Schedulıng algorıthms Res. Asst. Dr. Emine AKYOL ÖZER

Sımulated annealıng Let’s term, Sc=Candidate schedule So=Best schedule found so far Sk=Schedule constructed at k th iteration (k=iteration counter) G(So)=Value of best schedule G(Sk)=Value of schedule constructed at k th iteration G(Sc)=Value of candidate schedule 𝑃 𝑆 𝑘 , 𝑆 𝑐 =exp⁡( 𝐺 𝑆 𝑘 −𝐺 𝑆 𝑐 𝛽 𝑘 ) where 𝛽 𝑘 is called cooling parameter in annealing terminology, 𝛽 𝑘 = 𝑎 𝑘 where 𝑎= 0,1

Sımulated annealıng Step 1: Initialize Set k=1, set 𝛽 1 equal to given value. Form starting sequence by any heuristic; Call it S1, Let SO = S1, then G(SO) = G(S1) Step 2: Select SC from SK IF G(SO) < G(SC) < G(SK), THEN SK+1 = SC GO TO Step (3) IF G(SC) < G(SO), THEN SO = SK+1 = SC GO TO Step (3) IF G(SC) > G(SK), THEN generate a random number Uk ~ [0, 1] IF UK ≤ P(SK , SC), THEN SK+1 = SC ELSE SK+1 = SK GO TO STEP (3) Step 3: Set βK+1 ≤ βK. Set k = k + 1. IF k <= N THEN GO TO Step (2) ELSE Stop

Tabu search Step 1: Initialize Set k = 1 Form starting sequence by any heuristic; call it S1 Let SO = S1, Then G(SO) = G(S1) Step 2: Select SC from neighborhood of SK IF move from SK to SC is not allowed in the Tabu List THEN SK+1 = SK, GO TO step (3) IF G(SC) < G(S0) , THEN S0 = SC Delete the oldest Tabu move in the Tabu List Add fresh Tabu move at head of the list. GO TO Step (3) Step 3: Set k = k + 1. IF k <= N THEN GO TO Step (2) ELSE Stop.