dr Tomasz D.Gwiazda
 Assistant Professor

 
Home page
Short CV
    Publications
   
(e-)Books
   
Papers
My latest book
Students
Office hours
Teaching
 

Contents of e-Book
Index of authors
Index of experiment domains


Introduction

Standard operators
1-Point Crossover
k-Point Crossover
Shuffle Crossover
Reduced Surrogate Crossover
Uniform Crossover
Highly Disruptive Crossover,Heuristic Uniform Crossover
Average Crossover
Discrete Crossover
Flat Crossover
Heuristic Crossover,Intermediate Crossover
Blend Crossover


Binary coded operators
Random Respectful Crossover
Masked Crossover
1bit Adaptation Crossover
Multivariate Crossover
Homologous Crossover
Count-preserving Crossover
Elitist Crossover
    Masked Crossover  
         

 

 

(MX)

download PDF with first 40 pages
from my latest eBook

if you need more operators click here

Keywords
adaptive
, fitness driven crossover, schema preservation, epistasis

Motivation
   Protecting good schemata from destruction.
   Searching through the solution space in promising directions depending on fitness.

Source text
   Louis S.J., Rawlins G.J.E. (1991), Designer Genetic Algorithms: Genetic Algorithms in Structure Design, in Proceedings of the Fourth International Conference on genetic Algorithms, Morgan Kaufman, pp.53-60
WEB:     http://citeseer.ifi.unizh.ch/louis91designer.html

           
http://citeseer.ist.psu.edu/louis91designer.html

Read also
   Maini H., Mehrotra K., Mohan Ch., Ranka S. (1994), Knowledge-Based Nonuniform Crossover, in Proceedings of IEEE International Conference on Evolutionary Computation, Orlando
WEB:     http://intl.ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=350048

   Vekaria K., Clack C. (1999), Biases Introduced by Adaptive Recombination Operators, in Proceedings of the Genetic and Evolutionary Computation Conference, pp. 670-677
WEB:    
http://citeseer.ifi.unizh.ch/vekaria99biases.html
           
http://citeseer.ist.psu.edu/vekaria99biases.html

   Chou Ch.-H., Chen J.-N. (2000), Genetic Algorithms: initialization schemes and genes extraction, in Proceedings of The Ninth IEEE International Conference on Fuzzy Systems, pp. 965 - 968
WEB:     http://intl.ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=839167

See also
   Knowledge-Based Nonuniform Crossover

Algorithm
1.
        select two parents A(t) and B(t) from a parent pool

2.        create two offspring C(t+1) and D(t+1) as follows:

3.                for i = 1 to n do

4.                ci(t+1)=ai(t)

5.                di(t+1)=bi(t)

6.                end do

7.                for i = 1 to n do

8.                              if piB=1 and piA=0 then

9.                              ci(t+1)=bi(t) 

10.                            end if

11.                            if piB=0 and piA=1 then

12.                            di(t+1)=ai(t)

13.                            end if

14.             end do

where:
PA=(p1A,...,pnA) crossover mask of the parent A(t)  
PB
=(p1B,...,pnB)
crossover mask of the parent B(t)
  

Comments
   The MX operator uses a mask vector to determine which bits of which parent are inherited by the offspring. The first step is the duplication of the bits of the parents. The bits of the first parent are copied to the first offspring and, accordingly, of the second parent to the second offspring (rows: 3-6).  In the second step, the offspring exchange bits among each other (rows: 9 and 12) at those positions where the mask vectors of the parent were equal to 1, indicated domination of that parent at that position and the mask vectors of the other parent were equal to 0 (rows: 8 and 11).
   The mask vectors are initiated in P(0) randomly. During every GA iteration, the mask vectors are inherited by each offspring from its parent. Then the mask vectors of the offspring as well as  the parents undergo modification.  The modification process (not described here) is based on the comparison of fitness of the offspring and the parents. If good offspring were created, the masks of the parents do not need to be modified and the masks of the offspring may be very similar to those of the parents. In a situation where bad offspring were created the masks of the parents as well as of the offspring need to be modified.

Experiment domains
   n-bit parity checker
   n-bit adder

Compared to
   1-Point Crossover

 
   

    :: Copyrights tomaszgwiazda e-books 2006 :: webmaster ::