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SLIDE 1

❙❡❧❢✲❛❞❛♣t✐✈❡ ❙❡❛r❝❤ ❊q✉❛t✐♦♥✲❇❛s❡❞ ❆rt✐✜❝✐❛❧ ❇❡❡ ❈♦❧♦♥② ❆❧❣♦r✐t❤♠ ✇✐t❤ ❈▼❆✲❊❙ ♦♥ t❤❡ ◆♦✐s❡❧❡ss ❇❇❖❇ ❚❡st❜❡❞

❉♦➜❛♥ ❆②❞✙♥✱ ●ür❝❛♥ ❨❛✈✉③

❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②

❏✉❧② ✶✾✱ ✷✵✶✼

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✶ ✴ ✶✻

slide-2
SLIDE 2

❖✉t❧✐♥❡

❙❙❊❆❇❈ ❆❧❣♦r✐t❤♠ ❆rt✐✜❝✐❛❧ ❇❡❡ ❈♦❧♦♥② ❆❧❣♦r✐t❤♠ ❋r❛♠❡✇♦r❦ Pr♦♣♦s❡❞ ▼♦❞✐✜❝❛t✐♦♥s ♦♥ ❆❇❈

  • ❡♥❡r❛❧✐③❡❞ s❡❛r❝❤ ❡q✉❛t✐♦♥

❊①♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts ❈❊❈ ❈♦♠♣❡t✐t✐♦♥ ❘❡s✉❧ts ◆♦✐s❡❧❡ss ❇❇❖❇ t❡st❜❡❞ r❡s✉❧ts

❉✐s❝✉ss✐♦♥

❚❤❛♥❦s

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✷ ✴ ✶✻

slide-3
SLIDE 3

❙❙❊❆❇❈ ❆❧❣♦r✐t❤♠ ❆rt✐✜❝✐❛❧ ❇❡❡ ❈♦❧♦♥② ❆❧❣♦r✐t❤♠ ❋r❛♠❡✇♦r❦

Ps❡✉❞♦✲❝♦❞❡ ♦❢ ❚❤❡ ❆❇❈ ❢r❛♠❡✇♦r❦

✶✿ ❙t❡♣ ✶✳ ■♥✐t✐❛❧✐③❛t✐♦♥ ✷✿ ✇❤✐❧❡ t❡r♠✐♥❛t✐♦♥ ❝♦♥❞✐t✐♦♥ ✐s ♥♦t ♠❡t ❞♦ ✸✿

❙t❡♣ ✷✳ ❊♠♣❧♦②❡❞ ❇❡❡s ❙t❡♣

✹✿

❙t❡♣ ✸✳ ❈❛❧❝✉❧❛t❡ ❙❡❧❡❝t✐♦♥ Pr♦❜❛❜✐❧✐t✐❡s

✺✿

❙t❡♣ ✹✳ ❖♥❧♦♦❦❡r ❇❡❡s ❙t❡♣

✻✿

❙t❡♣ ✺✳ ❙❝♦✉t ❇❡❡s ❙t❡♣

✼✿

❙t❡♣ ✻✳ ❆♣♣❧② ▲♦❝❛❧ ❙❡❛r❝❤ ✭❖♣t✐♦♥❛❧✮

✽✿

❙t❡♣ ✼✳ ❆♣♣❧② P♦♣✉❧❛t✐♦♥ ❙tr❛t❡❣② ✭❖♣t✐♦♥❛❧✮

✾✿ ❡♥❞ ✇❤✐❧❡

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✸ ✴ ✶✻

slide-4
SLIDE 4

❙❙❊❆❇❈ ❆❧❣♦r✐t❤♠ ❆rt✐✜❝✐❛❧ ❇❡❡ ❈♦❧♦♥② ❆❧❣♦r✐t❤♠ ❋r❛♠❡✇♦r❦

▼♦st ❊✛❡❝t✐✈❡ ❈♦♠♣♦♥❡♥ts ✐♥ ❆❇❈ ❋r❛♠❡✇♦r❦

❈♦♠♣♦♥❡♥ts ❙❡❛r❝❤ ❡q✉❛t✐♦♥ ✐♥ ❊♠♣❧♦②❡❞ ❇❡❡s ❛♥❞ ❖♥❧♦♦❦❡r ❇❡❡s st❡♣s ▲♦❝❛❧ s❡❛r❝❤ str❛t❡❣② P♦♣✉❧❛t✐♦♥ str❛t❡❣② ❆②❞✙♥✱ ❉✳ ✭✷✵✶✺✮✳ ❈♦♠♣♦s✐t❡ ❛rt✐✜❝✐❛❧ ❜❡❡ ❝♦❧♦♥② ❛❧❣♦r✐t❤♠s✿ ❋r♦♠ ❝♦♠♣♦♥❡♥t✲❜❛s❡❞ ❛♥❛❧②s✐s t♦ ❤✐❣❤✲♣❡r❢♦r♠✐♥❣ ❛❧❣♦r✐t❤♠s✳ ❆♣♣❧✐❡❞ ❙♦❢t ❈♦♠♣✉t✐♥❣✱ ✸✷✱ ✷✻✻✲✷✽✺✳

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✹ ✴ ✶✻

slide-5
SLIDE 5

❙❙❊❆❇❈ ❆❧❣♦r✐t❤♠ Pr♦♣♦s❡❞ ▼♦❞✐✜❝❛t✐♦♥s ♦♥ ❆❇❈

■♠♣r♦✈❡♠❡♥ts ✐♥tr♦❞✉❝❡❞ ❜② t❤❡ ❙❙❊❆❇❈ ❛❧❣♦r✐t❤♠

❋♦r ❊♠♣❧♦②❡❞ ❇❡❡s ❛♥❞ ❖♥❧♦♦❦❡r ❇❡❡s ❙t❡♣s ❙❡❧❢✲❛❞❛♣t✐✈❡ s❡❛r❝❤ ❡q✉❛t✐♦♥ s❡❧❡❝t✐♦♥ ❋♦r ▲♦❝❛❧ ❙❡❛r❝❤ ❉✐✛❡r❡♥t ❧♦❝❛❧ s❡❛r❝❤ ♣r♦❝❡❞✉r❡s ❋♦r P♦♣✉❧❛t✐♦♥ ❙✐③❡ ■♥❝r❡♠❡♥t❛❧ ♣♦♣✉❧❛t✐♦♥ s✐③❡ str❛t❡❣②

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✺ ✴ ✶✻

slide-6
SLIDE 6

❙❙❊❆❇❈ ❆❧❣♦r✐t❤♠ Pr♦♣♦s❡❞ ▼♦❞✐✜❝❛t✐♦♥s ♦♥ ❆❇❈

P♦♣✉❧❛t✐♦♥ ❙✐③❡ ❙tr❛t❡❣②

■♥ ❙❙❊❆❇❈ ❛❧❣♦r✐t❤♠✱ t❤r❡❡ ♣♦♣✉❧❛t✐♦♥ s✐③❡ str❛t❡❣② ❛r❡ ✐♠♣❧❡♠❡♥t❡❞✿ ✜①✱ ✐♥❝r❡♠❡♥t❛❧ ❛♥❞ ❞②♥❛♠✐❝ ♣♦♣✉❧❛t✐♦♥ s✐③❡ str❛t❡❣✐❡s ■♥ t❤✐s ✇♦r❦✱ ✇❡ ♦♥❧② ✉s❡❞ ✐♥❝r❡♠❡♥t❛❧ ♣♦♣✉❧❛t✐♦♥ str❛t❡❣② ✇❤✐❝❤ ✐s ❜❡tt❡r t❤❛♥ t❤❡ ♦t❤❡rs ■♥ ✐♥❝r❡♠❡♥t❛❧ ♣♦♣✉❧❛t✐♦♥ s✐③❡ str❛t❡❣②✱ ❛ ♥❡✇ ❛❣❡♥t ✐s ❛❞❞❡❞ t♦ t❤❡ ♣♦♣✉❧❛t✐♦♥ ❜② ´ xnew,j = xnew,j + ϕi,j(xGbest,j − xnew,j) ✭✶✮

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✻ ✴ ✶✻

slide-7
SLIDE 7

❙❙❊❆❇❈ ❆❧❣♦r✐t❤♠ Pr♦♣♦s❡❞ ▼♦❞✐✜❝❛t✐♦♥s ♦♥ ❆❇❈

▲♦❝❛❧ ❙❡❛r❝❤ ❙tr❛t❡❣②

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✼ ✴ ✶✻

slide-8
SLIDE 8

❙❙❊❆❇❈ ❆❧❣♦r✐t❤♠

  • ❡♥❡r❛❧✐③❡❞ s❡❛r❝❤ ❡q✉❛t✐♦♥
  • ❡♥❡r❛❧ ❢♦r♠ ♦❢ ❣❡♥❡r❛t❡ s❡❛r❝❤ ❡q✉❛t✐♦♥

❙t❛♥❞❛r❞ ❙❡❛r❝❤ ❊q✉❛t✐♦♥ vi,j = xi,j + φi,j(xi,j − xr✶,j) ✭✷✮

  • ❡♥❡r❛❧✐③❡❞ ❙❡❛r❝❤ ❊q✉❛t✐♦♥ ✭●❙❊✮

❢♦r t = ✶ t♦ m ❞♦

✷✿

s❡❧❡❝t r❛♥❞♦♠ ❞✐♠❡♥s✐♦♥ j ✭✶ ≤ j ≤ D✮ xi,j = term✶ + term✷ + term✸ + term✹

✹✿ ❡♥❞ ❢♦r

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✽ ✴ ✶✻

slide-9
SLIDE 9

❙❙❊❆❇❈ ❆❧❣♦r✐t❤♠

  • ❡♥❡r❛❧✐③❡❞ s❡❛r❝❤ ❡q✉❛t✐♦♥

❱❡rs✳ ■ ✭✷✵✶✻✮✿ ❈♦♠♣♦♥❡♥t ❛❧t❡r♥❛t✐✈❡s ✐♥ ●❙❊

❚❛❜❧❡✿ ❆❧t❡r♥❛t✐✈❡ ♦♣t✐♦♥s ❢♦r ❡❛❝❤ ❝♦♠♣♦♥❡♥t ✐♥ t❤❡ ❣❡♥❡r❛❧✐③❡❞ s❡❛r❝❤ ❡q✉❛t✐♦♥✳ φ✶✱ φ✶ ❛♥❞ φ✶ ❝❛♥ t❛❦❡ t✇♦ ♣♦ss✐❜❧❡ r❛♥❣❡s✿ [−✶, −✶] ❛♥❞ [−SF, SF] ✇❤❡r❡ SF ✐s r❛♥❞♦♠❧② s❡❧❡❝t❡❞ ♣♦s✐t✐✈❡ r❡❛❧ ✈❛❧✉❡✳ ❚❤❡s❡ r❛♥❣❡s ❛r❡ ❞❡❝✐❞❡❞ r❛♥❞♦♠❧② ✇❤✐❧❡ ❝r❡❛t✐♥❣ ❡❛❝❤ ❝♦♠♣♦♥❡♥t ♦❢ ❡❛❝❤ r❛♥❞♦♠❧② ❣❡♥❡r❛t❡❞ s❡❛r❝❤ ❡q✉❛t✐♦♥✳

m term✶ term✷ term✸ term✹ ✶ xi,j φ✶(xi,j − xG,j) φ✷(xi,j − xG,j) φ✸(xi,j − xG,j) k ✭✶ ≤ k ≤ D✮ xG,j φ✶(xi,j − xr✶,j) φ✷(xi,j − xr✶,j) φ✸(xi,j − xr✶,j) [t, k] ✭✶ ≤ t < k ≤ D✮ xr✶,j φ✶(xG,j − xr✶,j) φ✷(xG,j − xr✶,j) φ✸(xG,j − xr✶,j) φ✶(xr✶,j − xr✷,j) φ✷(xr✶,j − xr✷,j) φ✸(xr✶,j − xr✷,j) φ✶(xi,j − xGD,j) φ✷(xi,j − xGD,j) φ✸(xi,j − xGD,j) ❞♦ ♥♦t ✉s❡ ❞♦ ♥♦t ✉s❡ ❞♦ ♥♦t ✉s❡

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✾ ✴ ✶✻

slide-10
SLIDE 10

❙❙❊❆❇❈ ❆❧❣♦r✐t❤♠

  • ❡♥❡r❛❧✐③❡❞ s❡❛r❝❤ ❡q✉❛t✐♦♥

❱❡rs✳ ■■ ✭✷✵✶✼✮✿ ❈♦♠♣♦♥❡♥t ❛❧t❡r♥❛t✐✈❡s ✐♥ ●❙❊

❚❛❜❧❡✿ ❆❧t❡r♥❛t✐✈❡ ♦♣t✐♦♥s ❢♦r ❡❛❝❤ ❝♦♠♣♦♥❡♥t ✐♥ t❤❡ ❣❡♥❡r❛❧✐③❡❞ s❡❛r❝❤ ❡q✉❛t✐♦♥✳ φ✶✱ φ✶ ❛♥❞ φ✶ ❝❛♥ t❛❦❡ t✇♦ ♣♦ss✐❜❧❡ r❛♥❣❡s✿ [−✶, −✶] ❛♥❞ [−SF, SF] ✇❤❡r❡ SF ✐s r❛♥❞♦♠❧② s❡❧❡❝t❡❞ ♣♦s✐t✐✈❡ r❡❛❧ ✈❛❧✉❡✳ ❚❤❡s❡ r❛♥❣❡s ❛r❡ ❞❡❝✐❞❡❞ r❛♥❞♦♠❧② ✇❤✐❧❡ ❝r❡❛t✐♥❣ ❡❛❝❤ ❝♦♠♣♦♥❡♥t ♦❢ ❡❛❝❤ r❛♥❞♦♠❧② ❣❡♥❡r❛t❡❞ s❡❛r❝❤ ❡q✉❛t✐♦♥✳

m term✶ term✷ term✸ term✹ ✶ xi,j φ✶(xi,j − xG,j ) φ✷(xi,j − xG,j ) φ✸(xi,j − xG,j ) k ✭✶ ≤ k ≤ D✮ xG,j φ✶(xi,j − xr✶,j ) φ✷(xi,j − xr✶,j ) φ✸(xi,j − xr✶,j ) [t, k] ✭✶ ≤ t < k ≤ D✮ xr✶,j φ✶(xG,j − xr✶,j ) φ✷(xG,j − xr✶,j ) φ✸(xG,j − xr✶,j ) φ✶(xr✶,j − xr✷,j ) φ✷(xr✶,j − xr✷,j ) φ✸(xr✶,j − xr✷,j ) φ✶(xi,j − xGD,j ) φ✷(xi,j − xGD,j ) φ✸(xi,j − xGD,j ) φ✶(xi,j − xSC,j ) φ✷(xi,j − xSC,j ) φ✸(xi,j − xSC,j ) φ✶(xi,j − xMD,j ) φ✷(xi,j − xMD,j ) φ✸(xi,j − xMD,j ) φ✶(xi,j − xWO,j ) φ✷(xi,j − xWO,j ) φ✸(xi,j − xWO,j ) φ✶(xSC,j − xMD,j ) φ✷(xSC,j − xMD,j ) φ✸(xSC,j − xMD,j ) φ✶(xMD,j − xWO,j ) φ✷(xMD,j − xWO,j ) φ✸(xMD,j − xWO,j ) φ✶(xG,j − xWO,j ) φ✷(xG,j − xWO,j ) φ✸(xG,j − xWO,j ) φ✶(xr✶,j − xMD,j ) φ✷(xr✶,j − xMD,j ) φ✸(xr✶,j − xMD,j ) φ✶(xG,j − xMD,j ) φ✷(xG,j − xMD,j ) φ✸(xG,j − xMD,j ) φ✶(xr✶,j − xWO,j ) φ✷(xr✶,j − xWO,j ) φ✸(xr✶,j − xWO,j ) φ✶(xSC,j − xr✶,j ) φ✷(xSC,j − xr✶,j ) φ✸(xSC,j − xr✶,j ) φ✶(xi,j − xAVE,j ) φ✷(xi,j − xAVE,j ) φ✸(xi,j − xAVE,j ) φ✶(xr✶,j − xAVE,j ) φ✷(xr✶,j − xAVE,j ) φ✸(xr✶,j − xAVE,j ) φ✶(xG,j − xAVE,j ) φ✷(xG,j − xAVE,j ) φ✸(xG,j − xAVE,j ) ❞♦ ♥♦t ✉s❡ ❞♦ ♥♦t ✉s❡ ❞♦ ♥♦t ✉s❡ ❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✶✵ ✴ ✶✻

slide-11
SLIDE 11

❙❙❊❆❇❈ ❆❧❣♦r✐t❤♠

  • ❡♥❡r❛❧✐③❡❞ s❡❛r❝❤ ❡q✉❛t✐♦♥

❙❡❛r❝❤ ❊q✉❛t✐♦♥ P♦♦❧

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✶✶ ✴ ✶✻

slide-12
SLIDE 12

❊①♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts ❈❊❈ ❈♦♠♣❡t✐t✐♦♥ ❘❡s✉❧ts

❙❙❊❆❇❈ ✭❱❡rs✐♦♥ ■✮ ✐♥ ❈❊❈✬✶✻ ❈♦♠♣❡t✐t✐♦♥

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✶✷ ✴ ✶✻

slide-13
SLIDE 13

❊①♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts ❈❊❈ ❈♦♠♣❡t✐t✐♦♥ ❘❡s✉❧ts

❙❙❊❆❇❈ ✭❱❡rs✐♦♥ ■ ❛♥❞ ■■✮ ✐♥ ❈❊❈✬✶✼ ❈♦♠♣❡t✐t✐♦♥

❇❡st ▼❡❞✐❛♥ ▼❡❛♥ ❋✉♥❝✳ ❙❙❊❆❇❈✈✷ ❙❙❊❆❇❈✈✶ ❙❙❊❆❇❈✈✷ ❙❙❊❆❇❈✈✶ ❙❙❊❆❇❈✈✷ ❙❙❊❆❇❈✈✶ ✶ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✷ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✸ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✹ ✺✳✻✼✺❊✲✵✶ ✵✳✵✵✵❊✰✵✵ ✺✳✽✺✻❊✰✵✶ ✺✳✽✺✻❊✰✵✶ ✺✳✶✵✼❊✰✵✶ ✹✳✸✶✵❊✰✵✶ ✺ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✷✳✾✽✺❊✰✵✵ ✷✳✾✽✺❊✰✵✵ ✸✳✶✹✹❊✰✵✵ ✸✳✹✼✸❊✰✵✵ ✻ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✼ ✸✳✷✻✷❊✰✵✶ ✹✳✷✺✷❊✰✵✶ ✸✳✹✶✻❊✰✵✶ ✺✳✺✶✺❊✰✵✶ ✸✳✹✻✻❊✰✵✶ ✺✳✺✼✻❊✰✵✶ ✽ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✷✳✾✽✺❊✰✵✵ ✸✳✾✽✵❊✰✵✵ ✷✳✻✾✷❊✰✵✵ ✸✳✼✻✺❊✰✵✵ ✾ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✵✳✵✵✵❊✰✵✵ ✶✵ ✶✳✷✹✸❊✰✵✷ ✶✳✶✸✹❊✰✵✶ ✾✳✶✵✼❊✰✵✷ ✶✳✽✹✸❊✰✵✸ ✾✳✷✾✶❊✰✵✷ ✶✳✻✽✼❊✰✵✸ ✶✶ ✶✳✹✹✷❊✰✵✵ ✾✳✾✺✵❊✲✵✶ ✻✳✻✺✶❊✰✵✵ ✷✳✻✶✾❊✰✵✶ ✶✳✷✹✶❊✰✵✶ ✷✳✾✻✼❊✰✵✶ ✶✷ ✷✳✹✽✺❊✰✵✷ ✷✳✺✼✷❊✰✵✷ ✶✳✷✹✸❊✰✵✸ ✶✳✷✻✶❊✰✵✸ ✶✳✷✸✸❊✰✵✸ ✶✳✷✷✺❊✰✵✸ ✶✸ ✸✳✵✽✵❊✰✵✵ ✶✳✾✽✸❊✰✵✶ ✷✳✷✺✶❊✰✵✶ ✾✳✼✼✶❊✰✵✶ ✹✳✽✻✺❊✰✵✶ ✶✳✾✺✽❊✰✵✷ ✶✹ ✻✳✼✼✸❊✰✵✶ ✻✳✸✼✽❊✰✵✶ ✶✳✷✵✺❊✰✵✷ ✶✳✷✶✺❊✰✵✷ ✶✳✶✽✹❊✰✵✷ ✶✳✷✻✼❊✰✵✷ ✶✺ ✼✳✺✶✼❊✰✵✵ ✷✳✸✺✺❊✰✵✶ ✾✳✻✽✻❊✰✵✶ ✶✳✸✽✻❊✰✵✷ ✶✳✶✻✼❊✰✵✷ ✶✳✼✵✸❊✰✵✷ ✶✻ ✸✳✵✸✺❊✰✵✵ ✸✳✷✺✶❊✰✵✵ ✶✳✼✾✵❊✰✵✶ ✶✳✻✷✵❊✰✵✷ ✸✳✺✺✹❊✰✵✶ ✶✳✽✷✵❊✰✵✷ ✶✼ ✷✳✻✻✸❊✰✵✶ ✷✳✾✼✾❊✰✵✶ ✹✳✽✾✷❊✰✵✶ ✻✳✻✼✶❊✰✵✶ ✺✳✵✾✽❊✰✵✶ ✼✳✺✶✷❊✰✵✶ ✶✽ ✷✳✶✹✼❊✰✵✶ ✸✳✹✸✺❊✰✵✶ ✼✳✽✵✺❊✰✵✶ ✶✳✷✸✻❊✰✵✷ ✽✳✻✸✶❊✰✵✶ ✶✳✶✽✺❊✰✵✷ ✶✾ ✷✳✷✾✼❊✰✵✶ ✶✳✺✵✵❊✰✵✶ ✺✳✼✹✻❊✰✵✶ ✻✳✷✷✵❊✰✵✶ ✻✳✶✻✼❊✰✵✶ ✻✳✷✸✸❊✰✵✶ ✷✵ ✷✳✸✵✾❊✰✵✶ ✽✳✷✶✼❊✰✵✵ ✸✳✽✶✷❊✰✵✶ ✺✳✼✽✸❊✰✵✶ ✸✳✽✽✶❊✰✵✶ ✺✳✼✽✵❊✰✵✶ ❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✶✸ ✴ ✶✻

slide-14
SLIDE 14

❊①♣❡r✐♠❡♥t❛❧ ❘❡s✉❧ts ◆♦✐s❡❧❡ss ❇❇❖❇ t❡st❜❡❞ r❡s✉❧ts

❘❡s✉❧ts ♦✈❡r ❆❧❧ ❋✉♥❝t✐♦♥s ✐♥ ❇❇❖❇ t❡st❜❡❞

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✶✹ ✴ ✶✻

slide-15
SLIDE 15

❉✐s❝✉ss✐♦♥

❉✐s❝✉ss✐♦♥

❙❙❊❆❇❈ ♦✉t♣❡r❢♦r♠s P❙❖✱ ❆❇❈ ❛♥❞ ●❆ ❢♦r ❛❧♠♦st ❛❧❧ ❢✉♥❝t✐♦♥s✳ ❙❙❊❆❇❈ s♦❧✈❡❞ ✶✶ ❢✉♥❝t✐♦♥s ✐♥ ❞✐♠❡♥s✐♦♥ ✺ ❛♥❞ ✺ ❢✉♥❝t✐♦♥s ✐♥ ❞✐♠❡♥s✐♦♥ ✷✵ ✇✐t❤ ✶✵✵ % s✉❝❝❡ss r❛t❡ ❋♦r ✷✱ ✺ ❛♥❞ ✷✵ ❞✐♠❡♥s✐♦♥❛❧ ❢✉♥❝t✐♦♥s✱ ❙❙❊❆❇❈ s♦❧✈❡❞ ✾ ❢✉♥❝t✐♦♥s ♦♣t✐♠❛❧❧② ❙❙❊❆❇❈ ✐s ♥♦t ❣♦♦❞ ✐♥ s❡♣❛r❛❜❧❡ ❢✉♥❝t✐♦♥s✳

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✶✺ ✴ ✶✻

slide-16
SLIDE 16

❚❤❛♥❦s

❚❤❛♥❦ ②♦✉✦ ◗✉❡st✐♦♥s❄

❆②❞✙♥ ❛♥❞ ❨❛✈✉③ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✮ ✭❉✉♠❧✉♣✙♥❛r ❯♥✐✈❡rs✐t②✱ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ❉❡♣❛rt♠❡♥t✱ ❚✉r❦❡②✮

  • ❊❈❈❖ ✷✵✶✼ ❇❇❖❇ ❲♦r❦s❤♦♣

❏✉❧② ✶✾✱ ✷✵✶✼ ✶✻ ✴ ✶✻