Machine Coded Genetic Algorithms for Real-valued Optimization Problems

Description

Machine coded genetic algorithm (MCGA) is a fast tool for real-valued optimization problems. It uses the byte representation of variables rather than real-values. It performs the classical crossover operations (uniform) on these byte representations. Mutation operator is also similar to classical mutation operator, which is to say, it changes a randomly selected byte value of a chromosome by +1 or -1 with probability 1/2. In MCGAs there is no need for encoding-decoding process and the classical operators are directly applicable on real-values. It is fast and can handle a wide range of a search space with high precision. Using a 256-unary alphabet is the main disadvantage of this algorithm but a moderate size population is convenient for many problems.

Author(s)

Mehmet Hakan Satman

Maintainer: Mehmet Hakan Satman <mhsatman@istanbul.edu.tr>

Examples

## Not run: 
# A sample optimization problem
# Min f(xi) = (x1-7)^2 + (x2-77)^2 + (x3-777)^2 + (x4-7777)^2 + (x5-77777)^2
# The range of xi is unknown. The solution is
# x1 = 7
# x2 = 77
# x3 = 777
# x4 = 7777
# x5 = 77777
# Min f(xi) = 0
require("mcga")
 f<-function(x){
    return ((x[1]-7)^2 + (x[2]-77)^2 +(x[3]-777)^2 +(x[4]-7777)^2 +(x[5]-77777)^2)
 }
 m <- mcga(	popsize=200, 
			chsize=5, 
			minval=0.0, 
			maxval=999999999.9, 
			maxiter=2500, 
			crossprob=1.0, 
			mutateprob=0.01, 
			evalFunc=f)
			
 cat("Best chromosome:\n")
 print(m$population[1,])
 cat("Cost: ",m$costs[1],"\n")

## End(Not run)

Mutation operator for byte representation of double values

Description

This function is a C++ wrapper for mutating byte representation of a given candidate solution

Usage

ByteCodeMutation(bytes1, pmutation)

Arguments

Value

Byte vector of mutated solution

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

ByteCodeMutationUsingDoubles

Examples

set.seed(1246)
print(pi)
bytes <- DoubleToBytes(pi)
mutated.bytes <- ByteCodeMutation(bytes, 0.10) 
new.var <- BytesToDouble(mutated.bytes)
print(new.var)

Mutation operator for byte representation of double values

Description

This function is a C++ wrapper for mutating byte representation of a given candidate solution

Usage

ByteCodeMutationUsingDoubles(d, pmutation)

Arguments

Value

Double vector of mutated solution

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

ByteCodeMutation

Examples

set.seed(1246)
print(pi)
print(exp(1))
new.var <- ByteCodeMutationUsingDoubles(c(pi, exp(1)), 0.10)
print(new.var)

Mutation operator for byte representation of double values

Description

This function is a C++ wrapper for mutating byte representation of a given candidate solution. This mutation operator randomly changes a byte in the range of [0,255].

Usage

ByteCodeMutationUsingDoublesRandom(d, pmutation)

Arguments

Value

Double vector of mutated solution

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

ByteCodeMutation

Examples

set.seed(1246)
print(pi)
print(exp(1))
new.var <- ByteCodeMutationUsingDoublesRandom(c(pi, exp(1)), 0.10)
print(new.var)

Converting p * sizeof(double) bytes to a vector of p double values

Description

This function converts a byte vector to a vector of doubles

Usage

ByteVectorToDoubles(b)

Arguments

Value

Corresponding vector of double typed values for a given vector of bytes

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

DoubleVectorToBytes

BytesToDouble

ByteVectorToDoubles

Examples

a <- DoubleVectorToBytes(c(56.54, 89.7666, 98.565))
b <- ByteVectorToDoubles(a)
print(b)

Converting sizeof(double) bytes to a double value

Description

This function converts sizeof(double) bytes to a double typed value

Usage

BytesToDouble(x)

Arguments

Value

Corresponding double typed value for a given vector of bytes

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

DoubleVectorToBytes

DoubleToBytes

ByteVectorToDoubles

Examples

print(BytesToDouble(DoubleToBytes(56.43)))

Byte representation of a double typed variable

Description

This function returns a vector of byte values with the length of sizeof(double) for a given double typed value

Usage

DoubleToBytes(x)

Arguments

Value

A vector of byte values with the length of sizeof(double) for a given double typed value

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

DoubleVectorToBytes

BytesToDouble

ByteVectorToDoubles

Examples

print(DoubleToBytes(56.43))

Byte representation of a vector of double typed variables

Description

This function returns a vector of byte values for a given vector of double typed values

Usage

DoubleVectorToBytes(d)

Arguments

Value

returns a vector of byte values for a given vector of double typed values

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

DoubleToBytes

BytesToDouble

ByteVectorToDoubles

Examples

print(DoubleVectorToBytes(c(56.54, 89.7666, 98.565)))

Altering vector of doubles to satisfy boundary constraints

Description

Byte based crossover and mutation operators can generate variables out of bounds of the decision variables. This function controls if variables are between their lower and upper bounds and if not, draws random numbers between these ranges. This function directly modifies the argument doubles and does not return a value.

Usage

EnsureBounds(doubles, mins, maxs)

Arguments

Value

Function directly modifies the argument doubles and does not return a result.

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

byte_crossover

byte_mutation

mcga2

Examples

set.seed(1234)
x <- runif(10)
print(x)
# [1] 0.113703411 0.622299405 0.609274733 0.623379442 0.860915384 0.640310605
# [7] 0.009495756 0.232550506 0.666083758 0.514251141
EnsureBounds(x, mins=rep(0,10), maxs=rep(0.2,10))
print(x)
# [1] 0.113703411 0.138718258 0.108994967 0.056546717 0.184686697 0.058463168
# [7] 0.009495756 0.167459126 0.057244657 0.053364156

Maximum value of a double typed variable

Description

Maximum value of a double typed variable

Usage

MaxDouble()

Value

Returns maximum value of a double typed variable in C++ compiler

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

Examples

print(MaxDouble())

One Point Crossover operation on the two vectors of bytes

Description

This function is a C++ wrapper for crossing-over of two byte vectors of candidate solutions

Usage

OnePointCrossOver(bytes1, bytes2, cutpoint)

Arguments

Value

List of two byte vectors of offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

UniformCrossOver

UniformCrossOverOnDoublesUsingBytes

Examples

b1 <- DoubleVectorToBytes(c(56.54, 89.7666, 98.565))
b2 <- DoubleVectorToBytes(c(79.76, 56.4443, 34.22121))
result <- OnePointCrossOver(b1,b2, round(runif(1,1,SizeOfDouble() * 3)))
print(ByteVectorToDoubles(result[[1]]))
print(ByteVectorToDoubles(result[[2]]))

One-point Crossover operation on the two vectors of doubles using their byte representations

Description

This function is a C++ wrapper for crossing-over of two double vectors of candidate solutions using their byte representations

Usage

OnePointCrossOverOnDoublesUsingBytes(d1, d2, cutpoint)

Arguments

Value

List of two double vectors of offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

OnePointCrossOver

UniformCrossOverOnDoublesUsingBytes

Examples

d1 <- runif(3)
d2 <- runif(3)
cutp <- sample(1:(length(d1)*SizeOfDouble()), 1)[1]
offspring <- OnePointCrossOverOnDoublesUsingBytes(d1,d2, cutp)
print("Parents:")
print(d1)
print(d2)
print("Offspring:")
print(offspring[[1]])
print(offspring[[2]])

Byte-length of a double typed variable

Description

Byte-length of a double typed variable in computer memory

Usage

SizeOfDouble()

Value

Returns the byte-length of a double typed variable in computer memory

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

Examples

print(SizeOfDouble())

Byte-length of a int typed variable

Description

Byte-length of a int typed variable in computer memory

Usage

SizeOfInt()

Value

Returns the byte-length of a int typed variable in computer memory

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

Examples

print(SizeOfInt())

Byte-length of a long typed variable

Description

Byte-length of a long typed variable in computer memory

Usage

SizeOfLong()

Value

Returns the byte-length of a long typed variable in computer memory

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

Examples

print(SizeOfLong())

Two Point Crossover operation on the two vectors of bytes

Description

This function is a C++ wrapper for crossing-over of two byte vectors of candidate solutions

Usage

TwoPointCrossOver(bytes1, bytes2, cutpoint1, cutpoint2)

Arguments

Value

List of two byte vectors of offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

OnePointCrossOver

OnePointCrossOverOnDoublesUsingBytes

UniformCrossOverOnDoublesUsingBytes

Examples

b1 <- DoubleVectorToBytes(c(56.54, 89.7666, 98.565))
b2 <- DoubleVectorToBytes(c(79.76, 56.4443, 34.22121))
cutpoints <- sort(sample(1:(length(b1)*SizeOfDouble()), 2, replace = FALSE))
result <- TwoPointCrossOver(b1,b2, cutpoints[1], cutpoints[2])
print(ByteVectorToDoubles(result[[1]]))
print(ByteVectorToDoubles(result[[2]]))

Two-point Crossover operation on the two vectors of doubles using their byte representations

Description

This function is a C++ wrapper for crossing-over of two double vectors of candidate solutions using their byte representations

Usage

TwoPointCrossOverOnDoublesUsingBytes(d1, d2, cutpoint1, cutpoint2)

Arguments

Value

List of two double vectors of offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

TwoPointCrossOver

OnePointCrossOver

UniformCrossOver

OnePointCrossOverOnDoublesUsingBytes

Examples

d1 <- runif(3)
d2 <- runif(3)
cutpoints <- sort(sample(1:(length(d1)*SizeOfDouble()), 2, replace = FALSE))
offspring <- TwoPointCrossOverOnDoublesUsingBytes(d1,d2,cutpoints[1], cutpoints[2])
print("Parents:")
print(d1)
print(d2)
print("Offspring:")
print(offspring[[1]])
print(offspring[[2]])

Uniform Crossover operation on the two vectors of bytes

Description

This function is a C++ wrapper for crossing-over of two byte vectors of candidate solutions

Usage

UniformCrossOver(bytes1, bytes2)

Arguments

Value

List of two byte vectors of offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

OnePointCrossOver

UniformCrossOverOnDoublesUsingBytes

Examples

b1 <- DoubleVectorToBytes(c(56.54, 89.7666, 98.565))
b2 <- DoubleVectorToBytes(c(79.76, 56.4443, 34.22121))
result <- UniformCrossOver(b1,b2)
print(ByteVectorToDoubles(result[[1]]))
print(ByteVectorToDoubles(result[[2]]))

Uniform Crossover operation on the two vectors of doubles using their byte representations

Description

This function is a C++ wrapper for crossing-over of two double vectors of candidate solutions using their byte representations

Usage

UniformCrossOverOnDoublesUsingBytes(d1, d2)

Arguments

Value

List of two double vectors of offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

See Also

OnePointCrossOver

OnePointCrossOverOnDoublesUsingBytes

Examples

d1 <- runif(3)
d2 <- runif(3)
offspring <- UniformCrossOverOnDoublesUsingBytes(d1,d2)
print("Parents:")
print(d1)
print(d2)
print("Offspring:")
print(offspring[[1]])
print(offspring[[2]])

Performs arithmetic crossover operation on a pair of two selected parent candidate solutions

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter crossover= is set to arithmetic_crossover than the arithmetic crossover operator is applied in the genetic search. arithmetic_crossover generates offspring using the weighted mean of parents' genes. Weights are drawn randomly.

Usage

arithmetic_crossover(object, parents, ...)

Arguments

Value

List of two generated offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- ga(type="real-valued", fitness = f, popSize = 100, maxiter = 100, 
           min = rep(-50,5), max = rep(50,5), crossover = arithmetic_crossover)
print(myga@solution)

Performs blx (blend) crossover operation on a pair of two selected parent candidate solutions

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter crossover= is set to blx_crossover than the blx crossover operator is applied in the genetic search.

Usage

blx_crossover(object, parents, ...)

Arguments

Value

List of two generated offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- ga(type="real-valued", fitness = f, popSize = 100, maxiter = 100, 
           min = rep(-50,5), max = rep(50,5), crossover = blx_crossover)
print(myga@solution)

Performs crossover operation on a pair of two selected parent candidate solutions

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter crossover= is set to byte_crossover than the byte-coded crossover operator is applied in the genetic search. In mcga2 function, the hard-coded crossover parameter is set to byte_crossover by definition. byte_crossover function simply takes two double vectors (parents) and combines the bytes of doubles using a Uniform distribution with parameters 0 and 1.

Usage

byte_crossover(object, parents, ...)

Arguments

Value

List of two generated offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

References

M.H.Satman (2013), Machine Coded Genetic Algorithms for Real Parameter Optimization Problems, Gazi University Journal of Science, Vol 26, No 1, pp. 85-95

See Also

mcga2

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- GA::ga(type="real-valued", fitness = f, popSize = 100, maxiter = 200, 
              lower = rep(-50,5), upper = rep(50,5), crossover = byte_crossover,
              mutation = byte_mutation)
print(myga@solution)

Performs one-point crossover operation on a pair of two selected parent candidate solutions

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter crossover= is set to byte_crossover_1p than the byte-coded one-point crossover operator is applied in the genetic search. In mcga2 function, the hard-coded crossover parameter is set to byte_crossover by definition. byte_crossover_1p function simply takes two double vectors (parents) and combines the bytes of doubles using given cut-point.

Usage

byte_crossover_1p(object, parents, ...)

Arguments

Value

List of two generated offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

References

M.H.Satman (2013), Machine Coded Genetic Algorithms for Real Parameter Optimization Problems, Gazi University Journal of Science, Vol 26, No 1, pp. 85-95

See Also

mcga2

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- GA::ga(type="real-valued", fitness = f, popSize = 100, maxiter = 200, 
              min = rep(-50,5), max = rep(50,5), crossover = byte_crossover_1p,
              mutation = byte_mutation)
print(myga@solution)

Performs two-point crossover operation on a pair of two selected parent candidate solutions

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter crossover= is set to byte_crossover_2p than the byte-coded two-point crossover operator is applied in the genetic search. In mcga2 function, the hard-coded crossover parameter is set to byte_crossover by definition. byte_crossover_2p function simply takes two double vectors (parents) and combines the bytes of doubles using given cutpoint1 and cutpoint2.

Usage

byte_crossover_2p(object, parents, ...)

Arguments

Value

List of two generated offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

References

M.H.Satman (2013), Machine Coded Genetic Algorithms for Real Parameter Optimization Problems, Gazi University Journal of Science, Vol 26, No 1, pp. 85-95

See Also

mcga2

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- GA::ga(type="real-valued", fitness = f, popSize = 100, maxiter = 200, 
              min = rep(-50,5), max = rep(50,5), crossover = byte_crossover_2p,
              mutation = byte_mutation)
print(myga@solution)

Performs mutation operation on a given double vector

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter mutation= is set to byte_mutation than the byte-coded mutation operator is applied in the genetic search. In mcga2 function, the hard-coded mutation parameter is set to byte_mutation by definition. Byte-mutation function simply takes an double vector and changes bytes of this values by +1 or -1 using the pre-determined mutation probabilty.

Usage

byte_mutation(object, parent, ...)

Arguments

Value

Mutated double vector

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

References

M.H.Satman (2013), Machine Coded Genetic Algorithms for Real Parameter Optimization Problems, Gazi University Journal of Science, Vol 26, No 1, pp. 85-95

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- GA::ga(type="real-valued", fitness = f, popSize = 100, maxiter = 200, 
              min = rep(-50,5), max = rep(50,5), crossover = byte_crossover,
              mutation = byte_mutation)
print(myga@solution)

Performs mutation operation on a given double vector using dynamic mutation probabilities

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter mutation= is set to byte_mutation_dynamic than the byte-coded mutation operator is applied in the genetic search. In mcga2 function, the hard-coded mutation parameter is set to byte_mutation by definition. Byte-mutation function simply takes an double vector and changes bytes of this values by +1 or -1 using the dynamically decreased and pre-determined mutation probabilty.

Usage

byte_mutation_dynamic(object, parent, ...)

Arguments

Value

Mutated double vector

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

References

M.H.Satman (2013), Machine Coded Genetic Algorithms for Real Parameter Optimization Problems, Gazi University Journal of Science, Vol 26, No 1, pp. 85-95

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- GA::ga(type="real-valued", fitness = f, popSize = 100, maxiter = 200, 
              min = rep(-50,5), max = rep(50,5), crossover = byte_crossover,
              mutation = byte_mutation_dynamic, pmutation = 0.10)
print(myga@solution)

Performs mutation operation on a given double vector

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter mutation= is set to byte_mutation_random than the byte-coded mutation operator is applied in the genetic search. In mcga2 function, the hard-coded mutation parameter is set to byte_mutation by definition. This function simply takes an double vector and changes bytes randomly in the range of [0,255] using the pre-determined mutation probabilty.

Usage

byte_mutation_random(object, parent, ...)

Arguments

Value

Mutated double vector

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

References

M.H.Satman (2013), Machine Coded Genetic Algorithms for Real Parameter Optimization Problems, Gazi University Journal of Science, Vol 26, No 1, pp. 85-95

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- GA::ga(type="real-valued", fitness = f, popSize = 100, maxiter = 200, 
              min = rep(-50,5), max = rep(50,5), crossover = byte_crossover,
              mutation = byte_mutation_random, pmutation = 0.20)
print(myga@solution)

Performs mutation operation on a given double vector with dynamic mutation probabilities

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter mutation= is set to byte_mutation_random_dynamic than the byte-coded mutation operator with dynamic probabilities is applied in the genetic search. In mcga2 function, the hard-coded mutation parameter is set to byte_mutation by definition. This function simply takes an double vector and changes bytes randomly in the range of [0,255] using the descrasing values of pre-determined mutation probabilty by generations.

Usage

byte_mutation_random_dynamic(object, parent, ...)

Arguments

Value

Mutated double vector

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

References

M.H.Satman (2013), Machine Coded Genetic Algorithms for Real Parameter Optimization Problems, Gazi University Journal of Science, Vol 26, No 1, pp. 85-95

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
# Increase popSize and maxiter for more precise solutions
myga <- GA::ga(type="real-valued", fitness = f, popSize = 100, maxiter = 200, 
              min = rep(-50,5), max = rep(50,5), crossover = byte_crossover,
              mutation = byte_mutation_random_dynamic, pmutation = 0.20)
print(myga@solution)

Performs flat crossover operation on a pair of two selected parent candidate solutions

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter crossover= is set to flat_crossover than the flat crossover operator is applied in the genetic search. flat_crossover draws a random number between parents' genes and returns a pair of generated offspring

Usage

flat_crossover(object, parents, ...)

Arguments

Value

List of two generated offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- ga(type="real-valued", fitness = f, popSize = 100, maxiter = 100, 
           min = rep(-50,5), max = rep(50,5), crossover = flat_crossover)
print(myga@solution)

Performs linear crossover operation on a pair of two selected parent candidate solutions

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter crossover= is set to linear_crossover than the linear crossover operator is applied in the genetic search. linear_crossover generates three offspring and performs a selection mechanism to determine best two of them.

Usage

linear_crossover(object, parents, ...)

Arguments

Value

List of two generated offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- ga(type="real-valued", fitness = f, popSize = 100, maxiter = 100, 
           min = rep(-50,5), max = rep(50,5), crossover = linear_crossover)
print(myga@solution)

Performs machine coded genetic algorithms on a function subject to be minimized.

Description

Machine coded genetic algorithm (MCGA) is a fast tool for real-valued optimization problems. It uses the byte representation of variables rather than real-values. It performs the classical crossover operations (uniform) on these byte representations. Mutation operator is also similar to classical mutation operator, which is to say, it changes a randomly selected byte value of a chromosome by +1 or -1 with probability 1/2. In MCGAs there is no need for encoding-decoding process and the classical operators are directly applicable on real-values. It is fast and can handle a wide range of a search space with high precision. Using a 256-unary alphabet is the main disadvantage of this algorithm but a moderate size population is convenient for many problems.

Usage

mcga(popsize, chsize, crossprob = 1.0, mutateprob = 0.01, 
	 elitism = 1, minval, maxval, maxiter = 10, evalFunc)

Arguments

Value

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

References

M.H.Satman (2013), Machine Coded Genetic Algorithms for Real Parameter Optimization Problems, Gazi University Journal of Science, Vol 26, No 1, pp. 85-95

Examples

# A sample optimization problem
# Min f(xi) = (x1-7)^2 + (x2-77)^2 + (x3-777)^2 + (x4-7777)^2 + (x5-77777)^2
# The range of xi is unknown. The solution is
# x1 = 7
# x2 = 77
# x3 = 777
# x4 = 7777
# x5 = 77777
# Min f(xi) = 0
require("mcga")
 f<-function(x){
    return ((x[1]-7)^2 + (x[2]-77)^2 +(x[3]-777)^2 +(x[4]-7777)^2 +(x[5]-77777)^2)
 }
 m <- mcga(	popsize=200, 
			chsize=5, 
			minval=0.0, 
			maxval=999999999.9, 
			maxiter=2500, 
			crossprob=1.0, 
			mutateprob=0.01, 
			evalFunc=f)
			
 cat("Best chromosome:\n")
 print(m$population[1,])
 cat("Cost: ",m$costs[1],"\n")

Internal mcga objects

Description

Internal mcga objects.

Details

These are not to be called by the user.

Performs a machine-coded genetic algorithm search for a given optimization problem

Description

mcga2 is the improvement version of the standard mcga function as it is based on the GA::ga function. The byte_crossover and the byte_mutation operators are the main reproduction operators and these operators uses the byte representations of parents in the computer memory.

Usage

mcga2(fitness, ..., min, max,
  population = gaControl("real-valued")$population,
  selection = gaControl("real-valued")$selection,
  crossover = byte_crossover, mutation = byte_mutation, popSize = 50,
  pcrossover = 0.8, pmutation = 0.1, elitism = base::max(1, round(popSize
  * 0.05)), maxiter = 100, run = maxiter, maxFitness = Inf,
  names = NULL, parallel = FALSE, monitor = gaMonitor, seed = NULL)

Arguments

Value

Returns an object of class ga-class

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

References

M.H.Satman (2013), Machine Coded Genetic Algorithms for Real Parameter Optimization Problems, Gazi University Journal of Science, Vol 26, No 1, pp. 85-95

Luca Scrucca (2013). GA: A Package for Genetic Algorithms in R. Journal of Statistical Software, 53(4), 1-37.

See Also

GA::ga

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- mcga2(fitness = f, popSize = 100, maxiter = 300, 
              min = rep(-50,5), max = rep(50,5))
print(myga@solution)

Performs multi objective machine coded genetic algorithms.

Description

Machine coded genetic algorithm (MCGA) is a fast tool for real-valued optimization problems. It uses the byte representation of variables rather than real-values. It performs the classical crossover operations (uniform) on these byte representations. Mutation operator is also similar to classical mutation operator, which is to say, it changes a randomly selected byte value of a chromosome by +1 or -1 with probability 1/2. In MCGAs there is no need for encoding-decoding process and the classical operators are directly applicable on real-values. It is fast and can handle a wide range of a search space with high precision. Using a 256-unary alphabet is the main disadvantage of this algorithm but a moderate size population is convenient for many problems.

This function performs multi objective optimization using the same logic underlying the mcga. Chromosomes are sorted by their objective values using a non-dominated sorting algorithm.

Usage

multi_mcga(popsize, chsize, crossprob = 1.0, mutateprob = 0.01, 
		   elitism = 1, minval, maxval, maxiter = 10, numfunc, evalFunc)

Arguments

Value

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

References

Deb, K. (2000). An efficient constraint handling method for genetic algorithms. Computer methods in applied mechanics and engineering, 186(2), 311-338.

Examples

## Not run: 
 # We have two objective functions.
 f1<-function(x){
   return(sin(x))
 }

 f2<-function(x){
   return(sin(2*x))
 }

 # This function returns a vector of cost functions for a given x sent from mcga
 f<-function(x){
   return ( c( f1(x), f2(x)) )
 }

 # main loop
 m<-multi_mcga(popsize=200, chsize=1, minval= 0, elitism=2, 
 	      maxval= 2.0 * pi, maxiter=1000, crossprob=1.0, 
	      mutateprob=0.01, evalFunc=f, numfunc=2)

 # Points show best five solutions. 
 curve(f1, 0, 2*pi)
 curve(f2, 0, 2*pi, add=TRUE)

 p <- m$population[1:5,]
 points(p, f1(p))
 points(p, f2(p))

## End(Not run)

Performs sbx (simulated binary) crossover operation on a pair of two selected parent candidate solutions

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter crossover= is set to sbx_crossover than the sbx crossover operator is applied in the genetic search. sbx_crossover mimics the classical single-point crossover operator in binary genetic algorithms.

Usage

sbx_crossover(object, parents, ...)

Arguments

Value

List of two generated offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

References

Deb, Kalyanmoy, and Ram Bhushan Agrawal. "Simulated binary crossover for continuous search space." Complex systems 9.2 (1995): 115-148.

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- ga(type="real-valued", fitness = f, popSize = 100, maxiter = 100, 
           min = rep(-50,5), max = rep(50,5), crossover = sbx_crossover)
print(myga@solution)

Performs unfair average crossover operation on a pair of two selected parent candidate solutions

Description

This function is not called directly but is given as a parameter in GA::ga function. In GA::ga, if the parameter crossover= is set to unfair_average_crossover than the unfair average crossover operator is applied in the genetic search.

Usage

unfair_average_crossover(object, parents, ...)

Arguments

Value

List of two generated offspring

Author(s)

Mehmet Hakan Satman - mhsatman@istanbul.edu.tr

Examples

f <- function(x){ 
  return(-sum( (x-5)^2 ) )
}
myga <- ga(type="real-valued", fitness = f, popSize = 100, maxiter = 100, 
           min = rep(-50,5), max = rep(50,5), crossover = unfair_average_crossover)
print(myga@solution)