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

Algorithm 4

ConvertMole(CCPS) converting a CCPS to an 𝑆.

(1)    for  𝑖=1; 𝑖≤|𝑉|; 𝑖++

(2)                      for  each CCP_𝑗 in molecule CCPS

(3)                              for  each cv_𝑘 in CCP_𝑗

(4)                                      𝑣_𝑖=cv_𝑘;

(5)                                      𝑓_𝑖=0;

(6)                                      𝑝_𝑖=sp_𝑗;

(7)                                      Generate a new tuple 𝑣_𝑖,𝑓_𝑖,𝑝_𝑖

(8)                             end for

(9)                      end for

(10) end for

(11)  Generate a new reaction molecule 𝑆=((𝑣₁,𝑓₁,𝑝₁),(𝑣₂,𝑓₂,𝑝₂),…,(𝑣_|𝑉|,𝑓_|𝑉|,𝑝_|𝑉|));

(12) for  each 𝑣_𝑖,𝑓_𝑖,𝑝_𝑖 in reaction molecule 𝑆

(13)                    find the first successor Succ(𝑣_𝑖) in DAG from 𝑖 to the end;

(14)                    for  each 𝑣_𝑗∈ (𝑣_𝑖, Succ(𝑣_𝑖))

(15)                           find the first predecessor 𝑣_𝑘 = Pred(𝑣_𝑗) from Succ(𝑣_𝑖) to the begin in reaction molecule 𝑆;

(16)                                    if  𝑘 < 𝑖

(17)                                          interchanged position of 𝑣_𝑖,𝑓_𝑖,𝑝_𝑖 and (𝑣_𝑗,𝑓_𝑗,𝑝_𝑗) in reaction molecule 𝑆;

(18)                                    end if

(19)                    end for

(20) end for

(21) for  each 𝑝_𝑖 in reaction molecule 𝑆 to randomly change;

(22)                    change 𝑝_𝑖 randomly

(23)  end for

(24) return 𝑆;