A Multipopulation PSO Based Memetic Algorithm for Permutation Flow Shop Scheduling

Algorithm 5

The basic flowchart of SA local search.

Basic flowchart of SA local search

Input the current job sequence 𝜋₀ and initial temperature 𝑇 and the annealing cooling rate 𝑑, compute

  makespan(𝜋₀);

For 𝑖=1∶𝑛∗(𝑛−1) (𝑛 is the number of job);

 Find two jobs 𝑖 and 𝑗 randomly in the job sequence and permute the jobs in the positions;

 Generate a random number rand;

 If rand<0.5,

  Swap to produce a new job sequence 𝜋₁

 Else

  Insert to produce a new job sequence 𝜋₁;

  Compute makespan(𝜋₁) and Δ𝐸=makespan(𝜋₀)−makespan(𝜋₁),

 If Δ𝐸<0,

   𝜋₀=𝜋₁;

 Else

  Generate a random number rand

  if rand<exp(−Δ𝐸/𝑇), 𝜋₀=𝜋₁; else 𝜋₀=𝜋₀

End for;

𝑇=𝑇⋅𝑑;

Return 𝜋₀.