# 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

1 2 | ```
mcga(popsize, chsize, crossprob = 1.0, mutateprob = 0.01,
elitism = 1, minval, maxval, maxiter = 10, evalFunc)
``` |

### Arguments

`popsize` |
Number of chromosomes. |

`chsize` |
Number of parameters. |

`crossprob` |
Crossover probability. By default it is 1.0 |

`mutateprob` |
Mutation probability. By default it is 0.01 |

`elitism` |
Number of best chromosomes to be copied directly into next generation. By default it is 1 |

`minval` |
The lower bound of the randomized initial population. This is not a constraint for parameters. |

`maxval` |
The upper bound of the randomized initial population. This is not a constraint for parameters. |

`maxiter` |
The maximum number of generations. By default it is 10 |

`evalFunc` |
An R function. By default, each problem is a minimization. |

### Value

`population` |
Sorted population resulted after generations |

`costs` |
Cost values for each chromosomes in the resulted population |

### 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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
# 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")
``` |

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