(MC)

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Keywords
variable-to-variable recombination

Motivation
●   Effective optimization of multivariate functions.

Source text
●   Konstam A.H., Hartley S.J., Carr W.L. (1992), Optimization in a Distributed Processing Environment using Genetic Algorithm with Multivariate Crossover, in Proceedings of the 1992 ACM annual conference on Communications, pp. 109-116
WEB:     http://portal.acm.org/citation.cfm?id=131228

Read also
●   Yang S.Y., Park L.-J., Park C.H., Ra J.W. (1995), A Hybrid Algorithm using Genetic Algorithm and Gradient-Based Algorithm for Iterative Microwave Inverse Scattering, in  IEEE International Conference on Evolutionary Computation, pp.450-455
WEB:     http://intl.ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=489190
●   Deb K., Goyal M., Optimizing Engineering Designs Using a Combined Genetic Search, in Proceedings of the Seventh International Conference on Genetic Algorithms, Morgan Kaufman, pp. 521-528
WEB:     http://citeseer.ifi.unizh.ch/deb95optimizing.html
            http://citeseer.ist.psu.edu/deb95optimizing.html

See also
●   Chromosome Shuffling
●   2N-Parent Parameter Wise Crossover

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

2.     assume that each parent vector is divided into  q  substrings s_ij^(t),
    where q is the number of parameters represented in each parent
    vector i.e. each s_ij^(t) (i=A,B; j=1,...,q) represents a  j^th parameter;
    hence A^(t)=(s_A1^(t),...,s_Aq^(t)), B^(t)=(s_B1^(t),...,s_Bq^(t))

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

4.              for j = 1 to q do

5.                             if Rnd ≤ p_c then

6.                             perform crossover between s_Aj^(t) and s_Bj^(t)

7.                             s_Cj^(t+1)=s_Aj^(t) X s_Bj^(t)

8.                             s_Dj^(t+1)=s_Aj^(t) X s_Bj^(t)

9.                             else

10.                           s_Cj^(t+1)=s_Aj^(t)  

11.                           s_Dj^(t+1)=s_Bj^(t)  

12.                           end if

13.           end do

where:
X - standard 1-Point Crossover
Rnd – uniform random real number, 0≤Rnd≤1

Comments
●  The most fundamental difference between the MC operator and other operators using variable-to-variable recombination is that the answer to the question “whether to crossover” is checked in the MC method separately for each substring (row: 5). As for the other operators, the answer to that question refers to the parent vector as a whole.

Experiment domains
●   function taken from the National Crime Survey

Compared to
●   k-Point Crossover