multi_mcga function

Performs multi objective machine coded genetic algorithms.

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.

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.

Returns

• 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 - 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)