A DAG Scheduling Scheme on Heterogeneous Computing Systems Using Tuple-Based Chemical Reaction Optimization

Algorithm 6

TMSCRO(DAG) The TMSCRO outline(framework).

(1)   Initialize PopSize, KELossRate, MoleColl and InitialKE, 𝜃 and 𝜗;

(2)   Call Algorithm 2 to generate the initial population of TMSCRO, CROPop;

(3)   Call Algorithm 3 to calculate PE of each molecule in CROPop;

(4)   while the stopping criteria is not met do

(5)          Generate 𝜀∈[0,1];

(6)          if  𝜀 > MoleColl

(7)                Select a reaction molecule 𝑆 from CROPop randomly;

(8)                 if  ((NumHit_𝑆−MinHit_𝑆) > 𝜃) & (𝑆≠InitS)

(9)                          Call DecompT to generate new molecules 𝑆^′₁ and 𝑆^′₂;

(10)                        Call Algorithm 3 to calculate PE_𝑆′1 and PE_𝑆′2;

(11)                         if Inequality (2) holds

(12)                              Remove 𝑆 from CROPop;

(13)                              Add 𝑆^′₁ and 𝑆^′₂ to CROPop;

(14)                        end if

(15)               else

(16)                       Call OnWallT to generate a new molecules 𝑆^′;

(17)                       Call Algorithm 3 to calculate PE_𝑆′;

(18)                        If  (𝑆=InitS)

(19)                              InitS = 𝑆^′;

(20)                        end if

(21)                       Remove 𝑆 from CROPop;

(22)                       Add 𝑆^′ to CROPop;

(23)              end if

(24)       else

(25)             Select two molecules 𝑆₁ and 𝑆₂ from CROPop randomly;

(26)              if (KE_𝑆1 < 𝜗) & (KE_𝑆2 < 𝜗) & (𝑆₁≠InitS) & (𝑆₂≠InitS)

(27)                       Call SynthT to generate a new molecule 𝑆^′;

(28)                       Call Algorithm 3 to calculate PE_𝑆′;

(29)                        if Inequality (10) holds

(30)                             Remove  𝑆₁ and 𝑆₂ from CROPop;

(31)                              Add 𝑆^′ to CROPop;

(32)                        end if

(33)              else

(34)                       Call IntermoleT to generate two new molecules 𝑆^′₁ and 𝑆^′₂;

(35)                       Call Algorithm 3 to calculate PE_𝑆′1 and PE_𝑆′2;

(36)                        if (𝑆₁=InitS)

(37)                              InitS=𝑆^′₁;

(38)                        else if  (𝑆₂=InitS)

(39)                              InitS=𝑆^′₂;

(40)                       end if

(41)                       Remove 𝑆₁ and 𝑆₂ from CROPop;

(42)                       Add 𝑆^′₁ and 𝑆^′₂ to CROPop;

(43)              end if

(44)       end if

(45) end while

(46) return the molecule with the lowest PE in CROPop;