Minimizing the Makespan for a Two-Stage Three-Machine Assembly Flow Shop Problem with the Sum-of-Processing-Time Based Learning Effect

Algorithm 2

An IG algorithm, IGLS3.

Initialization:

Randomly generate an initial solution S.

Improve S by a local search (e.g. LS3). The LS3 is as follows.

Randomly select one job among the n jobs.

Insert the selected job to n possible positions, keep the best (the lowest

) solution.

Repeat the steps until all n jobs have been selected and inserted back;

update the best solution if better solution is found.

Output the final solution, S₀.

Set S₀ = S₁ and ;

Do whileiter (a predetermined number of iterations is set equal to 30)

Destruction stage.

Divide S₁ into S_D and S_R, where S_D is a set of d removed jobs and S_R a set of

the remaining jobs;

Construction stage

For the removed d jobs, execute the NEH mechanism to S_R one after another

until it yields the best sequence, coded as S₂;

Improve S₂ by one of the four local search methods, LS1, LS2, LS3, LS4, coded

as S₃.

(Acceptance criterion)

If , then update S₁ by S₃;

If, then Update by S₃;

Else if then Update S₁ by S₃;

(Note that q ~ rand(0,1).)

End while

Output the final solution S_best