multi_mcga {mcga}

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

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.

numfunc

Number of objective functions.

evalFunc

An R function. By default, each problem is a minimization. This function must return a cost vector with dimension of numfunc. Each element of this vector points to the corresponding function to optimize.

Value

population

Sorted population resulted after generations

costs

Cost values for each chromosomes in the resulted population

ranks

Calculated ranks using a non-dominated sorting for each chromosome

Author(s)

Mehmet Hakan Satman - [e-mail]

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)