  dr Tomasz D.Gwiazda
Assistant Professor

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Standard operators

Binary coded operators Homologous Crossover (HX) download PDF with first 40 pages from my latest eBook if you need more operators click here Keywords information exchanging, information destruction, convergence speed, non-disruptive crossover, optimal crossover points Motivation ●   Reduction of the destructive action of a multi-point crossover operator resulting from random selection of crossover points Source text ●   Park J., Park J., Lee Ch., Han M. (1993), Robust and Efficient Genetic Crossover Operator: Homologous Recombination, in Proceedings of 1993 International Joint Conference on Neural Networks, pp. 2975-2978 Read also ●   Beyer H.-G. (1995), Toward a Theory of Evolution Strategies: On the Benefits of Sex – the (μ/μ,lambda) Theory, in Evolutionary Computation, vol. 3(1), pp. 81-111 WEB:     http://citeseer.ifi.unizh.ch/361714.html             http://citeseer.ist.psu.edu/361714.html See also ●   Spontaneous Crossover ●   Circle-ring Crossover ●   Sufficient Exchanging ●   Intermediate Crossover ●   Intermediate Crossover2 ●   Adaptive Number of Crossover Points Algorithm 1.     select two parents A(t) and B(t) from a current population P(t) 2.     randomly choose m crossover points {pc1,...,pcm} 3.     create two offspring A(t+1) and B(t+1) by restricted m-point crossover     as follows: 4.     for every pair of strings STA=(apck(t),...,apck+1(t)) and     STB=(bpck(t),...,bpck+1(t)) between two successive crossover points     pck and pck+1 do: 5.              if length_of_STA (= length_of_STB ) ≥ w then 6.              compute the degree of similarity DS of strings STA  and STB                 as follows: 7.              number_of_1 = 0 8.                              for i = k  to k+w do 9.                                             if apci(t) XOR bpci(t) =1 then 10.                                           number_of_1 = number_of_1 + 1 11.                                           end if 12.                           end do 13.            DS = number_of_1/length_of_STA 14.                           if DS ≥ u  then 15.                           swap bits 16.                           else 17.                           do nothing 18.                           end if 19.            else 20.            do nothing 21.            end if 22.  end do where: w and u – parameters of the method Comments ●   The HX operator is based on the standard k-Point Crossover operator. Introduced modification relies on the fact that only strings of bits which are at least of a certain length (row: 5) or of an admissible degree of  similarity (row: 14) are allowed to crossover. Determination of the degree of similarity is based on the XOR operator (rows: 9-13). ●   This strategy is aimed at transferring (hence also protecting) strings with specified parameters to the next generation. ●   In HX the value of w and u is determined à priori as constant or dynamically changed (increased) in the GA run. Experiment domains ●   De Jong’s function (F1) Compared to ●   k-Point Crossover ●   Uniform Crossover ●   Intermediate Crossover ●   Intermediate Crossover2        