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Tabu Search

Tabu Search. Contents 1. Basic Concepts 2. Algorithm 3. Practical considerations. Basic Concepts. Tabu-lists contains moves which have been made in the recent past but are forbidden for a certain number of iterations. Algorithm Step 1 . k =1

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Tabu Search

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  1. Tabu Search Contents 1. Basic Concepts 2. Algorithm 3. Practical considerations

  2. Basic Concepts Tabu-lists contains moves which have been made in the recent past butare forbidden for a certain number of iterations. Algorithm Step 1. k=1 Select an initial schedule S1 using some heuristic and set Sbest = S1 Step 2. Select ScN(Sk) If the move Sk Sc is prohibited by a move on the tabu-list then go to Step 2

  3. If the move Sk Sc is not prohibited by a move on the tabu-list then Sk+1 = Sc Enter reverse move at the top of the tabu-list Push all other entries in the tabu-list one position down Delete the entry at the bottom of the tabu-list If F(Sc) < F(Sbest) then Sbest = Sc Go to Step 3. Step 3. k = k+1 ; If stopping condition = true then STOP else go to Step 2

  4. Example. Minimize total wighted tardiness, where the tardiness of a job is the Amount it exceeds its deadline (or 0 if it is on time) Neighbourhood: all schedules that can be obtained throughadjacent pairwise interchanges. Tabu-list: pairs of jobs (j, k) that were swapped within the lasttwo moves

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

  6. S2 = 2, 4, 1, 3, F(S2) = 436 F(4, 2, 1, 3) =460 F(2, 1, 4, 3) (= 500) tabu! F(2, 4, 3, 1) = 608 Tabu-list: { (2, 4), (1, 4) } S3 = 4, 2, 1, 3, F(S3) = 460 F(2, 4, 1, 3) (=436)tabu! F(4, 1, 2, 3) = 440 F(4, 2, 3, 1) = 632 Tabu-list: { (2, 1), (2, 4) } S4 = 4, 1, 2, 3, F(S4) = 440 F(1, 4, 2, 3) =408 = F(Sbest) F(4, 2, 1, 3) (= 460) tabu! F(4, 1, 3, 2) = 586 Tabu-list: { (4, 1), (2, 4) } F(Sbest)= 408

  7. Practical considerations • Tabu tenure: the length of time t for which a move is forbiden • t too small - risk of cycling • t too large - may restrict the search too much • t=7 has often been found sufficient to prevent cycling • Number of tabu moves: 5 - 9 • If a tabu move is smaller than the aspiration level then we accept the move

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