Recombination
Christian Fabian
Table of contents
1. What is recombination 2. Classification
2.1. Binary valued recombination (crossover)
2.1.1. 1-point crossover 2.1.2. 2-point crossover 2.1.3. N-point crossover 2.1.4. cut and splice
2.2. Real valued recombination
2.2.1. discrete recombination
2.2.2. intermediate recombination 2.2.3. line recombination
2.2.4. extended line recombination
3. Summary 4. Reference
What is recombination
• Based on the observation of biological mechanism
• Information of parents are combined to creat new individuals
• Two ore more parents can be used
• Different algorithm are publisht
• Not necessary for EA, but mostly a good choice
Table of contents
1. What is recombination 2. Classification
2.1. Binary valued recombination (crossover)
2.1.1. 1-point crossover 2.1.2. 2-point crossover 2.1.3. N-point crossover 2.1.4. Cut and splice
2.2. Real valued recombination
2.2.1. Discrete recombination
2.2.2. intermediate recombination 2.2.3. line recombination
2.2.4. extended line recombination
3. Summary 4. Reference
1-point crossover
parent A parent B
offspring
crossover point
2-point crossover
parent A parent B
offspring
crossover point 1 crossover point 2
N-point crossover
parent A parent B
offspring
crossover point 1
crossover point 2
crossover point 3
crossover point 4
Cut and splice
parent A parent B
offspring
crossover point for parent A
crossover point for parent A
Table of contents
1. What is recombination 2. Classification
2.1. Binary valued recombination (crossover)
2.1.1. 1-point crossover 2.1.2. 2-point crossover 2.1.3. N-point crossover 2.1.4. cut and splice
2.2. Real valued recombination
2.2.1. discrete recombination
2.2.2. intermediate recombination 2.2.3. line recombination
2.2.4. extended line recombination
3. Summary 4. Reference
Discrete recombination
-exchange of variable values between the individuals
-can be used with any kind of variables (binary, real or symbols).
parent A
parent B
possible area of offspring
intermediate recombination
• only applicable to real variables (and not binary variables)
• Values chosen somewhere around and between the variable values of the parents
• offspring = parent 1 + Alpha (parent 2 - parent 1)
– Alpha….random scaling factor [-d, 1+d]
– intermediate recombination d = 0,
– for extended intermediate recombination d > 0 (good choice 0.25)
area of parents
parent A parent B
intermediate recombination
parent A
parent B Possible area of offspring
line recombination
• similar to intermediate recombination
• only one value of Alpha used for all variables
• can generate any point on the line defined by the parents
parent A
parent B
extended line recombination
• generates offspring in a direction defined by the parents (line recombination)
• probability of small step sizes is greater than bigger step sizes
offspring mostly in the near of the parents
• offspring 1 = parent 1 + RecMx·range·delta·diff,
• offspring 2 = parent 2 + RecMx·range·delta·(-diff).
• RecMx = 1 (- with probability 0.9),
• range = 0.5·domain of variable (search interval),
• delta = sum(a(i)· 2^-i), a(i) = 1 with probability 1/m, else a(i) = 0;
m = 20; i=0:(m-1),
• diff = (parent 1 - parent 2)/parent 1 - parent 2
Summary
• Several methods are available
• Depending on optimization problem a fitting algorithm has to be selected
• Variable values of the parents:
1. can copy to the offsprings
2. or can be changed (mutated)
Thanks for your attention !
Are there any question left ?
Reference
• Prof. Salomon [lecture „Soft Computing Methods“
2006]
• http://en.wikipedia.org/wiki/Crossover_
%28genetic_algorithm%29 [stand 22.06.2006]
• http://www.pohlheim.com/diss/text/diss_pohlheim_ea -08.html [stand 22.06.2006]
• http://www.systemtechnik.tu-
ilmenau.de/~pohlheim/GA_Toolbox/algrecom.html#n amerecombinationline [stand 23.06.2006]
