An Enhanced Two-Level Metaheuristic Algorithm with Adaptive Hybrid Neighborhood Structures for the Job-Shop Scheduling Problem

Algorithm 3

The procedure of MUPLA.

	Step 1. Let t ⟵ 1 and Score (Cbest) ⟵ + ∞. Generate each Ci (t) ≡ (c1i (t), c2i (t), c3i (t), c4i (t), pi (t)) (where i = 1, 2, …, N) by randomly generating cji (t) from (where j = 1, 2, 3, 4) and randomly generating pi (t) from any possible operation-based permutation.
	Step 2. Evaluate Score (Ci (t)), and update Cbest and Sbest by using Steps 2.1 to 2.5.
	Step 2.1. Let i ⟵ 1.
	Step 2.2. Transform Ci (t) into the values of PTBT, SD, PNO, PROB, and P of LOSAP by the relationships shown in Table 1.
	Step 2.3. Execute Algorithm 2 (LOSAP) by inputting the PTBT, SD, PNO, PROB, and P taken from Step 2.2 in order to receive Pfi (t) and Sfi (t). Then, let Score (Ci (t)) ⟵ Makespan (Sfi (t)).
	Step 2.4. If Score (Ci (t)) ≤ Score (Cbest), then let Cbest ⟵ Ci (t), Score (Cbest) ⟵ Score (Ci (t)), and Sbest ⟵ Sfi (t).
	Step 2.5. If i < N, then let i ⟵ i + 1 and repeat from Step 2.2; otherwise, go to Step 3.
	Step 3. Update Ci (t + 1), where i = 1, 2, …, N, by using Steps 3.1 to 3.4.
	Step 3.1. Let i ⟵ 1.
	Step 3.2. If t mod 1000 = 0, then randomly generate pi (t + 1) from any possible operation-based permutation; otherwise, let pi  (t + 1) ⟵ Pfi (t).
	Step 3.3. If t mod 25 = 0, then randomly generate cji (t + 1) from (where j = 1, 2, 3, 4); otherwise, generate cji (t + 1) by the following equation. Let u1 and u2 be randomly generated from .
	Step 3.4. If i < N, then let i ⟵ i + 1 and repeat from Step 3.2; otherwise, go to Step 4.
	Step 4. If the stopping criterion is not met, then let t ⟵ t + 1 and repeat from Step 2. Otherwise, return Sbest as the final result.