2 pairwiseadjacentinterchange

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Unformatted text preview: ess – Let G(S) be ΣwjTj under schedule S => G(S1)= … 5 Local search example (3) Neighborhood structure Manipulating S1 1. 2. Pairwise adjacent interchange Try to move a job to a different location in the sequence Rules 1 and 2 above define two types of neighborhoods N1 and N2 N1(S1)=… N2(S1)=… 6 Local search example (4) Choosing Sc Assume we use N1 Methods for choosing Sc from N1(Sk) 1. Randomly 2. Move the job forward that has the highest contribution to the objective Follow rule 2 ⇒ Interchange jobs … and … ⇒ Sc = ( , , , ) ⇒ G(Sc) = 7 Local search example (5) Acceptance criteria Is G(Sc) < G(Sk)? Should we consider accepting Sc if G(Sc) ≥ G(Sk) ? In this example we only accept if we get an improvement in the objective 8 Local search example (6) Stopping criteria Max number of iterations No or little improvement – We would terminate the search since we did not improve the current schedule Local optimal solution – No solution S in N(Sk) satisfies G(S)<G(Sk) 9 Local search example (7) Continuing S2=S1=(1,3,2,4) – Swap 3 and 2 => G(1,2,3,4) = 115 S3=(1,2,3,4) – Swap 4 and 3 => G(1,2,4,3) = 67 S4=(1,2,4,3) – Swap 4 and 2 => G(1,4,2,3) = 72 S5=S4 – Swap 2 and 1 => G(2,1,4,3) = 83 STOP and return (1,2,4,3) as the solution 10 Local search example (8) Total enumeration j1 j2 j3 j4 1 1 2 4 2 4 1 1 2 4 2 1 2 4 1 1 4 2 2 4 1 2 4 3 4 2 4 2 1 1 3 3 3 3 3 2...
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