Type:	Package
Title:	Many Objective Evolutionary Algorithm
Version:	0.6.2
Maintainer:	Dani Irawan <irawan_dani@yahoo.com>
Description:	A set of evolutionary algorithms to solve many-objective optimization. Hybridization between the algorithms are also facilitated. Available algorithms are: 'SMS-EMOA' <doi:10.1016/j.ejor.2006.08.008> 'NSGA-III' <doi:10.1109/TEVC.2013.2281535> 'MO-CMA-ES' <doi:10.1145/1830483.1830573> The following many-objective benchmark problems are also provided: 'DTLZ1'-'DTLZ4' from Deb, et al. (2001) <doi:10.1007/1-84628-137-7_6> and 'WFG4'-'WFG9' from Huband, et al. (2005) <doi:10.1109/TEVC.2005.861417>.
License:	GPL (≥ 3)
Encoding:	UTF-8
LazyData:	true
BugReports:	https://github.com/dots26/MaOEA/issues
URL:	https://github.com/dots26/MaOEA
RoxygenNote:	7.1.1
Imports:	reticulate, nsga2R, lhs, nnet, stringr, randtoolbox, e1071, MASS,gtools, stats, utils, pracma
Suggests:	testthat
SystemRequirements:	Python 3.x with following modules: PyGMO, NumPy, and cloudpickle
NeedsCompilation:	no
Packaged:	2020-08-15 01:27:01 UTC; irawan
Author:	Dani Irawan [aut, cre]
Repository:	CRAN
Date/Publication:	2020-08-31 09:40:07 UTC

Many-Objective Evolutionary Algorithm

Description

MaOEA contains several algorithms for solving many-objective optimization problems. The algorithms are provided as a sequence of operators used in a single iteration. For example, the SMSEMOA function calls the recombination (SBX) and mutation operator (polynomial mutation) to produce 1 offspring, and perform the S-metric selection. The function then returns a list containing the population and population objective after the procedure is conducted once. The purpose of only doing a single iteration is to support users if they wish to formulate hybrid algorithms.

Details

Alternatively, users can use the optimMaOEA function to solve an optimization problem with their chosen algorithm. This function is a simple wrapper to call the algorithms listed above for several iterations. Using this function, users can simply supply the initial population, objective function, the chosen algorithm, and the number of iterations. If number of iteration is not supplied, then only a single iteration is conducted.

Note: This package uses column-major ordering, i.e. an individual should be contained in a single column, each row represents different variable. All optimization variable should be scaled to 0-1.

Acknowledgments

This work is funded by the European Commission's H2020 programme through the UTOPIAE Marie Curie Innovative Training Network, H2020-MSCA-ITN-2016, under Grant Agreement No. 722734 as well as through the Twinning project SYNERGY under Grant Agreement No. 692286.

Maintainer

Dani Irawan irawan_dani@yahoo.com

Author(s)

Dani Irawan irawan_dani@yahoo.com

See Also

Main interface function is optimMaOEA.

Objective space normalization.

Description

Normalize the objectives to 0-1. The origin is the ideal point. (1,...,1) is not the nadir point. The normalization is done by using adaptive normalization used in NSGA-III.

Usage

AdaptiveNormalization(objectiveValue)

Arguments

Value

A list containing the following: normalizedObjective The normalized values idealPoint The ideal point corresponding to the origin nadirPoint The location of nadir point in the normalized Space

Examples

nObj <- 5
nIndividual <- 100
nVar <- 10
population <- InitializePopulationLHS(nIndividual,nVar,FALSE)
objective <- matrix(,nrow=nObj,ncol=nIndividual)
for(individual in 1:nIndividual){
   objective[,individual] <- WFG4(population[,individual],nObj)
}
AdaptiveNormalization(objective)

The DTLZ1 test function.

Description

The DTLZ1 test function.

Usage

DTLZ1(individual, nObj)

Arguments

Value

A matrix of size nObjective x population size, containing the objective values for each individual.

References

Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-Objective Optimization Test Problems. In: Congress on Evolutionary Computation (CEC). pp. 825–830. IEEE Press, Piscataway, NJ (2002)

Examples

individual <- stats::runif(14)
nObj <- 4
DTLZ1(individual,nObj)

The DTLZ2 test function.

Description

The DTLZ2 test function.

Usage

DTLZ2(individual, nObj)

Arguments

Value

A matrix of size nObjective x population size, containing the objective values for each individual.

References

Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-Objective Optimization Test Problems. In: Congress on Evolutionary Computation (CEC). pp. 825–830. IEEE Press, Piscataway, NJ (2002)

Examples

individual <- stats::runif(14)
nObj <- 4
DTLZ2(individual,nObj)

The DTLZ3 test function.

Description

The DTLZ3 test function.

Usage

DTLZ3(individual, nObj)

Arguments

Value

A matrix of size nObjective x population size, containing the objective values for each individual.

References

Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-Objective Optimization Test Problems. In: Congress on Evolutionary Computation (CEC). pp. 825–830. IEEE Press, Piscataway, NJ (2002)

Examples

individual <- stats::runif(14)
nObj <- 4
DTLZ3(individual,nObj)

The DTLZ4 test function.

Description

The DTLZ4 test function.

Usage

DTLZ4(individual, nObj, alpha = 100)

Arguments

Value

A matrix of size nObjective x population size, containing the objective values for each individual.

References

Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-Objective Optimization Test Problems. In: Congress on Evolutionary Computation (CEC). pp. 825–830. IEEE Press, Piscataway, NJ (2002)

Examples

individual <- stats::runif(14)
nObj <- 4
DTLZ4(individual,nObj)

Evaluate objective values of a single individual

Description

Evaluate individual with the specified test function. Non-feasible solution are given Inf as objective values.

Usage

EvaluateIndividual(individual, fun, ...)

Arguments

Value

A matrix of size nObjective, containing the objective values.

Examples

individual <- stats::runif(8)
EvaluateIndividual(individual,WFG4,3) # the 3 is passed to WFG4 nObj

Evaluate objective value of a set of individuals

Description

Evaluate a population with the specified test function. Non-feasible solution are given Inf as objective values.

Usage

EvaluatePopulation(pop, fun, ...)

Arguments

Value

A matrix of size nObjective, containing the objective values.

Examples

pop <- matrix(runif(8*50),nrow=8) # 8 variables, 50 individuals
EvaluatePopulation(pop,WFG4,3) # the 3 is passed to WFG4 nObj

Get HV contribution of all points.

Description

Get the hypervolume (HV) contribution of the population. Dominated front will give 0 contribution.

Usage

GetHVContribution(
  populationObjective,
  reference = NULL,
  method = "exact",
  ref_multiplier = 1.1
)

Arguments

Value

A vector of length ncol(populationObjective)

Examples

nObjective <- 5 # the number of objectives
nPoint <- 10 # the number of points that will form the hypervolume
objective <- matrix(stats::runif(nObjective*nPoint), nrow = nObjective, ncol = nPoint)
numpyready <- reticulate::py_module_available('numpy')
pygmoready <- reticulate::py_module_available('pygmo')
py_module_ready <- numpyready && pygmoready
if(py_module_ready) # prevent error on testing the example
GetHypervolume(objective,,"exact") # no reference supplied

reference <- rep(2,nObjective) # create a reference point at (2,2,2,2,2)
if(py_module_ready) # prevent error on testing the example
GetHVContribution(objective,reference)

Compute hypervolume

Description

Compute the hypervolume formed by the points w.r.t. a reference point. If no reference is supplied, use the nadir point*(1.1,...,1.1).

Usage

GetHypervolume(
  objective,
  reference = NULL,
  method = "exact",
  ref_multiplier = 1.1
)

Arguments

Value

Hypervolume size, a scalar value.

Examples

nObjective <- 5 # the number of objectives
nPoint <- 10 # the number of points that will form the hypervolume
objective <- matrix(stats::runif(nObjective*nPoint), nrow = nObjective, ncol = nPoint)
numpyready <- reticulate::py_module_available('numpy')
pygmoready <- reticulate::py_module_available('pygmo')
py_module_ready <- numpyready && pygmoready
if(py_module_ready) # prevent error on testing the example
GetHypervolume(objective,,"exact") # no reference supplied

reference <- rep(2,nObjective) # create a reference point at (2,2,2,2,2)
if(py_module_ready) # prevent error on testing the example
GetHypervolume(objective,reference,"exact") # using reference point

Get IGD value

Description

Get Inverted Generational Distance (IGD) value of the population objective w.r.t. a matrix of reference set (each row contain 1 point).

Usage

GetIGD(populationObjective, referenceSet)

Arguments

Value

The IGD metric. A Scalar value.

Get least HV contribution

Description

Get the hypervolume (HV) contribution of the individual with least HV contribution.

Usage

GetLeastContribution(
  populationObjective,
  reference = NULL,
  method = "exact",
  ref_multiplier = 1.1
)

Arguments

Value

The HV contribution value of the least contributor.

Examples

 
nObjective <- 5 # the number of objectives
nPoint <- 10 # the number of points that will form the hypervolume
objective <- matrix(stats::runif(nObjective*nPoint), nrow = nObjective, ncol = nPoint)
numpyready <- reticulate::py_module_available('numpy')
pygmoready <- reticulate::py_module_available('pygmo')
py_module_ready <- numpyready && pygmoready
if(py_module_ready) # prevent error on testing the example
GetHypervolume(objective,,"exact") # no reference supplied

reference <- rep(2,nObjective) # create a reference point at (2,2,2,2,2)
if(py_module_ready) # prevent error on testing the example
GetLeastContribution(objective,reference,"exact")

Get least HV contributor

Description

Get index of the individual with least hypervolume (HV) contribution. For the contribution itself, use GetLeastContribution()

Usage

GetLeastContributor(
  populationObjective,
  reference = NULL,
  method = "exact",
  hypervolumeMethodParam = list(),
  ref_multiplier = 1.1
)

Arguments

Value

The index of the least contributor, an integer.

Examples

nObjective <- 5 # the number of objectives
nPoint <- 10 # the number of points that will form the hypervolume
objective <- matrix(stats::runif(nObjective*nPoint), nrow = nObjective, ncol = nPoint)
# run a generation of MO-CMA-ES with standard WFG8 test function.
numpyready <- reticulate::py_module_available('numpy')
pygmoready <- reticulate::py_module_available('pygmo')
py_module_ready <- numpyready && pygmoready
if(py_module_ready) # prevent error on testing the example
GetHypervolume(objective,,"exact") # no reference supplied

reference <- rep(2,nObjective) # create a reference point at (2,2,2,2,2)
if(py_module_ready) # prevent error on testing the example
GetLeastContributor(objective,reference,"exact")

Initialize population with Latin Hypercube Sampling

Description

Create initial sample using Latin Hypercube Sampling (LHS) method. The variables will be ranged between 0-1

Usage

InitializePopulationLHS(
  numberOfIndividuals,
  chromosomeLength,
  minVal = 0,
  maxVal = 1,
  samplingMethod = 0
)

Arguments

Value

A matrix of size chromosomeLength x nIndividual.

Examples

nVar <- 14
nIndividual <- 100
InitializePopulationLHS(nIndividual,nVar,FALSE)

Multi-Objective CMA-ES

Description

Do an iteration of population based Multi-Objective Covariance Matrix Adaptation Evolution Strategy (MO-CMA-ES). The variation is using simulated binary crossover (SBX) and mutation following the CMA. The original MO-CMA-ES does not use crossover, to do this simply set crossoverProbability to zero.

Usage

MOCMAES(parent, nObjective, fun, control = list(), ...)

Arguments

Value

Returns a list for the next generation. It contains list$new_generation (class: cmaes_gen), list$population (basically a copy of list$new_generation[[]]$x), and list$populationObjective

References

Voß, T., Hansen, N., Igel, C.: Improved step size adaptation for the MO-CMA-ES. In: Genetic and Evolutionary Computation (GECCO). pp. 487–494. ACM, New York, NY (2010)

Examples

nVar <- 14
nObjective <- 5
nIndividual <- 100
crossoverProbability <- 1
ps_target <- 1 / (5 + ( 1 / 2  )^0.5 )
pop <- matrix(stats::runif(nIndividual*nVar), nrow = nVar) # create the population
a_list <- cmaes_gen(pop)
control <- list(successProbTarget=ps_target,crossoverProbability=crossoverProbability)

# run a generation of MO-CMA-ES with standard WFG8 test function.
numpyready <- reticulate::py_module_available('numpy')
pygmoready <- reticulate::py_module_available('pygmo')
py_module_ready <- numpyready && pygmoready
if(py_module_ready) # prevent error on testing the example
newGeneration <- MOCMAES(a_list,nObjective,WFG8,control,nObjective)

Elitist Non-dominated Sorting Genetic Algorithm version III

Description

Do an iteration of Elitist Non-dominated Sorting Genetic Algorithm version III (NSGA-III). THe variation is using SBX and polynomial mutation.

Usage

NSGA3(population, fun, nObjective, control = list(), ...)

Arguments

Value

#' @return Returns a list for the next generation population The new generation design points. Column major. populationObjective The new generation's objective values. Column major.

References

Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: Solving problems with box constraints. Trans. Evol. Comp. 18 (4), 577–601 (2014)

Examples

nVar <- 14
nObjective <- 5
nIndividual <- 100
#control for NSGA3
ctrl <- list(crossoverProbability = 1,
             mutationProbability = 1/nVar)
#Initial population
population <- matrix(runif(nIndividual*nVar), nrow = nVar)

# run a generation of NSGA-III with standard WFG8 test function.
NSGA3(population, WFG8,nObjective,ctrl,nObjective)

Objective space normalization.

Description

Normalize the objectives AND reference (combined) to 0-1. The origin is the ideal point. (1,...,1) is the nadir.

Usage

Normalize(objectiveValue, referencePoints = NULL)

Arguments

Value

A list containing the following: normalizedObjective The normalized values idealPoint The ideal point corresponding to the origin transformedReference The location of reference points in the normalized Space

Examples

nObj <- 5
nVar <- 10
nIndividual <- 100
population <- InitializePopulationLHS(nIndividual,nVar,FALSE)
objective <- matrix(,nrow=nObj,ncol=nIndividual)
for(individual in 1:nIndividual){
   objective[,individual] <- WFG4(population[,individual],nObj)
}
Normalize(objective)

Steady-state Multi-Objective CMA-ES

Description

Do an iteration of population based steady state Multi-Objective Covariance Matrix Adaptation Evolution Strategy (MO-CMA-ES). The variation is using simulated binary crossover (SBX) and mutation following the CMA. The original MO-CMA-ES does not use crossover, to do this simply set crossoverProbability to zero.

Usage

SMOCMAES(parent, nObjective, fun, control = list(), ...)

Arguments

Value

Returns a list for the next generation. It contains list$new_generation (class: cmaes_gen), list$population (basically a copy of list$new_generation[[]]$x), and list$populationObjective

References

Voß, T., Hansen, N., Igel, C.: Improved step size adaptation for the MO-CMA-ES. In: Genetic and Evolutionary Computation (GECCO). pp. 487–494. ACM, New York, NY (2010)

Examples

 
nVar <- 14
nObjective <- 5
nIndividual <- 100
crossoverProbability <- 1
ps_target <- 1 / (5 + ( 1 / 2  ) )
pop <- matrix(stats::runif(nIndividual*nVar), nrow = nVar) # create the population
a_list <- cmaes_gen(pop)
control <- list(successProbTarget=ps_target,crossoverProbability=crossoverProbability)
# run a generation of SMO-CMA-ES with standard WFG8 test function.
numpyready <- reticulate::py_module_available('numpy')
pygmoready <- reticulate::py_module_available('pygmo')
py_module_ready <- numpyready && pygmoready
if(py_module_ready) # prevent error on testing the example
newGeneration <- SMOCMAES(a_list,nObjective,WFG8,control,nObjective)

S-Metric Selection EMOA

Description

Do an iteration of S-Metric Selection (SMS)-EMOA. The variation used is simulated binary crossover (SBX) and polynomial mutation.

Usage

SMSEMOA(population, fun, nObjective, control = list(), ...)

Arguments

Value

Returns a list for the next generation population The new generation. Column major, each row contain 1 set of objectives. successfulOffspring Binary, 1 if the offspring is kept in the new generation. Used in some adaptive schemes. populationObjective The new generation's objective values.

References

Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective selection based on dominated hypervolume. Eur. J. Oper. Res. 181 (3), 1653 – 1669 (2007)

Examples

 
nVar <- 14
nObjective <- 5
nIndividual <- 100
crossoverProbability <- 1
mutationProbability <- 1/nVar
population <- matrix(runif(nIndividual*nVar), nrow = nVar)

# run a generation of SMS-EMOA with standard WFG6 test function.
numpyready <- reticulate::py_module_available('numpy')
pygmoready <- reticulate::py_module_available('pygmo')
py_module_ready <- numpyready && pygmoready
if(py_module_ready) # prevent error on testing the example
SMSEMOA(population,WFG6,nObjective,list(crossoverProbability = crossoverProbability,
                                          mutationProbability = mutationProbability),nObjective)

The WFG1 test function.

Description

The WFG1 test function.

Usage

WFG1(individual, nObj, k = nObj - 1)

Arguments

Value

A matrix of size nObjective, containing the objective values.

References

Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. Trans. Evol. Comp 10 (5), 477–506 (2006)

Examples

individual <- runif(14)
nObj <- 4
WFG1(individual,nObj)

The WFG2 test function.

Description

The WFG2 test function.

Usage

WFG2(individual, nObj, k = nObj - 1)

Arguments

Value

A matrix of size nObjective, containing the objective values.

References

Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. Trans. Evol. Comp 10 (5), 477–506 (2006)

Examples

individual <- runif(14)
nObj <- 4
WFG2(individual,nObj)

The WFG4 test function.

Description

The WFG4 test function.

Usage

WFG4(individual, nObj, k = nObj - 1)

Arguments

Value

A matrix of size nObjective, containing the objective values.

References

Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. Trans. Evol. Comp 10 (5), 477–506 (2006)

Examples

individual <- runif(14)
nObj <- 4
WFG4(individual,nObj)

The WFG5 test function.

Description

The WFG5 test function.

Usage

WFG5(individual, nObj, k = nObj - 1)

Arguments

Value

A matrix of size nObjective, containing the objective values.

References

Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. Trans. Evol. Comp 10 (5), 477–506 (2006)

Examples

individual <- runif(14)
nObj <- 4
WFG5(individual,nObj)

The WFG6 test function.

Description

The WFG6 test function.

Usage

WFG6(individual, nObj, k = nObj - 1)

Arguments

Value

A matrix of size nObjective, containing the objective values.

References

Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. Trans. Evol. Comp 10 (5), 477–506 (2006)

Examples

individual <- runif(14)
nObj <- 4
WFG6(individual,nObj)

The WFG7 test function.

Description

The WFG7 test function.

Usage

WFG7(individual, nObj, k = nObj - 1)

Arguments

Value

A matrix of size nObjective, containing the objective values.

References

Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. Trans. Evol. Comp 10 (5), 477–506 (2006)

Examples

individual <- runif(14)
nObj <- 4
WFG7(individual,nObj)

The WFG8 test function.

Description

The WFG8 test function.

Usage

WFG8(individual, nObj, k = nObj - 1)

Arguments

Value

A matrix of size nObjective, containing the objective values.

References

Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. Trans. Evol. Comp 10 (5), 477–506 (2006)

Examples

individual <- runif(14)
nObj <- 4
WFG8(individual,nObj)

The WFG9 test function.

Description

The WFG9 test function.

Usage

WFG9(individual, nObj, k = nObj - 1)

Arguments

Value

A matrix of size nObjective, containing the objective values.

References

Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. Trans. Evol. Comp 10 (5), 477–506 (2006)

Examples

individual <- runif(14)
nObj <- 4
WFG9(individual,nObj)

Generator for cmaes_gen class.

Description

Create a list with cmaes_gen class. Basically, the function transform the population into a class that is accepted by the MOCMAES and SMOCMAES function.

Usage

cmaes_gen(
  population,
  ps_target = (1/(5 + (1/2)^0.5)),
  stepSize = 0.5,
  evoPath = rep(0, nrow(population)),
  covarianceMatrix = diag(nrow(population))
)

Arguments

Value

An object of cmaes_gen class. It can be used as MO-CMA-ES parent. It is a 5 tuple: x (the design point, length = number of variable),averageSuccessRate (scalar),stepSize (scalar), evoPath (evolution path, vector, length = number of variable ),covarianceMatrix (square matrix with ncol = nrow = number of variable).

Examples

nVar <- 14
nObjective <- 5
nIndividual <- 100
crossoverProbability <- 1
ps_target <- 1 / (5 + ( 1 / 2  )^0.5 )
pop <- matrix(stats::runif(nIndividual*nVar), nrow = nVar) # create the population
a_list <- cmaes_gen(pop)
control <- list(successProbTarget=ps_target,crossoverProbability=crossoverProbability)
 
# run a generation of MO-CMA-ES with standard WFG8 test function.
numpyready <- reticulate::py_module_available('numpy')
pygmoready <- reticulate::py_module_available('pygmo')
py_module_ready <- numpyready && pygmoready
if(py_module_ready) # prevent error on testing the example
newGeneration <- MOCMAES(a_list,nObjective,WFG8,control,nObjective)

Modified powered tchebyscheff R2-indicator designed to approximate HV

Description

Compute the R2-HV from Shang et al.

Usage

compute_R2HV(dataPoints, reference, weights = NULL, nPoints = 100)

Arguments

Value

The function return the powered R2-indicator of the set.

References

Ke Shang, Hisao Ishibuchi, Min-Ling Zhang, and Yiping Liu. 2018. A new R2 indicator for better hypervolume approximation. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO '18), Hernan Aguirre (Ed.). ACM, New York, NY, USA, 745-752. DOI: https://doi.org/10.1145/3205455.3205543

Examples

nPointToSample <- 100
nObjective <- 3
points <- matrix(runif(nPointToSample*nObjective), nrow = nObjective) # sample the points
ranks <- nsga2R::fastNonDominatedSorting(t(points)) # non-dominated sorting
points <- points[,ranks[[1]],drop=FALSE] # take only the non-dominated front
nPoints <- ncol(points) # check how many points are on the non-dominated front
reference <- rep(2,nObjective)

compute_R2HV(points,reference)

Modified tchebyscheff R2-indicator contribution designed to approximate HV

Description

Compute the R2-HVC from Shang et al.

Usage

compute_R2HVC(
  dataPoints,
  reference,
  weights = NULL,
  alpha = 1,
  nWeight = 300,
  indexOfInterest = 1:ncol(dataPoints)
)

Arguments

Value

The function return R2-indicator contribution of each point.

References

K. Shang, H. Ishibuchi and X. Ni, "R2-based Hypervolume Contribution Approximation," in IEEE Transactions on Evolutionary Computation. doi: 10.1109/TEVC.2019.2909271

Examples

nPointToSample <- 100
nObjective <- 3
points <- matrix(runif(nPointToSample*nObjective), nrow = nObjective) # sample the points
ranks <- nsga2R::fastNonDominatedSorting(t(points)) # non-dominated sorting
points <- points[,ranks[[1]],drop=FALSE] # take only the non-dominated front
nPoints <- ncol(points) # check how many points are on the non-dominated front
reference <- rep(2,nObjective)

compute_R2HVC(points,reference)

Modified tchebyscheff R2-indicator

Description

Compute the R2-mtch indicator from Shang et al.

Usage

compute_R2mtch(dataPoints, reference, weights = NULL, nWeight = 100)

Arguments

Value

The function return the R2-indicator of the set.

References

Ke Shang, Hisao Ishibuchi, Min-Ling Zhang, and Yiping Liu. 2018. A new R2 indicator for better hypervolume approximation. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO '18), Hernan Aguirre (Ed.). ACM, New York, NY, USA, 745-752. DOI: https://doi.org/10.1145/3205455.3205543

Examples

nPointToSample <- 100
nObjective <- 3
points <- matrix(runif(nPointToSample*nObjective), nrow = nObjective) # sample the points
ranks <- nsga2R::fastNonDominatedSorting(t(points)) # non-dominated sorting
points <- points[,ranks[[1]],drop=FALSE] # take only the non-dominated front
nPoints <- ncol(points) # check how many points are on the non-dominated front
reference <- rep(2,nObjective)

compute_R2mtch(points,reference)

Das and Dennis's structured weight generation, normal boundary intersection (NBI).

Description

Generate a set of weights following Das and Dennis's method. Each column returned is a weight vector.

Usage

createWeights(nDim, axisDivision = nDim + 2, noZero = FALSE)

Arguments

Value

The function return a set of weight vectors.

References

Indraneel Das and J. E. Dennis. 1998. Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems. SIAM Journal on Optimization 1998 8:3, 631-657.

Examples

nObjective <- 3
axisDiv <- 6

createWeights(nObjective,axisDiv)

Sobol sequence weights

Description

Generate a set of weights following Sobol sequence generator

Usage

createWeightsSobol(nWeights, nDim, seed = 4177)

Arguments

Value

The function return a set of weight vectors.

Examples

nObjective <- 3
nPoint <- 1000

createWeightsSobol(nPoint,nObjective)

Install python modules required by MaOEA: numpy and PyGMO

Description

Install the required python package via conda.

Usage

install_python_dependencies(conda = "auto", envname = NULL, ...)

Arguments

Value

0 if dependencies installed and loaded successfully, 1 if fails.

Install python modules required by MaOEA: numpy and PyGMO

Description

Import the required python package if it fails onLoad.

Usage

load_python_dependencies()

Value

0 if dependencies loaded successfully, 1 if fails.

Elitist Non-dominated Sorting Genetic Algorithm version III

Description

Main interface for the many-objective optimization evolutionary algorithm (MaOEA) package.

Usage

optimMaOEA(
  x = NULL,
  fun,
  solver = NSGA3,
  nObjective,
  nGeneration = 1,
  nVar = nrow(x),
  populationSize = ncol(x),
  seed = 2000,
  control = list(),
  ...
)

Arguments

Value

Returns a list for the next generation population The new generation design points. populationObjective The new generation's objective values.

Examples

nVar <- 14
nObjective <- 5
nIndividual <- 100
#control for NSGA3
ctrl <- list(crossoverProbability = 1,
             mutationProbability = 1/nVar)
#Initial population can be supplied, like below but for this example, we skip it
#population <- matrix(runif(nIndividual*nVar), nrow = nVar)

numpyready <- reticulate::py_module_available('numpy')
pygmoready <- reticulate::py_module_available('pygmo')
py_module_ready <- numpyready && pygmoready
if(py_module_ready){ # prevent error on testing the example
# Hybrid NSGA-III and SMSEMOA example
# 2 calls for nObjective. 1 for optimMaOEA, 1 for WFG8
# generate initial population and run 10 gen. NSGA-III with standard WFG8 test function.
newPop <- optimMaOEA( , WFG8,NSGA3,nObjective,10,nVar,nIndividual,,ctrl,nObjective)$x

# run 5 generations of SMSEMOA with standard WFG8 test function starting with newPop.
result <- optimMaOEA( newPop, WFG8,SMSEMOA,nObjective,5,,,1000,ctrl,nObjective)
finalPop <- result$x
finalObjective <- result$y
}