1

jobs 1 2 3 4pj 10 10 13 4dj 4 2 1 12wj 14 12 1 12

Exercise

Apply the tabu-search technique starting out with the 2,1,4,3as an initial sequence.Neighbourhood: all schedules that can be obtained throughadjacent pairwise interchanges.

(a) Keep the length of the tabu-list equal to 1.Apply the technique for four iterations.

(b) Keep the length of the tabu-list equal to 3. Apply the technique for four iterations

2

S1 = 2, 1, 4, 3F(S1) = wjTj = 12·8 + 14·16 + 12·12 + 1 ·36 = 500 = F(Sbest)F(1, 2, 4, 3) = 480F(2, 4, 1, 3) = 436 = F(Sbest)F(2, 1, 3, 4) = 652Tabu-list: { (1, 4) }

S2 = 2, 4, 1, 3, F(S2) = 436F(4, 2, 1, 3) = 460F(2, 1, 4, 3) tabu!F(2, 4, 3, 1) = 608Tabu-list: { (2, 4) }

S3 = 4, 2, 1, 3, F(S3) = 460F(2, 4, 1, 3) tabu!F(4, 1, 2, 3) = 440F(4, 2, 3, 1) = 632Tabu-list: { (2, 1)}

(a)

3

S4 = 4, 1, 2, 3, F(S4) = 440F(1, 4, 2, 3) = 408 = F(Sbest) F(4, 2, 1, 3) tabu!F(4, 1, 3, 2) = 586Tabu-list: { (4, 1) }F(Sbest)= 408

4

(b) S1 = 2, 1, 4, 3F(S1) = 500 = F(Sbest)F(1, 2, 4, 3) = 480F(2, 4, 1, 3) = 436 = F(Sbest)F(2, 1, 3, 4) = 652Tabu-list: { (1, 4) }

S2 = 2, 4, 1, 3, F(S2) = 436F(4, 2, 1, 3) = 460F(2, 1, 4, 3) tabu!F(2, 4, 3, 1) = 608Tabu-list: { (2, 4), (1, 4) }

5

S3 = 4, 2, 1, 3, F(S3) = 460F(2, 4, 1, 3) tabu!F(4, 1, 2, 3) = 440F(4, 2, 3, 1) = 632Tabu-list: { (2, 1), (2, 4), (1, 4) }

S4 = 4, 1, 2, 3, F(S4) = 440F(1, 4, 2, 3) tabuF(4, 2, 1, 3) tabu!F(4, 1, 3, 2) = 586Tabu-list: { (2, 3), (2, 1), (2, 4) }F(Sbest)= 436 not optimal !