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chapter14localsearch

# Selectk1k setkk1

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Unformatted text preview: eases – Often, βk=Tak for some .9<a<1 and T>0 14 SA algorithm 1. 2. 1. Set k=1 and select β1. Select S1 and set S0=S1. Select Sc (randomly) from N(Sk). i. ii. iii. If G(S0)<G(Sc)<G(Sk) set Sk+1=Sc and go to 3 If G(Sc)<G(S0) set S0=Sk+1=Sc and go to 3 If G(Sc)>G(Sk), generate a uniform random number Uk from a Uniform(0,1) distribution (e.g., rand() in Excel) If Uk≤P(Sk,Sc), set Sk+1=Sc; otherwise set Sk+1=Sk. Select βk+1≤ βk. Set k=k+1. Stop if stopping criteria are satisfied; otherwise go to 2. 15 SA example: 1||Σ wjTj Jobs 1 2 3 4 wj 4 5 3 5 pj 12 8 15 9 dj 16 26 25 27 16 SA example Iteration 1 Step 1: S0=S1=(1,3,2,4). G(S1)=136. Let T=10 and a=.9 => β1=9 Step 2. Select randomly which jobs to swap, suppose a Uniform(0,1) random number is V1= .24 => swap first two jobs – Sc=(3,1,2,4), G(Sc)=174, P(Sk,Sc)=1.5% – U1=.91 => Reject Sc Step 3: Let k=2 17 SA example Iteration 2 Step 2. Select randomly which jobs to swap, suppose a Uniform(0,1) random number is V2= .46 => swap 2nd and 3rd jobs – Sc=(1,2,3,4), G(Sc)=115 => S3=S0=Sc Step 3: Let k=3 18 SA example Iteration 3 Step 2. V3= .88 => swap jobs in 3rd and 4th position – Sc=(...
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