A Hybrid Genetic Algorithm to Minimize Total Tardiness for Unrelated Parallel Machine Scheduling with Precedence Constraints

Algorithm 1

Priority rule-based heuristic algorithm.

1. Initialize: 𝑢=1, 𝐻=∅, tt=0;

    𝐼_𝑣=0,∀𝑣∈𝑀

2. WHILE (𝑢⩽𝑛) DO

   2.1. 𝑇={𝐼_𝑣∣𝑣∈𝑀}

   2.2. 𝑡=min{𝜏∣𝜏∈𝑇}

   2.3. 𝐶_𝑢={𝑗∣𝐹𝑇_𝑗⩽𝑡,∀𝑗∈𝐻}

   2.4. compute 𝐷_𝑢

   2.5. WHILE (𝐷_𝑢=∅) DO

       2.5.1. 𝑇∶=𝑇⧵{𝑡}

       2.5.2. 𝑡=min{𝜏∣𝜏∈𝑇}

       2.5.3. 𝐶_𝑢={𝑗∣FT_𝑗⩽𝑡,∀𝑗∈𝐻}

       2.5.4. compute 𝐷_𝑢

   2.6. 𝑗^∗∶𝑑_𝑗^∗=min{𝑑_𝑗∣𝑗∈𝐷_𝑢}

   2.7. FOR (𝑣=1∶𝑚)

      IF (𝐼_𝑣⩾𝑡)

         𝐹_𝑗^∗_𝑣=𝐼_𝑣+𝑝_𝑗∗𝑣

       ELSE

         𝐹_𝑗^∗_𝑣=𝑡+𝑝_𝑗∗𝑣

   2.8. IF (𝐹_𝑗^∗_𝑣⩾𝑑_𝑗^∗,∀𝑣∈𝑀)

        𝑣^∗∶𝐹_𝑗^∗_𝑣∗=min{𝐹_𝑗^∗_𝑣∣𝑣∈𝑀}

      ELSE

       randomly select 𝑣^∗ from {𝑣∣𝐹_𝑗^∗_𝑣<𝑑_𝑗^∗,𝑣∈𝑀}

   2.9. ST_𝑗^∗=𝐹_𝑗^∗_𝑣∗−𝑝_{𝑗∗𝑣∗},FT_𝑗^∗=𝐹_𝑗^∗_𝑣∗,𝐼_𝑣∗=FT_𝑗^∗

   2.10. 𝐻∶=𝐻∪{𝑗^∗}

   2.11. tt∶=tt+max(FT_𝑗^∗−𝑑_𝑗^∗,0)

   2.12. 𝑢∶=𝑢+1