An Improved Hierarchical Genetic Algorithm for Sheet Cutting Scheduling with Process Constraints

Algorithm 1

Step1. Initialization

 Set ACO parameters 𝛼, 𝛽, 𝜌, 𝜏_𝑦𝑗𝑚(0), 𝑁𝐶_max (Maximum iterations), 𝑄, 𝑁_ant (number of ant);

Step2. Generate 𝑁_ant ants, and place it on different nodes

Step3. for 𝑁𝐶=1:𝑁𝐶_max

     for 𝑘=1: 𝑁_ant

     for 𝑖=2: 𝑛

       Cumulating the transition probability of each ant will go to according (11), ants select the next node of max

    transition probability

     End;

     End;

Step4. Cumulating the best solution for the objective function (3) in this iteration. If the current solution is better than the

   former best solution, then update the former best solution.

Step5. updating the pheromone value according to (12), (13) and (14).

Step6.  if 𝑁𝐶<𝑁𝐶_max

      𝑁𝐶=𝑁𝐶+1;

    Go to Step 2;

     Else

    Output the optimal solution;

     End;

  End;