <- list(names = "stop_maxeval", maxevals = 10000) ExpDE(popsize, mutpars, recpars, selpars, stopcrit, probpars, seed = 1234)
Implements the "/best/nvecs" mutation for the ExpDE framework
mutation_best(X, mutpars)mutation_best(X, mutpars)
X |
population matrix |
mutpars |
mutation parameters (see |
Matrix M containing the mutated population
The mutpars parameter contains all parameters required to define the
mutation. mutation_best() understands the following fields in
mutpars:
f : scaling factor for difference vector(s).
Accepts numeric vectors of size 1 or nvecs.
nvecs : number of difference vectors to use.
Accepts 1 <= nvecs <= (nrow(X)/2 - 2)
Defaults to 1.
This routine will search for the performance vector
of population X (J) in the parent environment (using
parent.frame(). This variable must be defined for
mutation_best() to work.
K. Price, R.M. Storn, J.A. Lampinen, "Differential Evolution: A Practical Approach to Global Optimization", Springer 2005
Felipe Campelo ([email protected])
Implements the "/current-to-pbest" mutation for the ExpDE framework
mutation_current_to_pbest(X, mutpars)mutation_current_to_pbest(X, mutpars)
X |
population matrix |
mutpars |
mutation parameters (see |
This routine also implements one special case:
current-to-best mutation (current_to_best), by setting
mutpars$p = 1);
Flat recombination (flat), by setting
recpars$alpha = recpars$beta = 0)
Matrix M containing the mutated population
The mutpars parameter contains all parameters required to define the
mutation. mutation_current_to_pbest() understands the following fields in
mutpars:
f : scaling factor for difference vector(s).
Accepts numeric vectors of size 1 or nvecs.
p : either the number of "best" vectors to use (if given as a
positive integer) or the proportion of the population to use as "best"
vectors (if 0 < p < 1).
This routine will search for the performance vector
of population X (J) in the parent environment (using
parent.frame(). This variable must be defined for
mutation_current_to_pbest() to work.
J. Zhang, A.C. Sanderson, "JADE: Adaptive differential evolution with optional external archive". IEEE Transactions on Evolutionary Computation 13:945-958, 2009
Felipe Campelo ([email protected])
Implements the "/mean/nvecs" mutation for the ExpDE framework
mutation_mean(X, mutpars)mutation_mean(X, mutpars)
X |
population matrix |
mutpars |
mutation parameters (see |
Matrix M containing the mutated population
The mutpars parameter contains all parameters required to define the
mutation. mutation_mean() understands the following fields in
mutpars:
f : scaling factor for difference vector(s).
Accepts numeric vectors of size 1 or nvecs.
nvecs : number of difference vectors to use.
Accepts 1 <= nvecs <= (nrow(X)/2 - 2)
Defaults to 1.
K. Price, R.M. Storn, J.A. Lampinen, "Differential Evolution: A Practical Approach to Global Optimization", Springer 2005
Felipe Campelo ([email protected])
Implements the "/none" mutation (i.e., no mutation performed) for the ExpDE framework
mutation_none(X, mutpars)mutation_none(X, mutpars)
X |
population matrix |
mutpars |
mutation parameters (see |
@return The same matrix X used as an input.
The mutpars parameter contains all parameters required to define the
mutation. mutation_none() requires no fields in this parameter.
List all available mutation operators in the ExpDE package
mutation_operators()mutation_operators()
Character vector with the names of all mutation operators
Implements the "/rand/nvecs" mutation for the ExpDE framework
mutation_rand(X, mutpars)mutation_rand(X, mutpars)
X |
population matrix |
mutpars |
mutation parameters (see |
Matrix M containing the mutated population
The mutpars parameter contains all parameters required to define the
mutation. mutation_rand() understands the following fields in
mutpars:
f : scaling factor for difference vector(s).
Accepts numeric vectors of size 1 or nvecs.
nvecs : number of difference vectors to use.
Accepts 1 <= nvecs <= (nrow(X)/2 - 2)
Defaults to 1.
K. Price, R.M. Storn, J.A. Lampinen, "Differential Evolution: A Practical Approach to Global Optimization", Springer 2005
Felipe Campelo ([email protected])
Implements the "/wgi/nvecs" mutation (weighted global intermediate) for the ExpDE framework. This variant is based on a recombination strategy known as "weighted global intermediate recombination" (see the References section for details)
mutation_wgi(X, mutpars)mutation_wgi(X, mutpars)
X |
population matrix |
mutpars |
mutation parameters (see |
Matrix M containing the mutated population
The mutpars parameter contains all parameters required to define the
mutation. mutation_wgi() understands the following fields in
mutpars:
f : scaling factor for difference vector(s).
Accepts numeric vectors of size 1 or nvecs.
nvecs : number of difference vectors to use.
Accepts 1 <= nvecs <= (nrow(X)/2 - 2)
Defaults to 1.
D. Arnold, "Weighted multirecombination evolution strategies". Theoretical Computer Science 361(1): 18-37, 2006.
T. Glasmachers, C. Igel, "Uncertainty handling in model selection for support vector machines". Proc. International Conference on Parallel Problem Solving from Nature (PPSN'08), 185-194, 2008.
Felipe Campelo ([email protected])
Echoes the progress of DE to the terminal
print_progress()print_progress()
This routine accesses all variables defined in the calling environment using
parent.frame(), so it does not require any explicit input parameters.
However, the calling environment must contain:
showpars: list containing parameters that control the printed
output of moead(). Parameter showpars
can have the following fields:
$show.iters = c("dots", "numbers", "none"): type of output.
Defaults to "numbers".
$showevery: positive integer that determines how frequently
the routine echoes something to the terminal.
Defaults to 1.
iters() : counter function that registers the iteration
number
Implements the "/arith" (arithmetic) recombination for the ExpDE framework
recombination_arith(X, M, ...)recombination_arith(X, M, ...)
X |
population matrix (original) |
M |
population matrix (mutated) |
... |
optional parameters (unused) |
Matrix U containing the recombined population
F. Herrera, M. Lozano, A. M. Sanchez, "A taxonomy for the crossover operator for real-coded genetic algorithms: an experimental study", International Journal of Intelligent Systems 18(3) 309-338, 2003.
Implements the "/bin" (binomial) recombination for the ExpDE framework
recombination_bin(X, M, recpars)recombination_bin(X, M, recpars)
X |
population matrix (original) |
M |
population matrix (mutated) |
recpars |
recombination parameters (see |
Matrix U containing the recombined population
The recpars parameter contains all parameters required to define the
recombination. recombination_bin() understands the following fields in
recpars:
cr : component-wise probability of using the value in
M.
Accepts numeric value 0 < cr <= 1.
minchange : logical flag to force each new candidate solution
to inherit at least one component from its
mutated 'parent'.
Defaults to TRUE
K. Price, R.M. Storn, J.A. Lampinen, "Differential Evolution: A Practical Approach to Global Optimization", Springer 2005
Implements the "/blxAlphaBeta" (Blend Alpha Beta) recombination for the ExpDE framework
recombination_blxAlphaBeta(X, M, recpars)recombination_blxAlphaBeta(X, M, recpars)
X |
population matrix (original) |
M |
population matrix (mutated) |
recpars |
recombination parameters (see |
This routine also implements two special cases:
BLX-alpha recombination (blxAlpha), by setting
recpars$alpha = recpars$beta);
Flat recombination (flat), by setting
recpars$alpha = recpars$beta = 0)
Matrix U containing the recombined population
The recpars parameter contains all parameters required to define the
recombination. recombination_blxAlpha() understands the following
fields in recpars:
alpha : extrapolation parameter for 'best' parent vector.
Accepts real value 0 <= alpha <= 0.5.
beta : extrapolation parameter for 'worst' parent vector.
Accepts real value 0 <= beta <= 0.5.
@section Warning:
This recombination operator evaluates the candidate solutions in M,
which adds an extra popsize evaluations per iteration.
F. Herrera, M. Lozano, A. M. Sanchez, "A taxonomy for the crossover operator for real-coded genetic algorithms: an experimental study", International Journal of Intelligent Systems 18(3) 309-338, 2003.
Implements the "/eigen" (eigenvector-based) recombination for the ExpDE framework
recombination_eigen(X, M, recpars)recombination_eigen(X, M, recpars)
X |
population matrix (original) |
M |
population matrix (mutated) |
recpars |
recombination parameters (see |
Matrix U containing the recombined population
The recpars parameter contains all parameters required to define the
recombination. recombination_eigen() understands the following fields
in recpars:
othername: name of the recombination operator to be applied
after the projection in the eigenvector basis
... : parameters required (or optional) to the operator
defined by recpars$othername
Shu-Mei Guo e Chin-Chang Yang, "Enhancing differential evolution utilizing eigenvector-based crossover operator", IEEE Transactions on Evolutionary Computation 19(1):31-49, 2015.
Implements the "/exp" (exponential) recombination for the ExpDE framework
recombination_exp(X, M, recpars)recombination_exp(X, M, recpars)
X |
population matrix (original) |
M |
population matrix (mutated) |
recpars |
recombination parameters (see |
Matrix U containing the recombined population
The recpars parameter contains all parameters required to define the
recombination. recombination_exp() understands the following
fields in recpars:
cr : component-wise probability of selection as a cut-point.
Accepts numeric value 0 < cr <= 1.
K. Price, R.M. Storn, J.A. Lampinen, "Differential Evolution: A Practical Approach to Global Optimization", Springer 2005
Implements the "/geo" (geometric) recombination for the ExpDE framework
recombination_geo(X, M, recpars)recombination_geo(X, M, recpars)
X |
population matrix (original) |
M |
population matrix (mutated) |
recpars |
recombination parameters (see |
Matrix U containing the recombined population
The recpars parameter contains all parameters required to define the
recombination. recombination_geo() understands the following
fields in recpars:
alpha : exponent for geometrical recombination.
Accepts numeric value 0 <= alpha <= 1 or NULL (in which
case a random value is chosen for each recombination).
F. Herrera, M. Lozano, A. M. Sanchez, "A taxonomy for the crossover operator for real-coded genetic algorithms: an experimental study", International Journal of Intelligent Systems 18(3) 309-338, 2003.
Implements the "/lbga" (Linear Breeder Genetic Algorithm) recombination for the ExpDE framework
recombination_lbga(X, M, ...)recombination_lbga(X, M, ...)
X |
population matrix (original) |
M |
population matrix (mutated) |
... |
optional parameters (unused) |
Matrix U containing the recombined population
This recombination operator evaluates the candidate solutions in M,
which adds an extra popsize evaluations per iteration.
F. Herrera, M. Lozano, A. M. Sanchez, "A taxonomy for the crossover
operator for real-coded genetic algorithms: an experimental study",
International Journal of Intelligent Systems 18(3) 309-338, 2003.
D. Schlierkamp-voosen , H. Muhlenbein, "Strategy Adaptation by
Competing Subpopulations", Proc. Parallel Problem Solving from Nature
(PPSN III), 199-208, 1994.
Implements the "/linear" recombination for the ExpDE framework
recombination_linear(X, M, ...)recombination_linear(X, M, ...)
X |
population matrix (original) |
M |
population matrix (mutated) |
... |
optional parameters (unused) |
Matrix U containing the recombined population
This recombination operator evaluates 3*popsize candidate solutions
per iteration of the algorithm. The value of the nfe counter and the
vector of performance values G are updated in the calling environment.
F. Herrera, M. Lozano, A. M. Sanchez, "A taxonomy for the crossover
operator for real-coded genetic algorithms: an experimental study",
International Journal of Intelligent Systems 18(3) 309-338, 2003.
A.H. Wright, "Genetic Algorithms for Real Parameter Optimization",
Proc. Foundations of Genetic Algorithms, 205-218, 1991.
Implements the "/mmax" (min-max-arithmetical) recombination for the ExpDE framework
recombination_mmax(X, M, recpars = list(lambda = NULL))recombination_mmax(X, M, recpars = list(lambda = NULL))
X |
population matrix (original) |
M |
population matrix (mutated) |
recpars |
recombination parameters (see |
Matrix U containing the recombined population
This recombination operator evaluates 4*popsize candidate solutions
per iteration of the algorithm. The value of the nfe counter and the
vector of performance values G are updated in the calling environment.
The recpars parameter contains all parameters required to define the
recombination. recombination_pbest() understands the following
fields in recpars:
lambda : Recombination multiplier.
Optional. Defaults to NULL
Accepts numeric value 0 < lambda < 1 or
NULL (in which case a random value is
independently used for each variable of each
recombination pair).
F. Herrera, M. Lozano, A. M. Sanchez, "A taxonomy for the crossover
operator for real-coded genetic algorithms: an experimental study",
International Journal of Intelligent Systems 18(3):309-338, 2003.
F Herrera, M. Lozano, J.L. Verdegay, "Tuning fuzzy logic controllers by
genetic algorithms.", International Journal of Approximate Reasoning
12(3):299-315, 1995.
Implements the "/none" recombination (i.e., no recombination performed) for the ExpDE framework
recombination_none(X, M, ...)recombination_none(X, M, ...)
X |
population matrix (original) |
M |
population matrix (mutated) |
... |
optional parameters (unused) |
The same matrix M used as an input.
Implements the "/npoint" (n-point) recombination for the ExpDE (as used in the Simple GA).
recombination_npoint(X, M, recpars = list(N = NULL))recombination_npoint(X, M, recpars = list(N = NULL))
X |
population matrix (original) |
M |
population matrix (mutated) |
recpars |
recombination parameters (see |
Matrix U containing the recombined population
The recpars parameter contains all parameters required to define the
recombination. recombination_npoint() understands the following
fields in recpars:
N : cut number points for crossover.
Accepts integer value 0 <= N < n, where n is the
dimension of the problem; Use N = 0 or N = NULL for randomly
choosing a number of cut points.
Defaults to NULL.
L.J. Eshelman, R.A. Caruana, J.D. Schaffer (1989), "Biases in the crossover landscape. In: Proceedings of the Third International Conference on Genetic Algorithms, pp. 10-19, San Francisco, CA, USA.
Implements the one-point recombination (as used in the Simple GA).
recombination_onepoint(X, M, recpars = list(K = NULL))recombination_onepoint(X, M, recpars = list(K = NULL))
X |
population matrix (original) |
M |
population matrix (mutated) |
recpars |
recombination parameters (see |
Matrix U containing the recombined population
The recpars parameter contains all parameters required to define the
recombination. recombination_onepoint() understands the following
fields in recpars:
K : cut point for crossover.
Accepts integer value 0 <= K < n, where n is the
dimension of the problem; Use K = 0 or K = NULL for randomly
choosing a position for each pair of points.
Defaults to NULL.
F. Herrera, M. Lozano, A. M. Sanchez, "A taxonomy for the crossover operator for real-coded genetic algorithms: an experimental study", International Journal of Intelligent Systems 18(3) 309-338, 2003.
List all available recombination operators in the ExpDE package
recombination_operators()recombination_operators()
Character vector with the names of all recombination operator routines
Implements the "/pbest" (p-Best) recombination for the ExpDE framework
recombination_pbest(X, M, recpars)recombination_pbest(X, M, recpars)
X |
population matrix (original) |
M |
population matrix (mutated) |
recpars |
recombination parameters (see |
Matrix U containing the recombined population
The recpars parameter contains all parameters required to define the
recombination. recombination_pbest() understands the following
fields in recpars:
cr : component-wise probability of using the value in
M.
Accepts numeric value 0 < cr <= 1.
This routine will search for the iterations counter (t), the maximum
number of iterations (stopcrit$maxiter), and the performance vector
of population X (J) in the parent environment (using
parent.frame(). These variables must be defined for
recombination_pbest() to work.
S.M. Islam, S. Das, S. Ghosh, S. Roy, P.N. Suganthan, "An Adaptive Differential Evolution Algorithm With Novel Mutation and Crossover Strategies for Global Numerical Optimization", IEEE. Trans. Systems, Man and Cybernetics - Part B 42(2), 482-500, 2012
Implements the "/sbx" (Simulated Binary) recombination for the ExpDE framework
recombination_sbx(X, M, recpars)recombination_sbx(X, M, recpars)
X |
population matrix (original) |
M |
population matrix (mutated) |
recpars |
recombination parameters (see |
Matrix U containing the recombined population
The recpars parameter contains all parameters required to define the
recombination. recombination_sbx() understands the following field in
recpars:
eta : spread factor.
Accepts numeric value eta > 0.
K. Price, R.M. Storn, J.A. Lampinen, "Differential Evolution: A
Practical Approach to Global Optimization", Springer 2005
F. Herrera, M. Lozano, A. M. Sanchez, "A taxonomy for the crossover
operator for real-coded genetic algorithms: an experimental study",
International Journal of Intelligent Systems 18(3) 309-338, 2003.
K. Deb, R.B. Agrawal, "Simulated binary crossover for continuous search
space", Complex Systems (9):115-148, 1995.
Implements the "/wright" (Heuristic Wright) recombination for the ExpDE framework.
recombination_wright(X, M, ...)recombination_wright(X, M, ...)
X |
population matrix (original) |
M |
population matrix (mutated) |
... |
optional parameters (unused) |
Matrix U containing the recombined population
This recombination operator evaluates the candidate solutions in M,
which adds an extra popsize evaluations per iteration.
F. Herrera, M. Lozano, A. M. Sanchez, "A taxonomy for the crossover
operator for real-coded genetic algorithms: an experimental study",
International Journal of Intelligent Systems 18(3) 309-338, 2003.
A.H. Wright, "Genetic Algorithms for Real Parameter Optimization",
Proc. Foundations of Genetic Algorithms, 205-218, 1991.
Implements the standard selection (greedy) for the ExpDE framework
selection_standard(X, U, J, G)selection_standard(X, U, J, G)
X |
population matrix (original) |
U |
population matrix (recombined) |
J |
performance vector for population |
G |
performance vector for population |
list object containing the selected population (Xsel) and
its corresponding performance values (Jsel).