PowerPoint Presentation15780/slides/780s18-20.pdf · 2018-04-04 · Rangers Use Artificial...
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Transcript of PowerPoint Presentation15780/slides/780s18-20.pdf · 2018-04-04 · Rangers Use Artificial...
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• 𝑠2𝑥1
o 𝑠2o 𝑥1
• 𝑥1∗
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σ𝑠1∈𝑆𝑥1 𝑠1 𝑢1(𝑠1, 𝑠2)
∀𝑠2′ ∈ 𝑆,
∀𝑠1 ∈ 𝑆, 𝑥1 𝑠1 ∈ [0,1]
σ𝑠1∈𝑆𝑥1 𝑠1 𝑢2 𝑠1, 𝑠2 ≥ σ𝑠1∈𝑆
𝑥1 𝑠1 𝑢2 𝑠1, 𝑠2′
σ𝑠1∈𝑆𝑥1 𝑠1 = 1
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• 𝑇 = {1,… , 𝑛}
• 𝑚𝑅
• Σ ⊆ 2𝑇
• 𝑟
𝐴 𝑟 ⊆ Σ
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• 𝑡𝑢𝑑+ 𝑡 ≥ 𝑢𝑑
− 𝑡𝑢𝑎+ 𝑡 ≤ 𝑢𝑎
− 𝑡
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𝒄 = (𝑐1, … , 𝑐𝑛)
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𝑡𝑢𝑑 𝑡, 𝒄 = 𝑢𝑑
+ 𝑡 ⋅ 𝑐𝑡 + 𝑢𝑑− 𝑡 1 − 𝑐𝑡
𝑢𝑎 𝑡, 𝒄 = 𝑢𝑎+ 𝑡 ⋅ 𝑐𝑡 + 𝑢𝑎
− 𝑡 1 − 𝑐𝑡
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{1}
{1,2}
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• Σ = 𝑇
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𝑢𝑑 𝑡∗, 𝒄∀𝑟 ∈ 𝑅, ∀𝑡 ∈ 𝐴 𝑟 , 0 ≤ 𝑐𝑟,𝑡 ≤ 1
∀𝑡 ∈ 𝑇, 𝑐𝑡 =
𝑟∈𝑅:𝑡∈𝐴 𝑟
𝑐𝑟,𝑡 ≤ 1
∀𝑟 ∈ 𝑅,
𝑡∈𝐴 𝑟
𝑐𝑟,𝑡 ≤ 1
∀𝑡 ∈ 𝑇, 𝑢𝑎 𝑡, 𝒄 ≤ 𝑢𝑎(𝑡∗, 𝒄)
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𝑡1
𝑡2
𝑡3
𝑟1
𝑟2
0.7
0.20.1
0.3
0.7
𝑡1 𝑡2 𝑡3
𝑟1 0.7 0.2 0.1
𝑟2 0 0.3 0.7
𝑡1 𝑡2 𝑡3
𝑟1 0 0 1
𝑟2 0 1 0
𝑡1
𝑡2
𝑡3
𝑟1
𝑟2
0.1𝑡1 𝑡2 𝑡3
0 1 0
0 0 1
𝑡1
𝑡2
𝑡3
𝑟1
𝑟2
0.2𝑡1 𝑡2 𝑡3
1 0 0
0 1 0
𝑡1
𝑡2
𝑡3
𝑟1
𝑟2
0.2𝑡1 𝑡2 𝑡3
1 0 0
0 0 1
𝑡1
𝑡2
𝑡3
𝑟1
𝑟2
0.5
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0.5
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0.5
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𝜖, 𝛿 > 0 1 − 𝛿𝜖
𝑛 1/𝜖 1/𝛿
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o 𝒄
o 𝒫𝑡o
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𝑢𝑑(𝑡, 𝒄)𝑡 𝒄𝒄
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𝒫1
𝒫2
𝑐2
𝑐1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
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