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Tabu Search

Tabu Search. Contents 1. Basic Concepts 2. Algorithm 3. Practical considerations. Literature 1. Modern Heuristic Techniques for Combinatorial Problems, (Ed) C.Reeves 1995, McGraw-Hill. Chapter 3.

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Tabu Search

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

  2. Literature 1. Modern Heuristic Techniques for Combinatorial Problems, (Ed) C.Reeves 1995, McGraw-Hill. Chapter 3. 2. Operations Scheduling with Applications in Manufacturing and Services, Michael Pinedo and Xiuli Chao, McGraw Hill, 2000, Chapter 3.6. or Scheduling, Theory, Algorithms, and Systems, Second Addition, Michael Pinedo, Prentice Hall, 2002, Chapter 14.4

  3. 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

  4. 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

  5. Example. 1 | dj | wjTj Neighbourhood: all schedules that can be obtained throughadjacent pairwise interchanges. Tabu-list: pairs of jobs (j, k) that were swapped within the lasttwo moves 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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