tst st - - PowerPoint PPT Presentation
t Prr tst st Prr rr rts
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✷ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✸ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✸ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✸ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✸ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✹ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 1 Linear cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✹ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 1 Linear cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✹ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 1 Linear cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✹ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 2 Linear cuts
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✹ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3 Linear cuts
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✹ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 6 Linear cuts
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✹ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 All linear cuts
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✹ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✺ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 Non convex cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✺ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 Non convex cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✺ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 Non convex cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✺ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 Non convex cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✺ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 6 Sharp cuts - = 0.7
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✺ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 All Sharp cuts - = 0.7
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✺ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✻ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✻ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✼ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✼ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✼ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✼ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✼ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✼ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✽ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✽ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✾ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✵ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✵ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✵ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✵ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✵ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✶ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✷ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✷ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✷ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✷ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✸ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 xbase Non convex cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✸ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 xbase Non convex cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✸ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 xbase Non convex cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✸ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✸ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✸ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✸ ✴ ✶✽
3 2 1 1 2 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Cost function
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✹ ✴ ✶✽
3 2 1 1 2 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Cost function
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✹ ✴ ✶✽
3 2 1 1 2 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Stage 7
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✹ ✴ ✶✽
3 2 1 1 2 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Stage 7
Algorithm used Q SLDP ADDP ❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✹ ✴ ✶✽
3 2 1 1 2 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Stage 6
Algorithm used Q SLDP ADDP ❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✹ ✴ ✶✽
3 2 1 1 2 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Stage 5
Algorithm used Q SLDP ADDP ❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✹ ✴ ✶✽
3 2 1 1 2 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Stage 4
Algorithm used Q SLDP ADDP ❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✹ ✴ ✶✽
3 2 1 1 2 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Stage 3
Algorithm used Q SLDP ADDP ❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✹ ✴ ✶✽
3 2 1 1 2 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Stage 2
Algorithm used Q SLDP ADDP ❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✹ ✴ ✶✽
3 2 1 1 2 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Stage 1
Algorithm used Q SLDP ADDP ❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✹ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✹ ✴ ✶✽
§ r❡❧❛①❡s ❛ ❧✐tt❧❡ t❤❡ ❝♦♠♣❧❡t❡ ❝♦♥t✐♥✉♦✉s r❡❝♦✉rs❡ ❛s✉♠♣t✐♦♥s✳
§ ❝♦✉❧❞ ❛❞❞ ♠❛♥② ♠♦r❡ ❜✐♥❛r② ✈❛r✐❛❜❧❡s
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✺ ✴ ✶✽
§ r❡❧❛①❡s ❛ ❧✐tt❧❡ t❤❡ ❝♦♠♣❧❡t❡ ❝♦♥t✐♥✉♦✉s r❡❝♦✉rs❡ ❛s✉♠♣t✐♦♥s✳
§ ❝♦✉❧❞ ❛❞❞ ♠❛♥② ♠♦r❡ ❜✐♥❛r② ✈❛r✐❛❜❧❡s
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✺ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 xbase Non convex cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✻ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 xbase Non convex cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✻ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 xbase Non convex cut
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✻ ✴ ✶✽
3 2 1 1 2 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Stage 2
Algorithm used Q SLDP ADDP ❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✻ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 xbase Cut at 0.5 Ceiling ❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✼ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 xbase Cut at 0.3 Ceiling ❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✼ ✴ ✶✽
3 2 1 1 2 3 0.5 0.0 0.5 1.0 1.5 2.0 2.5 xbase Cut at 0.1 Ceiling ❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✼ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✽ ✴ ✶✽
❙✳ ❆❤♠❡❞ ❋✳ ❈❛❜r❛❧ ❇✳ ❋P❈ ❙▲❉P ■❈❙P✬✶✾ ✶✽ ✴ ✶✽