Benchmarking in Data Envelopment Analysis: An Approach Based on Genetic Algorithms and Parallel Programming

Algorithm 5

Crossover.

Require: Chromosome 𝑐₁, Chromosome 𝑐₂.

Ensure:  Chromosome 𝑐₃, Chromosome 𝑐₄

  Generate 0≤𝛾≤1 randomly.

  Generate 0≤𝜙≤4 randomly.

   if  𝜙=0  then

   {Crossing 𝛽_𝑘}

    𝛽³_𝑘←𝛽¹_𝑘∗𝛾+(1−𝛾)∗𝛽²_𝑘

    𝛽⁴_𝑘←𝛽²_𝑘∗𝛾+(1−𝛾)∗𝛽¹_𝑘

   else if  𝜙≤1  then

    {Crossing 𝛼_𝑗𝑘}

      for  𝑗:=1,…,𝑛   do

     𝛼³_𝑗𝑘←𝛼¹_𝑗𝑘∗𝛾+(1−𝛾)∗𝛼²_𝑗𝑘

     𝛼⁴_𝑗𝑘←𝛼²_𝑗𝑘∗𝛾+(1−𝛾)∗𝛼¹_𝑗𝑘

      end for

   else if  𝜙≤2  then

    {Crossing 𝑡⁻_𝑖𝑘}

      for  𝑖:=1,…,𝑚   do

     𝑡^−,3_𝑖𝑘←𝑡^−,1_𝑖𝑘∗𝛾+(1−𝛾)∗𝑡^−,2_𝑖𝑘

    𝑡^−,4_𝑖𝑘←𝑡^−,2_𝑖𝑘∗𝛾+(1−𝛾)∗𝑡^−,1_𝑖𝑘

      end for

   else if  𝜙≤3  then

    {Crossing 𝑡⁺_𝑟𝑘}

    for  𝑟:=1,…,𝑠  do

    𝑡^+,3_𝑟𝑘←𝑡^+,1_𝑟𝑘∗𝛾+(1−𝛾)∗𝑡^+,2_𝑟𝑘

    𝑡^+,4_𝑟𝑘←𝑡^+,2_𝑟𝑘∗𝛾+(1−𝛾)∗𝑡^+,1_𝑟𝑘

    end for

   end for

  Deduce 𝛼_𝑗𝑘, 𝑏_𝑗𝑘, 𝑡⁻_𝑖𝑘 and 𝑡⁺_𝑟𝑘 for 𝑐₁ and 𝑐₂ in order to satisfy (3)