| Type: | Package |
| Title: | Elitist Non-Dominated Sorting Genetic Algorithm |
| Version: | 1.1 |
| Date: | 2022-05-21 |
| Author: | Ching-Shih (Vince) Tsou <cstsou@mail.ntcb.edu.tw> |
| Maintainer: | Ming-Chang (Alan) Lee <alan9956@ydu.edu.tw> |
| Description: | Box-constrained multiobjective optimization using the elitist non-dominated sorting genetic algorithm - NSGA-II. Fast non-dominated sorting, crowding distance, tournament selection, simulated binary crossover, and polynomial mutation are called in the main program. The methods are described in Deb et al. (2002) <doi:10.1109/4235.996017>. |
| Depends: | mco |
| License: | LGPL-3 |
| Packaged: | 2022-05-22 06:45:54 UTC; user |
| NeedsCompilation: | no |
| Repository: | CRAN |
| Date/Publication: | 2022-05-23 09:10:06 UTC |
Elitist Non-dominated Sorting Genetic Algorithm based on R
Description
Functions for box-constrained multiobjective optimization using the elitist non-dominated sorting genetic algorithm - NSGA-II.
Details
| Package: | nsga2R |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2013-06-12 |
| License: | LGPL-3 |
This package provide functions for box-constrained multiobjective optimization using the elitist non-dominated sorting genetic algorithm - NSGA-II. Fast non-dominated sorting, crowding distance, tournament selection, simulated binary crossover, and polynomial mutation are called in the main program, nsga2R, to complete the search.
Author(s)
Ching-Shih (Vince) Tsou <cstsou@mail.ntcb.edu.tw>
Maintainer: Ming-Chang (Alan) Lee <alan9956@ydu.edu.tw>
References
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002), " A fast and elitist multiobjective genetic algorithm: NSGA-II", IEEE Transactions on Evolutionary Computation, 6(2), 182-197.
Bounded Polynomial Mutation Operator
Description
The bounded polynomial mutation operator is a real-parameter genetic operator. Like in the simulated binary crossover operator, the probability distribution is also a polynomial function instead of a normal distribution.
Usage
boundedPolyMutation(parent_chromosome, lowerBounds, upperBounds, mprob, mum)
Arguments
parent_chromosome |
Mating pool with decision variables |
lowerBounds |
Lower bounds of each decision variable |
upperBounds |
Upper bounds of each decision variable |
mprob |
Mutation probability |
mum |
Mutation distribution index, it can be any nonnegative real number |
Value
Return the offspring population with decision variables
Author(s)
Ching-Shih (Vince) Tsou cstsou@mail.ntcb.edu.tw
References
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002), " A fast and elitist multiobjective genetic algorithm: NSGA-II", IEEE Transactions on Evolutionary Computation, 6(2), 182-197.
Examples
set.seed(1234)
lowerBounds <- rep(0,30)
upperBounds <- rep(1,30)
mprob <- 0.2
MutDistIdx <- 20
matingPool <- matrix(runif(1200, 0, 1), nrow=40, ncol=30)
childAfterM <- boundedPolyMutation(matingPool,lowerBounds,upperBounds,mprob,MutDistIdx)
childAfterM
Bounded Simulated Binary Crossover Operator
Description
The simulated binary crossover operator is a real-parameter genetic operator. It simulates the working principal of the single-point crossover operator on binary strings.
Usage
boundedSBXover(parent_chromosome, lowerBounds, upperBounds, cprob, mu)
Arguments
parent_chromosome |
Mating pool with decision variables |
lowerBounds |
Lower bounds of each decision variable |
upperBounds |
Upper bounds of each decision variable |
cprob |
Crossover probability |
mu |
Crossover distribution index, it can be any nonnegative real number |
Value
Return the offspring population with decision variables
Author(s)
Ching-Shih (Vince) Tsou cstsou@mail.ntcb.edu.tw
References
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002), " A fast and elitist multiobjective genetic algorithm: NSGA-II", IEEE Transactions on Evolutionary Computation, 6(2), 182-197.
Examples
set.seed(1234)
lowerBounds <- rep(0,30)
upperBounds <- rep(1,30)
cprob <- 0.7
XoverDistIdx <- 20
matingPool <- matrix(runif(1200, 0, 1), nrow=40, ncol=30)
childAfterX <- boundedSBXover(matingPool,lowerBounds,upperBounds,cprob,XoverDistIdx)
childAfterX
Crowding Distance Assignment for Each Front
Description
This function estimates the density of solutions surrounding a particular solution within each front. It calculates the crowding distances of solutions according to their objectives and those within the same front.
Usage
crowdingDist4frnt(pop, rnk, rng)
Arguments
pop |
Population matrix including decision variables, objective functions, and nondomination rank |
rnk |
List of solution indices for each front |
rng |
Vector of each objective function range, i.e. the difference between the maximum and minimum objective function value of each objective |
Value
Return a matrix of crowding distances of all solutions
Author(s)
Ching-Shih (Vince) Tsou cstsou@mail.ntcb.edu.tw
References
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002), " A fast and elitist multiobjective genetic algorithm: NSGA-II", IEEE Transactions on Evolutionary Computation, 6(2), 182-197.
See Also
Examples
library(mco)
popSize <- 50
lowerBounds <- rep(0,30)
upperBounds <- rep(1,30)
varNo <- length(lowerBounds)
objDim <- 2
set.seed(1234)
population <- t(sapply(1:popSize, function(u) array(runif(length(lowerBounds),
lowerBounds,upperBounds))))
population <- cbind(population, t(apply(population,1,zdt2)))
ranking <- fastNonDominatedSorting(population[,(varNo+1):(varNo+objDim)])
rnkIndex <- integer(popSize)
i <- 1
while (i <= length(ranking)) {
rnkIndex[ranking[[i]]] <- i
i <- i + 1
}
population <- cbind(population,rnkIndex)
objRange <- apply(population[,(varNo+1):(varNo+objDim)], 2, max) -
apply(population[,(varNo+1):(varNo+objDim)], 2, min)
cd <- crowdingDist4frnt(population,ranking,objRange)
cd
Fast Non-dominated Sorting
Description
A fast approach to sort non-dominated solutions into different nondomination levels.
Usage
fastNonDominatedSorting(inputData)
Arguments
inputData |
Matrix of solutions with objective function values |
Value
Return a list of indices for all fronts.
Author(s)
Ching-Shih (Vince) Tsou cstsou@mail.ntcb.edu.tw
References
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002), " A fast and elitist multiobjective genetic algorithm: NSGA-II", IEEE Transactions on Evolutionary Computation, 6(2), 182-197.
Examples
set.seed(1234)
# randomly generate a polulation of fifty chromosomes, each with two objectives
y <- matrix(runif(100, -5, 5), nrow=50, ncol=2)
rankIdxList <- fastNonDominatedSorting(y)
rankIdxList
R Based Non-dominated Sorting Genetic Algorithm II
Description
A fast and elitist multiobjective genetic algorithm based on R.
Usage
nsga2R(fn, varNo, objDim, lowerBounds = rep(-Inf, varNo), upperBounds = rep(Inf, varNo),
popSize = 100, tourSize = 2, generations = 20, cprob = 0.7, XoverDistIdx = 5,
mprob = 0.2, MuDistIdx = 10)
Arguments
fn |
Objective functions to be minimized |
varNo |
Number of decision variables |
objDim |
Number of objective functions |
lowerBounds |
Lower bounds of each decision variable |
upperBounds |
Upper bounds of each decision variable |
popSize |
Size of population |
tourSize |
Size of tournament |
generations |
Number of generations |
cprob |
Crossover probability |
XoverDistIdx |
Crossover distribution index, it can be any nonnegative real number |
mprob |
Mutation probability |
MuDistIdx |
Mutation distribution index, it can be any nonnegative real number |
Value
The returned value is a 'nsga2R' object with the following fields in additional to above NSGA-II settings:
parameters |
Solutions of decision variables found |
objectives |
Non-dominated objective function values |
paretoFrontRank |
Nondomination ranks (or levels) that each non-dominated solution belongs to |
crowdingDistance |
Crowding distance of each non-dominated solution |
Author(s)
Ching-Shih (Vince) Tsou cstsou@mail.ntcb.edu.tw
References
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002), " A fast and elitist multiobjective genetic algorithm: NSGA-II", IEEE Transactions on Evolutionary Computation, 6(2), 182-197.
Examples
# find the non-dominated solutions of zdt3 test problem
results <- nsga2R(fn=zdt3, varNo=30, objDim=2, lowerBounds=rep(0,30), upperBounds=rep(1,30),
popSize=50, tourSize=2, generations=50, cprob=0.9, XoverDistIdx=20, mprob=0.1,MuDistIdx=3)
plot(results$objectives)
Tournament Selection
Description
Tournaments are played among several solutions. The best one is chosen according to their nondomination levels and crowding distances. And it is placed in the mating pool.
Usage
tournamentSelection(pop, pool_size, tour_size)
Arguments
pop |
Population matrix with nondomination rank and crowding distance |
pool_size |
Size of mating pool, usually same as the population size |
tour_size |
Size of tournament, the selection pressure can be adjusted by varying the tournament size |
Value
Return the mating pool with decision variables, objective functions, nondomination level, and crowding distance
Author(s)
Ching-Shih (Vince) Tsou cstsou@mail.ntcb.edu.tw
References
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002), " A fast and elitist multiobjective genetic algorithm: NSGA-II", IEEE Transactions on Evolutionary Computation, 6(2), 182-197.
Examples
library(mco)
tourSize <- popSize <- 10
lowerBounds <- rep(0,30)
upperBounds <- rep(1,30)
varNo <- length(lowerBounds)
objDim <- 2
set.seed(1234)
population <- t(sapply(1:popSize, function(u) array(runif(length(lowerBounds),
lowerBounds,upperBounds))))
population <- cbind(population, t(apply(population,1,zdt3)))
ranking <- fastNonDominatedSorting(population[,(varNo+1):(varNo+objDim)])
rnkIndex <- integer(popSize)
i <- 1
while (i <= length(ranking)) {
rnkIndex[ranking[[i]]] <- i
i <- i + 1
}
population <- cbind(population,rnkIndex);
objRange <- apply(population[,(varNo+1):(varNo+objDim)], 2, max) -
apply(population[,(varNo+1):(varNo+objDim)], 2, min);
cd <- crowdingDist4frnt(population,ranking,objRange)
population <- cbind(population,apply(cd,1,sum))
matingPool <- tournamentSelection(population,popSize,tourSize)
matingPool