(BLX-a,BLX-a-b)

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Read also
●   Takahashi M., Kita H.  (2001), A Crossover Operator Using Independent Component Analysis for Real-Coded Genetic Algorithm, in Proceedings of the 2001 Congress on Evolutionary Computation, pp. 643-649
WEB:     http://ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=934452
●   Herrera F. , Lozano M. , Sánchez A.M.  (2003), A taxonomy for the Crossover Operator for Real-Coded Genetic Algorithms: An Experimental Study, in International Journal of Intelligent Systems, Wiley, vol. 18, pp. 309-338
WEB:     http://www3.interscience.wiley.com
            http://dx.doi.org/10.1002/int.10091

Algorithm BLX-a
1.     select two parents X^(t) and Y^(t) from a parent pool

2.     create two offspring  X^(t+1) and Y^(t+1)  as follows:

3.              for i = 1 to n do

4.              d_i=|x_i^(t)-y_i^(t)|

5.              choose a uniform random real number u from interval
             <min(x_i^(t),y_i^(t))-ad_i, max(x_i^(t),y_i^(t))+ad_i>

6.              x_i^(t+1)=u

7.              choose a uniform random real number u from interval
             <min(x_i^(t),y_i^(t))-ad_i, max(x_i^(t),y_i^(t))+ad_i>

8.              y_i^(t+1)=u

9.              end do

where:
a  – positive real parameter

Algorithm BLX-a-b
1.     select two parents X^(t) and Y^(t) from a parent pool

2.     assume that X^(t) is better than Y^(t)

3.     create two offspring  X^(t+1) and Y^(t+1)  as follows:

4.              for i = 1 to n do

5.              d_i=|x_i^(t)-y_i^(t)|

6.                              if x_i^(t)≤y_i^(t) than

7.                              choose a uniform random real number u from interval
                             <x_i^(t)-ad_i, y_i^(t)+bd_i>

8.                              x_i^(t+1)=u

9.                              choose a uniform random real number u from interval
                             <x_i^(t)-ad_i, y_i^(t)+bd_i>

10.                            y_i^(t+1)=u

11.                            else

12.                            choose a uniform random real number u from interval
                            <y_i^(t)-bd_i, y_i^(t)+ad_i>

13.                            x_i^(t+1)=u  

14.                            choose a uniform random real number u from interval
                            <y_i^(t)-bd_i, y_i^(t)+ad_i>   

15.                            y_i^(t+1)=u

16.                            end if

17.           end do

where:
a, b – positive real parameters