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

Algorithm 2

Revised forward recursion algorithm.

1. Initialize unscheduled job-set 𝑈={1,…,𝑛} and the release times of all machines

  𝐼_𝑣=0,∀𝑣∈𝑀.

2. Repeat the following steps until 𝑈 is empty:

  2.1. randomly select a job 𝑗 from 𝑈.

  2.2. Assign job 𝑗 to machine 𝑘 (𝑘 is known for job 𝑗 according to the chromosome).

    2.2.1. If the finish time of predecessor 𝑖 of job 𝑗 is not known, execute step 2.2

      for job 𝑖 recursively.

    2.2.2. Let 𝜉_𝑗 denote the maximum finish time of the predecessors of job 𝑗.

      Compute the start time and finish time of job 𝑗:

      ST_𝑗=max(𝜉_𝑗,𝐼_𝑘),FT_𝑗=ST_𝑗+𝑝_𝑗𝑘.

    2.2.3. Update the unscheduled job-set and the release time of machine 𝑘:

      𝑈∶=𝑈⧵{𝑗},𝐼_𝑘=FT_𝑗.

3. tt=∑^𝑛_𝑗=1max(FT_𝑗−𝑑_𝑗,0).