MÉTODOS DE OTIMIZAÇÃO MULTIOBJETIVO E DE SIMULAÇÃO APLICADOS AO PROBLEMA DE PLANEJAMENTO OPERACIONAL DE LAVRA EM MINAS A CÉU ABERTO

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▼■◆■❙❚➱❘■❖ ❉❆ ❊❉❯❈❆➬➹❖ ❊ ❉❖ ❉❊❙P❖❘❚❖ ❊s❝♦❧❛ ❞❡ ▼✐♥❛s ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❖✉r♦ Pr❡t♦

❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞❡ ▼✐♥❛s

Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ▼✐♥❡r❛❧ ✲ PP●❊▼

▼➱❚❖❉❖❙ ❉❊ ❖❚■▼■❩❆➬➹❖ ▼❯▲❚■❖❇❏❊❚■❱❖ ❊ ❉❊

❙■▼❯▲❆➬➹❖ ❆P▲■❈❆❉❖❙ ❆❖ P❘❖❇▲❊▼❆ ❉❊

P▲❆◆❊❏❆▼❊◆❚❖ ❖P❊❘❆❈■❖◆❆▲ ❉❊ ▲❆❱❘❆ ❊▼

▼■◆❆❙ ❆ ❈➱❯ ❆❇❊❘❚❖

❆✉t♦r✿ ●✉✐❞♦ P❛♥t✉③❛ ❏ú♥✐♦r

❖r✐❡♥t❛❞♦r❡s✿ ▼❛r❝♦♥❡ ❏❛♠✐❧s♦♥ ❋r❡✐t❛s ❙♦✉③❛ ■✈♦ ❊②❡r ❈❛❜r❛❧

❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ▼✐♥❡r❛❧ ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞❡ ▼✐✲ ♥❛s ❞❛ ❊s❝♦❧❛ ❞❡ ▼✐♥❛s ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❖✉r♦ Pr❡t♦✱ ❝♦♠♦ ♣❛rt❡ ✐♥t❡✲ ❣r❛♥t❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❊♥❣❡♥❤❛r✐❛ ▼✐♥❡r❛❧✳

➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ▲❛✈r❛ ❞❡ ▼✐✲ ♥❛s✳

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▼➱❚❖❉❖❙ ❉❊ ❖❚■▼■❩❆➬➹❖ ▼❯▲❚■❖❇❏❊❚■❱❖ ❊ ❉❊

❙■▼❯▲❆➬➹❖ ❆P▲■❈❆❉❖❙ ❆❖ P❘❖❇▲❊▼❆ ❉❊

P▲❆◆❊❏❆▼❊◆❚❖ ❖P❊❘❆❈■❖◆❆▲ ❉❊ ▲❆❱❘❆ ❊▼

▼■◆❆❙ ❆ ❈➱❯ ❆❇❊❘❚❖

●✉✐❞♦ P❛♥t✉③❛ ❏ú♥✐♦r

❊st❛ ❞✐ss❡rt❛çã♦ ❢♦✐ ❛♣r❡s❡♥t❛❞❛ ❡♠ s❡ssã♦ ♣ú❜❧✐❝❛ ❡ ❛♣r♦✈❛❞❛ ❡♠ ✷✺ ❞❡ ♠❛rç♦ ❞❡ ✷✵✶✶✱ ♣❡❧❛ ❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛ ❝♦♠♣♦st❛ ♣❡❧♦s s❡❣✉✐♥t❡s ♠❡♠❜r♦s✿

Pr♦❢✳ ❉r✳ ▼❛r❝♦♥❡ ❏❛♠✐❧s♦♥ ❋r❡✐t❛s ❙♦✉③❛ ✭❖r✐❡♥t❛❞♦r✴❯❋❖P✮

Pr♦❢✳ ❉r✳ ■✈♦ ❊②❡r ❈❛❜r❛❧ ✭❖r✐❡♥t❛❞♦r✴❯❋❖P✮

Pr♦❢✳ ❉r✳ ❍❛r♦❧❞♦ ●❛♠❜✐♥✐ ❙❛♥t♦s ✭❯❋❖P✮

Pr♦❢✳ ❉r✳ ❏♦sé ❊❧✐❛s ❈❧á✉❞✐♦ ❆rr♦②♦ ✭❯❋❱✮

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❆❣r❛❞❡❝✐♠❡♥t♦s

➱ ❜♦♠✱ s❡♠ ❞ú✈✐❞❛✱ ❝♦♥❤❡❝❡r✲s❡ t✉❞♦ ♦ q✉❡ ♣r♦❞✉③✐r❛♠ ♦s ❣r❛♥❞❡s ❤♦♠❡♥s ❞♦s ♦✉tr♦s ♣♦✈♦s❀ ♣♦ré♠ ♠✉✐t♦ ♠❡❧❤♦r é s❛❜❡r s❡r✈✐r✲s❡ ❞♦ q✉❡ ❡❧❡s ✜③❡r❛♠ ♣❛r❛ ❢❛③❡r ♥♦✈❛s ❞❡s❝♦❜❡rt❛s✳✳✳ ❈❧❛✉❞❡ ❍❡♥r✐ ●♦r❝❡✐①✳

❋✉♥❞❛❞♦r ❞❛ ❊s❝♦❧❛ ❞❡ ▼✐♥❛s

➚ ♠✐♥❤❛ ♠ã❡ ❊❞♥❛ ❡ ♠❡✉ ♣❛✐ ●✉✐❞♦✱ ♦s ❣r❛♥❞❡s r❡s♣♦♥sá✈❡✐s ♣❡❧❛ ♠✐♥❤❛ ❢♦r♠❛çã♦✱ ♣❡❧♦ ❛♠♦r ❡ ❝♦♥✜❛♥ç❛✳ ❆♦s ♠❡✉s ✐r♠ã♦s ❡ ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ♣♦r t♦❞❛s ❛s ✈❡③❡s q✉❡ ♠❡ ❛♣♦✐❛r❛♠ ❡ ❝♦♥✜❛r❛♠ ❡♠ ♠✐♠✳

➚ ▼❛②r❛ ♣❡❧♦ ❛♠♦r✱ ❝❛r✐♥❤♦✱ ✐♥❝❡♥t✐✈♦ ❡ ❛❥✉❞❛ ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s✳

❆♦ ♣r♦❢❡ss♦r ▼❛r❝♦♥❡✱ q✉❡ ♥ã♦ ♠❡❞✐✉ ❡s❢♦rç♦s ♣❛r❛ ♠❡ ❛❥✉❞❛r ❡ t♦r♥♦✉ ❡st❡ tr❛❜❛❧❤♦ ♣♦ssí✈❡❧ ♣❛rt✐❝✐♣❛♥❞♦ ❝♦♠♦ ♦r✐❡♥t❛❞♦r✱ ♣❡sq✉✐s❛❞♦r ❡ ❛♠✐❣♦✱ s❡♥❞♦ ♣❛r❛ ♠✐♠ ✉♠❛ r❡❢❡rê♥❝✐❛ ❡♠ t♦❞♦s ♦s ❛s♣❡❝t♦s✳

❆ t♦❞♦s ♦s ♠❡✉s ❛♠✐❣♦s q✉❡ ♠❡ ❛❥✉❞❛r❛♠ ❡ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ❡st❛ ❝♦♥✲ q✉✐st❛✳

➚ ❊s❝♦❧❛ ❞❡ ▼✐♥❛s✱ ♣♦r ♠❡ ♣r♦♣♦r❝✐♦♥❛r ♦s ❡♥s✐♥❛♠❡♥t♦s ❞♦ q✉❡ é s❡r ✉♠ ❡♥❣❡♥❤❡✐r♦ ét✐❝♦ ❡ ❝♦♠♣❡t❡♥t❡✳

➚ ❘❡♣ú❜❧✐❝❛ ❙❡♥③❛❧❛ ❡ t♦❞♦s ♦s ❡s❝r❛✈♦s ❡ ❡①✲❛❧✉♥♦s✱ ♣♦r ♠❡ ❛❝♦❧❤❡r ❡♠ s✉❛ ❢❛♠í❧✐❛✱ ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ❢♦rç❛ ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s✳

❆♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ▼✐♥❡r❛❧ ❞❛ ❊s❝♦❧❛ ❞❡ ▼✐♥❛s ♣❡❧♦s r❡❝✉rs♦s ❞✐s♣♦♥✐❜✐❧✐③❛❞♦s

❆ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s q✉❡ ♣❛rt✐❝✐♣❛r❛♠✱ ❞❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ♣r♦✜ss✐♦♥❛❧ ❡

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❝r❡s❝✐♠❡♥t♦ ♣❡ss♦❛❧✳

❆ ❈❛♣❡s✱ ❋❆P❊▼■● ❡ ❛♦ ❈◆Pq ♣❡❧♦s r❡❝✉rs♦s ❞✐s♣♦♥✐❜✐❧✐③❛❞♦s ♣❛r❛ ♦ ❞❡✲ s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳

❋✐♥❛❧♠❡♥t❡✱ ❛ t♦❞♦s q✉❡✱ ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛♠❡♥t❡✱ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ❛ ❝♦♥✲ ❝❧✉sã♦ ❞❡st❡ tr❛❜❛❧❤♦✳

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❘❡s✉♠♦

❊st❡ tr❛❜❛❧❤♦ t❡♠ s❡✉ ❢♦❝♦ ♥♦ ♣r♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ♦♣❡r❛❝✐♦♥❛❧ ❞❡ ❧❛✈r❛ ❞❡ ♠✐♥❛ ❛ ❝é✉ ❛❜❡rt♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛❧♦❝❛çã♦ ❞✐♥â♠✐❝❛ ❞❡ ❝❛♠✐♥❤õ❡s✳ ❈♦♥s✐❞❡r❛✲s❡ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠❛ ❢r♦t❛ ❤❡t❡r♦❣ê♥❡❛ ❞❡ ❝❛♠✐♥❤õ❡s✱ ❛ ❡①✐stê♥❝✐❛ ❞❡ ❞♦✐s ♣♦♥t♦s ❞❡ ❞❡s❝❛r❣❛ ♣❛r❛ ♦ ♠❛t❡r✐❛❧ ❧❛✈r❛❞♦✱ s❡♥❞♦ ♦ ❜r✐t❛❞♦r ♣❛r❛ ❞❡s❝❛r❣❛ ❞❡ ♠✐♥ér✐♦ ❡ ❛ ♣✐❧❤❛ ❞❡ ❡stér✐❧ ♣❛r❛ ❞❡s❝❛r❣❛ ❞❡ ❡stér✐❧✳ ❖ t❡♠♣♦ ❞❡ ❝✐❝❧♦ ❞♦s ❡q✉✐♣❛♠❡♥t♦s t❛♠✲ ❜é♠ ❢♦✐ ❝♦♥s✐❞❡r❛❞♦ ❝♦♠♦ ✉♠ ♣❛râ♠❡tr♦ q✉❡ ❞❡♣❡♥❞❡ ❞❛ ❢r❡♥t❡ ❞❡ ❧❛✈r❛✱ ❞♦ t✐♣♦ ❞❡ ❝❛♠✐♥❤ã♦ ❡ ❞♦ t✐♣♦ ❞❡ ♠❛t❡r✐❛❧ tr❛♥s♣♦rt❛❞♦✳ P❛r❛ s✉❛ r❡s♦❧✉çã♦✱ ♣r♦♣õ❡✲s❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♠✉❧t✐♦❜❥❡t✐✈♦✱ ✉♠❛ ✈❡③ q✉❡ ♦ ♣r♦❜❧❡♠❛ é ❝♦♥st✐t✉í❞♦ ❞❡ ❞✐✈❡rs❛s ♠❡t❛s ❝♦♥✢✐t❛♥t❡s✳ ❙ã♦ ♣r♦♣♦st♦s ✉♠ ♠♦❞❡❧♦ ❞❡ ♣r♦❣r❛♠❛çã♦ ❧✐♥❡❛r ♣♦r ♠❡t❛s✱ ✉♠ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ❤í❜r✐❞♦ ❜❛s❡❛❞♦ ♥♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ♠✉❧t✐♦❜❥❡✲ t✐✈♦ ◆❙●❆ ■■✱ ❛ss✐♠ ❝♦♠♦ ✉♠ ♠♦❞❡❧♦ ❞❡ s✐♠✉❧❛çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♣❛r❛ ✈❛❧✐❞❛r ♦s ♠♦❞❡❧♦s ❡①❛t♦ ❡ ❤❡✉ríst✐❝♦✱ ❜❡♠ ❝♦♠♦ ♣❛r❛ ❢❛③❡r ♦ s❡q✉❡♥❝✐❛♠❡♥t♦ ❞❛s ✈✐❛❣❡♥s r❡✲ ❛❧✐③❛❞❛s ♣❡❧♦s ❝❛♠✐♥❤õ❡s✳ ❖s ❡①♣❡r✐♠❡♥t♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ♠♦str❛♠ ❛ ❡❢❡t✐✈✐❞❛❞❡ ❞❛ ♣r♦♣♦st❛✳

P❛❧❛✈r❛s✲❈❤❛✈❡s✿ P❧❛♥❡❥❛♠❡♥t♦ ❞❡ ❧❛✈r❛✱ ◆❙●❆ ■■✱ Pr♦❣r❛♠❛çã♦ ▲✐♥❡❛r ♣♦r ▼❡t❛s✱ ❙✐♠✉❧❛çã♦ ❈♦♠♣✉t❛❝✐♦♥❛❧✳

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❆❜str❛❝t

❚❤✐s ✇♦r❦ ❞❡❛❧s ✇✐t❤ t❤❡ ❖♣❡♥✲P✐t✲▼✐♥✐♥❣ ❖♣❡r❛t✐♦♥❛❧ P❧❛♥♥✐♥❣ ♣r♦❜❧❡♠ ❝♦♥❝❡r♥✐♥❣ ❞②♥❛♠✐❝ tr✉❝❦ ❛❧❧♦❝❛t✐♦♥✳ ❲❡ ❛❧s♦ ❝♦♥s✐❞❡r t❤❛t t❤❡r❡ ✐s ❛ ❤❡t❡r♦❣❡♥❡♦✉s ✢❡❡t ♦❢ tr✉❝❦s✱ t✇♦ ❞✐s❝❤❛r❣❡ ♣♦✐♥ts ❢♦r t❤❡ ♠❛t❡r✐❛❧ ♠✐♥❡❞ ✭t❤❡ ❝r✉s❤❡r ❢♦r t❤❡ ❞✐s❝❤❛r❣❡ ♦❢ ♦r❡ ❛♥❞ t❤❡ ✇❛st❡ ❞✉♠♣ ❢♦r t❤❡ ❞✐s❝❤❛r❣❡ ♦❢ ✇❛st❡✮ ❛♥❞ t❤❡ ❝②❝❧❡ t✐♠❡ ♦❢ t❤❡ tr✉❝❦s ❞❡♣❡♥❞s ♦❢ t❤❡ ♣✐t✱ t❤❡ tr✉❝❦ t②♣❡ ❛♥❞ t❤❡ ❧♦❛❞❡❞ ♠❛t❡r✐❛❧ ✭♦r❡ ♦r ✇❛st❡✮✳ ❋♦r ✐ts r❡s♦❧✉t✐♦♥✱ ❛ ♠✉❧t✐✲♦❜❥❡❝t✐✈❡ ♦♣t✐♠✐③❛t✐♦♥ ❛♣♣r♦❛❝❤ ✐s ♣r♦♣♦s❡❞✱ s✐♥❝❡ t❤❡ ♣r♦❜❧❡♠ ✐s ❝♦♥st✐t✉t❡❞ ♦❢ ❞✐✈❡rs❡ ❣♦❛❧s t❤❛t ♠✉st s✐♠✉❧t❛♥❡♦✉s❧② ❜❡ r❡❛❝❤❡❞✳ ❲❡ ♣r♦♣♦s❡ ❛ ❧✐♥❡❛r ❣♦❛❧ ♣r♦❣r❛♠♠✐♥❣✱ ❛ ❤②❜r✐❞ ♠✉❧t✐✲♦❜❥❡❝t✐✈❡ ❛❧❣♦r✐t❤♠ ❜❛s❡❞ ♦♥ ◆❙●❆✲■■✱ ❛s ✇❡❧❧ ❛ ❝♦♠♣✉t❛t✐♦♥❛❧ s✐♠✉❧❛t✐♦♥ ♠♦❞❡❧ ❢♦r ✈❛❧✐❞❛t❡ t❤❡ ♠♦❞❡❧s ❛♥❞ t♦ ❞❡t❡r♠✐♥❡ t❤❡ s❡q✉❡♥❝❡ ♦❢ tr✐♣s ♠❛❞❡ ❜② t❤❡ tr✉❝❦s✳ ❚❤❡ ❝♦♠♣✉t❛t✐♦♥❛❧ ❡①♣❡r✐♠❡♥ts s❤♦✇ t❤❡ ❡✛❡❝t✐✈❡♥❡ss ♦❢ t❤❡ ♣r♦♣♦s❛❧✳

❑❡②✇♦r❞s✿ ❖♣❡♥ P✐t ▼✐♥❡ P❧❛♥✱ ◆❙●❆ ■■✱ ●♦❛❧ Pr♦❣r❛♠♠✐♥❣✱ ❈♦♠♣✉t❛✲ t✐♦♥❛❧ ❙✐♠✉❧❛t✐♦♥✳

(7)

❈♦♥t❡ú❞♦

✶ Pr❡❧✐♠✐♥❛r❡s ✶

✶✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶

✶✳✷ ❏✉st✐✜❝❛t✐✈❛ ❡ ❘❡❧❡✈â♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹

✶✳✸ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✶✳✸✳✶ ❖❜❥❡t✐✈♦ ●❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✶✳✸✳✷ ❖❜❥❡t✐✈♦s ❊s♣❡❝í✜❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

✷ Pr♦❜❧❡♠❛ ❆❜♦r❞❛❞♦ ✽

✸ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛ ✶✶

✸✳✶ ❖t✐♠✐③❛çã♦ ▼✉❧t✐♦❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶

✸✳✶✳✶ ❈♦♥❝❡✐t♦s ❇ás✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷

✸✳✶✳✷ ▼ét♦❞♦s ❞❡ ❖t✐♠✐③❛çã♦ ▼✉❧t✐♦❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹

✸✳✶✳✸ ❈❧❛ss✐✜❝❛çã♦ ❞♦s ▼ét♦❞♦s ❞❡ ❖t✐♠✐③❛çã♦ ▼✉❧t✐♦❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✶✺

✸✳✶✳✹ ▼ét♦❞♦s ❈❧áss✐❝♦s ❞❡ ❖t✐♠✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✸✳✷ ❚é❝♥✐❝❛s ❍❡✉ríst✐❝❛s ▼✉❧t✐♦❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✸✳✷✳✶ ❍❡✉ríst✐❝❛s ❈♦♥str✉t✐✈❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✸✳✷✳✷ ❍❡✉ríst✐❝❛s ❞❡ ❘❡✜♥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

(8)

✸✳✷✳✸ ▼❡t❛❤❡✉ríst✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷

✸✳✸ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ▼✉❧t✐♦❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

✸✳✸✳✶ ◆❙●❆ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

✸✳✹ ❙✐♠✉❧❛çã♦ ❈♦♠♣✉t❛❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✸✳✹✳✶ ❈♦♥❝❡✐t♦s ❇ás✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

✸✳✺ P❡sq✉✐s❛ ❖♣❡r❛❝✐♦♥❛❧ ❆♣❧✐❝❛❞❛ à ▼✐♥❡r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

✹ ▼❡t♦❞♦❧♦❣✐❛ ✸✽

✹✳✶ ▼♦❞❡❧♦ ▼❛t❡♠át✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾

✹✳✷ ▼♦❞❡❧♦ ❍❡✉ríst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✹✳✷✳✶ ◆❙●❆ ■■ ❆♣❧✐❝❛❞♦ ❛♦ P❖▲❆❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✹✳✷✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ ■♥❞✐✈í❞✉♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✹✳✷✳✸ P♦♣✉❧❛çã♦ ■♥✐❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

✹✳✷✳✹ ❆✈❛❧✐❛çã♦ ❞❛ P♦♣✉❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽

✹✳✷✳✺ ❋❛s❡ ❞❡ ❙❡❧❡çã♦ ❡ ❘❡♣r♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✹✳✷✳✻ ❇✉s❝❛ ❧♦❝❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✹✳✷✳✼ ❊str✉t✉r❛s ❞❡ ❱✐③✐♥❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✹✳✷✳✽ P♦♣✉❧❛çã♦ ❙♦❜r❡✈✐✈❡♥t❡ ✭Pg+1✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✹✳✸ ▼♦❞❡❧♦ ❞❡ ❙✐♠✉❧❛çã♦ ❈♦♠♣✉t❛❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✹✳✸✳✶ ❉❡✜♥✐çã♦ ❞♦ Pr♦❜❧❡♠❛ ❡ ❈♦❧❡t❛ ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽

✹✳✸✳✷ ■❞❡♥t✐✜❝❛çã♦ ❞❛s ❱❛r✐á✈❡✐s ❡ ❞❛s ❈♦♥❞✐çõ❡s ❞♦ ❙✐st❡♠❛ ✳ ✳ ✳ ✳ ✺✽

✹✳✸✳✸ ❈♦♥str✉çã♦ ❞♦ ▼♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾

✹✳✸✳✹ ▼♦❞❡❧♦ ❞❡ ❙✐♠✉❧❛çã♦ ✐♠♣❧❡♠❡♥t❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵

✹✳✸✳✺ ❱❛❧✐❞❛çã♦ ❞♦ ▼♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷

✹✳✸✳✻ ❉❡s❝r✐çã♦ ❞♦s ❈❡♥ár✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

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✺ ❘❡s✉❧t❛❞♦s ❡ ❆♥á❧✐s❡ ✻✺

✺✳✶ ■♥stâ♥❝✐❛s✲❚❡st❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺

✺✳✷ ❘❡s✉❧t❛❞♦s ❞♦ ▼ét♦❞♦ ❊①❛t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺

✺✳✸ ❘❡s✉❧t❛❞♦s ❞♦ ❆❧❣♦r✐t♠♦ ◆❙●❆✲■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽

✺✳✹ ❘❡s✉❧t❛❞♦s ❞♦ ▼♦❞❡❧♦ ❞❡ ❙✐♠✉❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵

✻ ❈♦♥❝❧✉sõ❡s ✼✹

❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✼✺

■ ❋❛s❡ ❞❡ ❘❡♣r♦❞✉çã♦ ✽✶

■■ ❊str✉t✉r❛s ❞❡ ❱✐③✐♥❤❛♥ç❛ ✽✷

■■■ P✉❜❧✐❝❛çõ❡s ✽✽

(10)

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✹✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ♣❛rt❡sl ❞♦ ✐♥❞✐✈í❞✉♦ S ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻

✹✳✷ ❉❡s❝r✐çã♦ ❞♦s ❝❡♥ár✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹

✺✳✶ ❈❛r❛❝t❡ríst✐❝❛s ❞❛s ✐♥stâ♥❝✐❛s✲t❡st❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻

✺✳✷ P❛râ♠❡tr♦s ❞❡ ❡♥tr❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻

✺✳✸ P❡♥❛❧✐❞❛❞❡ ♣♦r ❞❡s✈✐♦ ❡♠ r❡❧❛çã♦ à ♠❡t❛ ❞♦ ♣❛râ♠❡tr♦j ♥❛ ♠✐st✉r❛ ✳ ✻✻

✺✳✹ ❘❡s✉❧t❛❞♦s ❞♦ ♠♦❞❡❧♦ ❡①❛t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼

✺✳✺ ❘❡s✉❧t❛❞♦s ❞♦ ♠♦❞❡❧♦ ❡①❛t♦ ❛♣ós ✶✽✵✵ s❡❣✉♥❞♦s ❞❡ ❡①❡❝✉çã♦ ✳ ✳ ✳ ✳ ✳ ✻✼

✺✳✻ ❘❡s✉❧t❛❞♦s ❞♦ ▼ét♦❞♦ ❍❡✉ríst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽

✺✳✼ ❚❡♠♣♦ ❞❡ ❊①❡❝✉çã♦ ✭s❡❣✉♥❞♦s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾

✺✳✽ ❘❡s✉❧t❛❞♦s ❞♦ ♠♦❞❡❧♦ ❞❡ s✐♠✉❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

■✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❢❛s❡ ❞❡ r❡♣r♦❞✉çã♦ ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶

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▲✐st❛ ❞❡ ❋✐❣✉r❛s

✷✳✶ ■❧✉str❛çã♦ ❞♦ P❖▲❆❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

✸✳✶ ■❧✉str❛çã♦ ❞♦ ❝á❧❝✉❧♦ ❞❛ ❞✐stâ♥❝✐❛ ❞❡ ♠✉❧t✐❞ã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

✸✳✷ ❊❧❡♠❡♥t♦s ❞❛ ♥♦t❛çã♦ ❝❧áss✐❝❛ ❞❡ ✉♠ ❉❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

✹✳✶ ❊t❛♣❛s ❞❛ s✐♠✉❧❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✹✳✷ ❉✐❛❣r❛♠❛ ❞❡ ❝✐❝❧♦ ❞❡ ❛t✐✈✐❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾

✹✳✸ ▼♦❞❡❧♦ ❞❡ s✐♠✉❧❛çã♦ ✐♠♣❧❡♠❡♥t❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵

✹✳✹ ❙✉❜♠♦❞❡❧♦ ❈r✐❛❴■♥✐❝✐❛❧✐③❛❴❊♥t✐❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

✹✳✺ ❙✉❜♠♦❞❡❧♦ ❘♦t❡❛❞♦r ❞❡ ❱❡í❝✉❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

✹✳✻ ❊st❛çã♦ ❋r❡♥t❡ ❞❡ ▲❛✈r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷

✹✳✼ ❙✉❜♠♦❞❡❧♦s ❇r✐t❛❞♦r Pr✐♠ár✐♦ ❡ P✐❧❤❛ ❞❡ ❊stér✐❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷

✺✳✶ ❖❜❥❡t✐✈♦✿ ♠❡t❛ ❞❡ ♣r♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾

✺✳✷ ❖❜❥❡t✐✈♦✿ ♠❡t❛ ❞❡ q✉❛❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵

✺✳✸ ❖❜❥❡t✐✈♦✿ ♥ú♠❡r♦ ❞❡ ❝❛♠✐♥❤õ❡s ✉t✐❧✐③❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵

✺✳✹ ❈r✐tér✐♦ ❞❡ ❘♦t❡❛♠❡♥t♦ ❞❡ ❱❡í❝✉❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✺✳✺ ❘❡s✉❧t❛❞♦s ❞♦ ♠♦❞❡❧♦ ❞❡ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠ét♦❞♦ ❊①❛t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✺✳✻ ❘❡s✉❧t❛❞♦s ❞♦ ♠♦❞❡❧♦ ❞❡ s✐♠✉❧❛çã♦ ♣❛r❛ ♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✼✷

■■✳✶ ■❧✉str❛çã♦ ❞♦ ▼♦✈✐♠❡♥t♦ ◆ú♠❡r♦ ❞❡ ❱✐❛❣❡♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷

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■■✳✷ ■❧✉str❛çã♦ ❞♦ ▼♦✈✐♠❡♥t♦ ❈❛r❣❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸

■■✳✸ ■❧✉str❛çã♦ ❞♦ ❚r♦❝❛ ❞❡ ❈❛rr❡❣❛❞❡✐r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹

■■✳✹ ■❧✉str❛çã♦ ❞♦ ▼♦✈✐♠❡♥t♦ ❘❡❛❧♦❝❛r ❱✐❛❣❡♠ ❞❡ ✉♠ ❈❛♠✐♥❤ã♦ ✳ ✳ ✳ ✳ ✳ ✽✺

■■✳✺ ■❧✉str❛çã♦ ❞♦ ▼♦✈✐♠❡♥t♦ ❘❡❛❧♦❝❛r ❱✐❛❣❡♠ ❞❡ ✉♠❛ ❋r❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻

■■✳✻ ■❧✉str❛çã♦ ❞♦ ▼♦✈✐♠❡♥t♦ ❘❡❛❧♦❝❛r ❈❛rr❡❣❛❞❡✐r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼

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▲✐st❛ ❞❡ ❙✐❣❧❛s

❆● ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦

❆●▼ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ▼✉❧t✐♦❜❥❡t✐✈♦

❉❈❆ ❉✐❛❣r❛♠❛ ❞❡ ❈✐❝❧♦ ❞❡ ❆t✐✈✐❞❛❞❡s

▼❖●❆ ▼✉❧t✐♦❜❥❡❝t✐✈❡ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠

◆P●❆ ◆✐❝❤❡ P❛r❡t♦ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠

◆❙●❆ ◆♦♥✲❉♦♠✐♥❛t❡❞ ❙♦rt✐♥❣ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠

P❆❈ Pr♦❜❧❡♠❛ ❞❛ ❆❧♦❝❛çã♦ ❞❡ ❈❛♠✐♥❤õ❡s

P❆❉❈ Pr♦❜❧❡♠❛ ❞❛ ❆❧♦❝❛çã♦ ❉✐♥â♠✐❝❛ ❞❡ ❈❛♠✐♥❤õ❡s

P❆❊❈ Pr♦❜❧❡♠❛ ❞❛ ❆❧♦❝❛çã♦ ❊stát✐❝❛ ❞❡ ❈❛♠✐♥❤õ❡s

P▲▼ Pr♦❣r❛♠❛çã♦ ▲✐♥❡❛r P♦r ▼❡t❛s

P❖ P❡sq✉✐s❛ ❖♣❡r❛❝✐♦♥❛❧

P❖▲❆❉ P❧❛♥❡❥❛♠❡♥t♦ ❖♣❡r❛❝✐♦♥❛❧ ❞❡ ▲❛✈r❛ ❝♦♠ ❆❧♦❝❛çã♦ ❉✐♥â♠✐❝❛ ❞❡

❈❛♠✐♥❤õ❡s

❘❊▼ ❘❡❧❛çã♦ ❊stér✐❧ ▼✐♥ér✐♦

❙P❊❆ ❙tr❡♥❣t❤ P❛r❡t♦ ❊✈♦❧✉t✐♦♥❛r② ❆❧❣♦r✐t❤♠

❱❊●❆ ❱❡❝t♦r ❊✈❛❧✉❛t❡❞ ●❡♥❡t✐❝ ❆❧❣♦r✐t❤♠

❱◆❉ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❉❡s❝❡♥t

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▲✐st❛ ❞❡ ❆❧❣♦r✐t♠♦s

✶ ❱◆❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶

✷ ❋❛st ◆♦♥ ❉♦♠✐♥❛t❡❞ ❙♦rt✐♥❣ ✭■ ✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

✸ ❈r♦✇❞✐♥❣ ❉✐st❛♥❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾

✹ ◆❙●❆ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶

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❈❛♣ít✉❧♦ ✶

Pr❡❧✐♠✐♥❛r❡s

✶✳✶ ■♥tr♦❞✉çã♦

❆s ♠✉❞❛♥ç❛s q✉❡ ♦❝♦rr❡r❛♠ ♥❛s ú❧t✐♠❛s ❞é❝❛❞❛s ♦❜r✐❣❛r❛♠ ❛s ❡♠♣r❡s❛s ❛ r❡❞✉③✐r❡♠ ❣❛st♦s✱ ❣❡r❡♥❝✐❛r ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❡ ✢❡①✐❜✐❧✐③❛r ♦s ♠❡✐♦s ❞❡ ♣r♦❞✉çã♦ ❡ ❞❡ s❡r✈✐ç♦s ♣❛r❛ s♦❜r❡✈✐✈❡r ❡ ❝r❡s❝❡r ❡♠ ✉♠ ❛♠❜✐❡♥t❡ ♠❛✐s ❝♦♠♣❡t✐t✐✈♦✳ ❆❧é♠ ❞✐ss♦✱ ❛ ♣r❡♦❝✉✲ ♣❛çã♦ ❝♦♠ ♦ ♠❡✐♦ ❛♠❜✐❡♥t❡ ❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ s✉st❡♥tá✈❡❧ t❛♠❜é♠ ❡♥tr❛r❛♠ ♥❛ ♣❛✉t❛ ❞❡ ❞✐s❝✉ssã♦ ❞❛s ❣r❛♥❞❡s ♦r❣❛♥✐③❛çõ❡s✳

◆❡st❡ ❝♦♥t❡①t♦✱ ❛q✉❡❧❛s ❡♠♣r❡s❛s q✉❡ ♥ã♦ ❣❛r❛♥t✐r❡♠ ❛ ♠❡❧❤♦r✐❛ ❝♦♥tí♥✉❛ ❞❡ s❡✉s ♣r♦❝❡ss♦s ♣r♦❞✉t✐✈♦s✱ ❛❧é♠ ❞❛ ❞✐♠✐♥✉✐çã♦ ❞❡ s❡✉s ✐♠♣❛❝t♦s s♦❜r❡ ♦ ♠❡✐♦ ❛♠❜✐❡♥t❡✱ ♣❡r❞❡rã♦ s✉❛ ❝♦♠♣❡t✐t✐✈✐❞❛❞❡ ♥♦ ♠❡r❝❛❞♦ ✐♥t❡r♥❛❝✐♦♥❛❧✳

❯♠❛ ❢♦r♠❛ ❞❡ ✐♠♣❧❡♠❡♥t❛r ❡ss❛ ♠❡❧❤♦r✐❛ é ❡str✉t✉r❛r ✉♠ ❡✜❝✐❡♥t❡ ❝♦♥tr♦❧❡ ❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❡str❛té❣✐❝♦ ❞❛ ♣r♦❞✉çã♦✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❚✉❜✐♥♦ ✭✶✾✾✼✮✱ ♦ ♣❧❛♥❡✲ ❥❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦ ❝♦♥s✐st❡ ❡♠ ❣❡r❛r ❝♦♥❞✐çõ❡s ♣❛r❛ q✉❡ ❛s ❡♠♣r❡s❛s ♣♦ss❛♠ ❞❡❝✐❞✐r r❛♣✐❞❛♠❡♥t❡ ♣❡r❛♥t❡ ♦♣♦rt✉♥✐❞❛❞❡s ❡ ❛♠❡❛ç❛s✱ ♦t✐♠✐③❛♥❞♦ s✉❛s ✈❛♥t❛❣❡♥s ❝♦♠♣❡t✐t✐✈❛s ❡♠ r❡❧❛çã♦ ❛♦ ❛♠❜✐❡♥t❡ ❝♦♥❝♦rr❡♥❝✐❛❧ ♥♦ q✉❛❧ ❛t✉❛♠✱ ❣❛r❛♥t✐♥❞♦ s✉❛ ♣❡r♣❡t✉❛çã♦ ♥♦ t❡♠♣♦✳

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❝✉st♦s ❡❧❡✈❛❞♦s✳

❊st❡s ❝✉st♦s ❡stã♦ r❡❧❛❝✐♦♥❛❞♦s✱ ❡♥tr❡ ♦✉tr♦s✱ à ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛s ❢r❡♥t❡s ❞❡ ❡stér✐❧ ✲ ♠❛t❡r✐❛❧ s❡♠ ✈❛❧♦r ❝♦♠❡r❝✐❛❧ ✲ ❡ s✉❛s ♣✐❧❤❛s ❞❡ ❞❡♣ós✐t♦ ✭♣✐❧❤❛s ❞❡ ❡stér✐❧✮✳ ❊ss❛s ❞✐stâ♥❝✐❛s ❡stã♦ ✜❝❛♥❞♦ ❝❛❞❛ ✈❡③ ♠❛✐♦r❡s ❞❡✈✐❞♦ à ♣r❡♦❝✉♣❛çã♦ ❝♦♠ ♦ ♠❡✐♦ ❛♠❜✐❡♥t❡✱ ❥á q✉❡ ❡♠ ♠✉✐t♦s ❝❛s♦s ❛s ❥❛③✐❞❛s s❡ ❡♥❝♦♥tr❛♠ ❡♠ ár❡❛s ❞❡ ♣r❡s❡r✈❛çã♦ ❛♠❜✐❡♥t❛❧ ✭❆P❆✬s✮ ❡ ♦ ❡stér✐❧ ❞❡✈❡ s❡r ❞❡♣♦s✐t❛❞♦ ❡♠ ❧♦❝❛❧ ❛❞❡q✉❛❞♦✳

❙❡❣✉♥❞♦ P❛♥t✉③❛ ❏r ✭✷✵✵✽✮✱ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ♦♣❡r❛❝✐♦♥❛❧ ❞❡ ❧❛✈r❛ ❞❡ ✉♠❛ ♠✐♥❛ ❛ ❝é✉ ❛❜❡rt♦ ❝♦♥s✐❞❡r❛♥❞♦ ❛❧♦❝❛çã♦ ❞✐♥â♠✐❝❛ ✭P❖▲❆❉✮ ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐✲ ♥❛r ♦ r✐t♠♦ ❞❡ ❧❛✈r❛ ❞❡ ❝❛❞❛ ❢r❡♥t❡✱ ♦✉ s❡❥❛✱ ♦ ♥ú♠❡r♦ ❞❡ ✈✐❛❣❡♥s ❛ s❡r❡♠ r❡❛❧✐③❛❞❛s ♣♦r ❝❛❞❛ t✐♣♦ ❞❡ ❝❛♠✐♥❤ã♦ ❡♠ ❝❛❞❛ ❢r❡♥t❡ ❞❡ ❧❛✈r❛✳ ❊st❡ r✐t♠♦ ❞❡✈❡ ❛t❡♥❞❡r ❛❧❣✉✲ ♠❛s ❡s♣❡❝✐✜❝❛çõ❡s✱ t❛✐s ❝♦♠♦ ❛ ♣♦r❝❡♥t❛❣❡♠ ❞❡ ❞❡t❡r♠✐♥❛❞♦s ❡❧❡♠❡♥t♦s q✉í♠✐❝♦s ♦✉ ❛ ❣r❛♥✉❧♦♠❡tr✐❛ ❞♦ ♠✐♥ér✐♦✱ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ♠✐♥ér✐♦ ❛ s❡r ❧❛✈r❛❞♦✱ ❛❧é♠ ❞❛ ❞❡✲ t❡r♠✐♥❛çã♦ ❞❛ q✉❛♥t✐❞❛❞❡ ❡ t✐♣♦ ❞❡ ❝❛♠✐♥❤õ❡s q✉❡ ❞❡✈❡rã♦ s❡r ❝❛rr❡❣❛❞♦s ❡♠ ❝❛❞❛ ❢r❡♥t❡ ❞❡ ❧❛✈r❛✳ ❊st❛s ❡s♣❡❝✐✜❝❛çõ❡s ✈❛r✐❛♠ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❝❛❞❛ ❢r❡♥t❡ ❞❡ ❧❛✈r❛✱ q✉❡ sã♦ ❞❡t❡r♠✐♥❛❞❛s ♣❡❧♦s ❝❧✐❡♥t❡s✳

❊st❡ ♣❧❛♥❡❥❛♠❡♥t♦ ♦♣❡r❛❝✐♦♥❛❧ t❛♠❜é♠ ✐♠♣❧✐❝❛ ♥♦ ❣❡r❡♥❝✐❛♠❡♥t♦ ❞♦s ❡q✉✐✲ ♣❛♠❡♥t♦s ❞❡ ❝❛r❣❛✱ ✐st♦ é✱ ♥❛ ❡s❝♦❧❤❛ ❞❛ ❢r❡♥t❡ ❞❡ ❧❛✈r❛ q✉❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❡q✉✐✲ ♣❛♠❡♥t♦ ❞❡ ❝❛r❣❛ s❡rá ❛❧♦❝❛❞♦✳ ❊st❡ ❣❡r❡♥❝✐❛♠❡♥t♦ ❞❡ ❡q✉✐♣❛♠❡♥t♦s ❞❡✈❡ r❡s♣❡✐t❛r ❛s r❡str✐çõ❡s ♦♣❡r❛❝✐♦♥❛✐s ❞❛ ♠✐♥❛ ❡ ❛s ♠❡t❛s ❞❡ q✉❛❧✐❞❛❞❡ ❡ ❞❡ ♣r♦❞✉çã♦✳

❚♦❞❛s ❛s ♠❡t❛s ❡ r❡str✐çõ❡s ❞❡st❡ ♣r♦❜❧❡♠❛ ❞❡✈❡♠ s❡r ❝♦♥s✐❞❡r❛❞❛s ❝♦♥❥✉♥✲ t❛♠❡♥t❡ ♣❛r❛ s❡ ❛t✐♥❣✐r ✉♠ r❡s✉❧t❛❞♦ ót✐♠♦✳ ❖ ❢❛t♦ ❞❡st❛s r❡str✐çõ❡s ❡ ♠❡t❛s s❡r❡♠ ❛❜♦r❞❛❞❛s s❡♣❛r❛❞❛♠❡♥t❡ ♣♦❞❡ ❣❡r❛r ❝♦♥✢✐t♦s q✉❡ ✐♥✈✐❛❜✐❧✐③❛♠ ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❛s s♦❧✉çõ❡s ✭❈♦st❛ ❡t ❛❧✳✱ ✷✵✵✹✮✳

◆❡st❡ tr❛❜❛❧❤♦ ❝♦♥s✐❞❡r❛♠♦s ❞♦✐s ♣♦♥t♦s ❞❡ ❞❡s❝❛r❣❛ ♣❛r❛ ♦ ♠❛t❡r✐❛❧ ❧❛✲ ✈r❛❞♦✱ s❡♥❞♦ ♦ ❜r✐t❛❞♦r ♣❛r❛ ❞❡s❝❛r❣❛ ❞❡ ♠✐♥ér✐♦ ❡ ❛ ♣✐❧❤❛ ❞❡ ❡stér✐❧ ♣❛r❛ ❞❡s❝❛r❣❛ ❞❡ ❡stér✐❧✳

❆♦ ❝♦♥trár✐♦ ❞♦s tr❛❜❛❧❤♦s ❛♥t❡r✐♦r❡s ❡♥❝♦♥tr❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛✱ t❛♠❜é♠ ❝♦♥s✐❞❡r❛♠♦s ♦ t❡♠♣♦ ❞❡ ❝✐❝❧♦ ❞♦s ❡q✉✐♣❛♠❡♥t♦s ❝♦♠♦ ✉♠❛ ✈❛r✐á✈❡❧ q✉❡ ❞❡♣❡♥❞❡ ❞❛ ❞✐stâ♥❝✐❛ ❞♦ ♣♦♥t♦ ❞❡ ❞❡s❝❛r❣❛ à ❢r❡♥t❡ ❞❡ ❧❛✈r❛✱ ❞♦ t✐♣♦ ❞❡ ❝❛♠✐♥❤ã♦✱ ❡ ❞♦

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t✐♣♦ ❞❡ ♠❛t❡r✐❛❧ tr❛♥s♣♦rt❛❞♦✳ ■st♦ ♣♦rq✉❡ ❝❛❞❛ ♠♦❞❡❧♦ ❞❡ ❝❛♠✐♥❤ã♦ ♥♦r♠❛❧♠❡♥t❡ ❧❡✈❛ ✉♠ t❡♠♣♦ ❞✐❢❡r❡♥t❡ ♣❛r❛ ♣❡r❝♦rr❡r ✉♠ ♠❡s♠♦ tr❛❥❡t♦ ❡ ❡st❡ t❡♠♣♦ t❛♠❜é♠ é ✐♥✢✉❡♥❝✐❛❞♦ ♣❡❧♦ t✐♣♦ ❞❡ ❝❛r❣❛ ✭♠✐♥ér✐♦ ♦✉ ❡stér✐❧✮✳

❆♣r❡s❡♥t❛♠♦s ✉♠❛ ♥♦✈❛ ❢♦r♠✉❧❛çã♦ ♠❛t❡♠át✐❝❛ ♣❛r❛ ♦ P❖▲❆❉✱ q✉❡ ✉t✐❧✐③❛ ♦ ♠♦❞❡❧♦ ❞❡ ✢✉①♦ ❡♠ r❡❞❡s ♣❛r❛ ❢❛③❡r ❛ ❛❧♦❝❛çã♦ ❞♦s ❝❛♠✐♥❤õ❡s ❞❡ ❢♦r♠❛ ❞✐♥â♠✐❝❛✳ ◆❡ss❡ s✐st❡♠❛ ❞❡ ❛❧♦❝❛çã♦✱ ♦s ❝❛♠✐♥❤õ❡s ♥ã♦ ✜❝❛♠ ✜①♦s ❛ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❢r❡♥t❡ ❞❡ ❧❛✈r❛✱ ✐st♦ é✱ ❛ ❝❛❞❛ ❞❡s❝❛r❣❛ ❡❧❡s ♣♦❞❡♠ s❡ ❞❡s❧♦❝❛r ♣❛r❛ ❞✐❢❡r❡♥t❡s ❢r❡♥t❡s✱ ♣❡r♠✐t✐♥❞♦ ✉♠ ♠❡❧❤♦r ❛♣r♦✈❡✐t❛♠❡♥t♦ ❞❛ ❢r♦t❛ ✭❈♦st❛✱ ✷✵✵✺✮✳ ❊❧❡ s❡ ❛♣r♦①✐♠❛ ♠❛✐s ❞♦ ♣r♦❜❧❡♠❛ r❡❛❧✱ t♦r♥❛♥❞♦ ♣♦ssí✈❡❧ ❛ ❛♣❧✐❝❛çã♦ ❞♦ ♠♦❞❡❧♦ ♣❡❧❛ ❡♠♣r❡s❛✱ ❛♦ ❝♦♥trár✐♦ ❞❛s ♦✉tr❛s ❢♦r♠✉❧❛çõ❡s✱ ❝♦♠♦ ▼❡rs❝❤♠❛♥♥ ❡ P✐♥t♦ ✭✷✵✵✶✮✱ ❈♦st❛ ❡t ❛❧✳ ✭✷✵✵✺✮ ❡ ●✉✐♠❛r❛❡s ❡t ❛❧✳ ✭✷✵✵✼✮✱ q✉❡ ♥ã♦ ♦❜t✐♥❤❛♠ r❡s✉❧t❛❞♦s ♣rát✐❝♦s ❛♣❧✐❝á✈❡✐s ♣♦r ♥ã♦ ❝♦♥s✐❞❡r❛r❡♠ ❛ t❛①❛ ❞❡ ✉t✐❧✐③❛çã♦ ❡ ♦ t❡♠♣♦ ❞❡ ❝✐❝❧♦ r❡❛❧ ❞❡ t♦❞♦s ♦s ❡q✉✐♣❛♠❡♥t♦s ❡♥✈♦❧✈✐❞♦s✳

P❛r❛ ♦ P❖▲❆❉✱ ❡♥tr❡ ❛s ♠❡t♦❞♦❧♦❣✐❛s ❡♥❝♦♥tr❛❞❛s ♥❛ ❧✐t❡r❛t✉r❛✱ ❞❡st❛❝❛♠✲ s❡ ❛ ♣r♦❣r❛♠❛çã♦ ❧✐♥❡❛r ✭▼❡rs❝❤♠❛♥♥ ❡ P✐♥t♦✱ ✷✵✵✶✮ ❡ ❛ ♣r♦❣r❛♠❛çã♦ ❧✐♥❡❛r ♣♦r ♠❡t❛s ✭❈♦st❛ ❡t ❛❧✳✱ ✷✵✵✹✮ ❡ ✭●✉✐♠❛r❛❡s ❡t ❛❧✳✱ ✷✵✵✼✮✳ ❉✐❢❡r❡♥t❡♠❡♥t❡ ❞❛ ❢♦r♠❛ ✉s✉❛❧ ❝♦♠ q✉❡ ♦ P❖▲❆❉ é ❛❜♦r❞❛❞♦ ♥❛ ❧✐t❡r❛t✉r❛✱ ♥♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❡❧❡ s❡rá tr❛t❛❞♦ ❝♦♠♦ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦✳ ■ss♦ s❡ ❞❡✈❡ ❛♦ ❢❛t♦ ❞❡ ❡❧❡ s❡r ❝♦♠♣♦st♦ ♣♦r ✈ár✐❛s ♠❡t❛s ❝♦♥✢✐t❛♥t❡s ❡♥tr❡ s✐✱ s❡♥❞♦✿ ♣r♦❞✉çã♦ ❞❡ ♠✐♥ér✐♦✱ t❡♦r ❞♦s ♣❛râ♠❡tr♦s ❞❡ q✉❛❧✐❞❛❞❡ ❡ ♥ú♠❡r♦ ❞❡ ❝❛♠✐♥❤õ❡s✳ ❖✉ s❡❥❛✱ ♥ã♦ s❡ ❝♦♥s❡❣✉❡ ✉♠❛ ú♥✐❝❛ s♦❧✉çã♦ q✉❡ ♠✐♥✐♠✐③❡ ♦ ♥ú♠❡r♦ ❞❡ ❝❛♠✐♥❤õ❡s ✉t✐❧✐③❛❞♦s ❡ ♦s ❞❡s✈✐♦s ❞❡ ♣r♦❞✉çã♦ ❡ q✉❛❧✐❞❛❞❡ s✐♠✉❧t❛♥❡❛♠❡♥t❡✳

◆❛ ❛❜♦r❞❛❣❡♠ ♠✉❧t✐♦❜❥❡t✐✈♦ ♦❜té♠✲s❡ ✉♠ ❝♦♥❥✉♥t♦✲s♦❧✉çã♦ ót✐♠♦ ❝♦♠ ✐♥ú✲ ♠❡r❛s s♦❧✉çõ❡s ✐♥❞✐❢❡r❡♥t❡s ❡♥tr❡ s✐ s❡❣✉♥❞♦ ❛❧❣✉♠ ❝r✐tér✐♦ ♣ré✲❡st❛❜❡❧❡❝✐❞♦✱ ❝❛❜❡♥❞♦ ❛♦ ❛♥❛❧✐st❛ ❞❡❝✐❞✐r q✉❛❧ s♦❧✉çã♦ ❛❞♦t❛r✳

◆♦ t♦❝❛♥t❡ à ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦ ♣r♦❜❧❡♠❛✱ s❡❣✉♥❞♦ ❈♦st❛ ✭✷✵✵✺✮✱ ♦ P❖▲❆❉ é ❡♥q✉❛❞r❛❞♦ ♥❛ ❝❧❛ss❡ ❞❡ ♣r♦❜❧❡♠❛s ◆P✲❞✐❢í❝❡✐s✱ ♦✉ ◆P✲❍❛r❞✱ ♦ q✉❡ ❥✉st✐✜❝❛ ❛ ❛♣❧✐❝❛çã♦ ❞❡ té❝♥✐❝❛s ❤❡✉ríst✐❝❛s ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞❡ ✐♥stâ♥❝✐❛s r❡❛✐s ❞♦ ♣r♦❜❧❡♠❛✱ ♥♦r♠❛❧♠❡♥t❡ ❛q✉❡❧❛s ❞❡ ♠❛✐♦r ♣♦rt❡✳

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❊♠ ✈✐st❛ ❞✐ss♦✱ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ✉♠ ❛❧❣♦r✐t♠♦ ❤❡✉ríst✐❝♦ ♠✉❧t✐♦❜❥❡t✐✈♦✳ ❊ss❡ ❛❧❣♦r✐t♠♦ é ❜❛s❡❛❞♦ ♥♦ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ◆❙●❆✲■■ ❡ ❡①♣❧♦r❛ ♦ ❡s♣❛ç♦ ❞❡ s♦❧✉çõ❡s ✉t✐❧✐③❛♥❞♦ ♦ ♠ét♦❞♦ ❞❡ ❞❡s❝✐❞❛ ❡♠ ✈✐③✐♥❤❛♥ç❛ ✈❛r✐á✈❡❧ ♣♦r ♠❡✐♦ ❞❡ s❡✐s ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ♠♦✈✐♠❡♥t♦s✳

P❛r❛ ✈❛❧✐❞❛r ♦ ❛❧❣♦r✐t♠♦ ❤❡✉ríst✐❝♦ ❡ ♦ ♠♦❞❡❧♦ ❞❡ ♣r♦❣r❛♠❛çã♦ ❧✐♥❡❛r ♣♦r ♠❡t❛s ❞❡s❡♥✈♦❧✈✐❞♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ✉♠ ♠♦❞❡❧♦ ❞❡ s✐♠✉❧❛çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♣❛r❛ ✈❡r✐✜❝❛r s❡ ❛ s♦❧✉çã♦ ♣r♦❞✉③✐❞❛ ♣♦r ❡❧❡s ♣♦❞✐❛ s❡r ✐♠♣❧❡♠❡♥t❛❞❛✳ ■ss♦ s❡ ❞❡✈❡ ❛♦ ❢❛t♦ ❞❡ q✉❡ ♦s t❡♠♣♦s ❞❡ ✜❧❛ ❞♦s ❝❛♠✐♥❤õ❡s ♥ã♦ ♣♦❞✐❛♠ s❡r ♣r❡✈✐st♦s ♣❡❧♦s ♠♦❞❡❧♦s ❞❡ ♦t✐♠✐③❛çã♦✳

✶✳✷ ❏✉st✐✜❝❛t✐✈❛ ❡ ❘❡❧❡✈â♥❝✐❛

❯♠ ❞♦s ♠❛✐♦r❡s ❞❡s❛✜♦s ❡♥❢r❡♥t❛❞♦s ♣❡❧❛s ❡♠♣r❡s❛s ♠✐♥❡r❛❞♦r❛s✱ s❡❣✉♥❞♦ ❈r❛✇❢♦r❞ ❡ ❍✉str✉❧✐❞ ✭✶✾✼✾✮✱ é ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ♦♣❡r❛❝✐♦♥❛❧ ❞❡ ❧❛✈r❛✳ ❊ss❡ ♣❧❛♥❡❥❛♠❡♥t♦ ✐♥❝❧✉✐ ❛ ❛❧♦❝❛çã♦ ❞❡ r❡❝✉rs♦s ❢ís✐❝♦s✱ ❝♦♠♦ ❝❛♠✐♥❤õ❡s ❡ ❝❛rr❡❣❛❞❡✐r❛s✱ ❞❡ ❢♦r♠❛ q✉❡ ❛s r❡str✐çõ❡s ♦♣❡r❛❝✐♦♥❛✐s ❞❡ ♣r♦❞✉çã♦ ❡ q✉❛❧✐❞❛❞❡ s❡❥❛♠ r❡s♣❡✐t❛❞❛s✳

❆❧é♠ ❞✐ss♦✱ ❛ q✉❛❧✐❞❛❞❡ ❞♦ ♣r♦❞✉t♦ ✜♥❛❧ ❞❡✈❡ s❡r ❣❛r❛♥t✐❞❛✱ ♣♦✐s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❈❛♠♣♦s ✭✶✾✾✾✮✱ ❛ q✉❛❧✐❞❛❞❡ só é ❛❧❝❛♥ç❛❞❛ ♣♦r ✉♠ ♣❧❛♥❡❥❛♠❡♥t♦ ❡♠ t♦❞♦s ♦s ♥í✈❡✐s ❞❛ ❡♠♣r❡s❛✳

❖ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦ q✉❛♥❞♦ ❜❡♠ r❡❛❧✐③❛❞♦✱ s❡❣✉♥❞♦ ▼❡rs❝❤♠❛♥♥ ✭✷✵✵✷✮✱ ♣♦❞❡ ❣❡r❛r ❜❡♥❡❢í❝✐♦s ♣❛r❛ ❛ ❡♠♣r❡s❛✱ ♣♦✐s ♠❡❧❤♦r❛ ❛ ❡✜❝✐ê♥❝✐❛ ❞❛ ✉s✐♥❛ ❞❡ tr❛t❛♠❡♥t♦✱ ♠✐♥✐♠✐③❛ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ❡❢❡t✉❛r ✉♠❛ ❧❛✈r❛ s❡❧❡t✐✈❛✱ r❡❞✉③ ❝✉st♦s ❞❡ ❧❛✈r❛✱ ❛✉♠❡♥t❛ ❛ ♣r♦❞✉çã♦ ❞❛ ♠✐♥❛ ❡ ❝♦♥tr✐❜✉✐ ♣❛r❛ q✉❡ ❡st❛ ♣♦ss✉❛ ✉♠❛ ✈✐❞❛ út✐❧ ♠❛✐s ❧♦♥❣❛✳

◆♦ ❡♥t❛♥t♦✱ ♥❛ ♠❛✐♦r✐❛ ❞♦s ❝❛s♦s✱ ♣❡r❞❡✲s❡ ♠✉✐t♦ t❡♠♣♦ ❝♦♠ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❡ ♦s r❡s✉❧t❛❞♦s ♥ã♦ sã♦ s❛t✐s❢❛tór✐♦s✱ ♦ q✉❡ ❣❡r❛ ❝✉st♦s ❞❡s♥❡❝❡ssár✐♦s ♣❛r❛ ❛ ❡♠♣r❡s❛✳

❯♠❛ ❢♦r♠❛ ❞❡ ♠❡❧❤♦r❛r ❡ss❡ ❝❡♥ár✐♦ é ❛♣❧✐❝❛r té❝♥✐❝❛s ❞❡ ♣❡sq✉✐s❛ ♦♣❡r❛❝✐✲ ♦♥❛❧✳ ◆♦ ❡♥t❛♥t♦✱ s❡❣✉♥❞♦ ▼❡rs❝❤♠❛♥♥ ✭✷✵✵✷✮✱ t❛✐s té❝♥✐❝❛s ❛✐♥❞❛ sã♦ ♠✉✐t♦ ♣♦✉❝♦ ✉s❛❞❛s ♣❡❧♦s ♣r♦✜ss✐♦♥❛✐s ❞❛ ♠✐♥❡r❛çã♦✳ ❙❡❣✉♥❞♦ ❘❛♠♦s ◆❡t♦ ❡ P✐♥t♦ ✭✷✵✵✹✮✱ ✐ss♦ s❡ ❞❡✈❡✱ ❡♥tr❡ ♦✉tr♦s ❢❛t♦s✱ à ❢❛❧t❛ ❞❡ ✐♥❢♦r♠❛çã♦✱ ♣♦r ♣❛rt❡ ❞♦s ♣r♦✜ss✐♦♥❛✐s ❞❛ ár❡❛✱

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s♦❜r❡ ❛ ❛♠♣❧❛ ❢❛✐①❛ ❞❡ ❛♣❧✐❝❛çõ❡s ❞❡ss❛ ❢❡rr❛♠❡♥t❛ ♥❛ ♠✐♥❡r❛çã♦✳

❆✐♥❞❛ ❞❡♥tr♦ ❞❡ss❡ ❝♦♥t❡①t♦✱ ●❡r♠❛♥✐ ✭✷✵✵✷✮ ❛✜r♠❛ q✉❡ ❤á ❞❡✜❝✐ê♥❝✐❛ ❞❡ ❢♦r♠❛çã♦ ❞❡ r❡❝✉rs♦s ❤✉♠❛♥♦s ❡♠ ár❡❛s ✐♠♣♦rt❛♥t❡s ❞❛ ♠✐♥❡r❛çã♦✳ ❊①✐st❡ t❛♠❜é♠✱ ♣♦r ❡st❛ r❛③ã♦✱ ✉♠❛ ❞❡♠♦r❛ ❡①❝❡ss✐✈❛ ❡♠ ✐♠♣❧❡♠❡♥t❛r✱ ♥❛s ♠✐♥❛s✱ ♦s ♥♦✈♦s s♦❢t✇❛r❡s ❛❞q✉✐r✐❞♦s✳

❊st❛s ❝❛rê♥❝✐❛s ❢❛③❡♠ ❝♦♠ q✉❡ ❝♦♠✉♠❡♥t❡ ♥ã♦ s❡ ✉t✐❧✐③❡♠ ❛s ❢❡rr❛♠❡♥t❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❡♠ t♦❞♦ ♦ s❡✉ ♣♦t❡♥❝✐❛❧✳ ❆❧é♠ ❞✐ss♦✱ ♥ã♦ ❤á ❛ ✐♥t❡❣r❛çã♦ ❡♥tr❡ ❛s ✈ár✐❛s ❢✉♥çõ❡s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❝♦♠ ❛ ♦♣❡r❛çã♦✱ ✐♥❞✉③✐♥❞♦✱ ✉♠❛ ✈❡③ ♠❛✐s✱ às s♦❧✉çõ❡s ❞❡ ❝❛♠♣♦✳

❆ ♣❛rt✐r ❞❡ss❡s ❢❛t♦s ❡ ❞❛ ✈❡r✐✜❝❛çã♦ ❞❡ ♣♦✉❝❛s ♣❡sq✉✐s❛s ❞❡s❡♥✈♦❧✈✐❞❛s ♥♦ s❡t♦r ❞❛ ♠✐♥❡r❛çã♦ ✉t✐❧✐③❛♥❞♦ ❛s ❢❡rr❛♠❡♥t❛s ❞❛ P❡sq✉✐s❛ ❖♣❡r❛❝✐♦♥❛❧✱ ❡st❡ tr❛❜❛❧❤♦ ♣r❡t❡♥❞❡ ❝♦♥tr✐❜✉✐r ❝♦♠ ❛ ❛♣r❡s❡♥t❛çã♦ ❞❡ ❢❡rr❛♠❡♥t❛s ❡✜❝✐❡♥t❡s ❞❡ ♦t✐♠✐③❛çã♦ ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ ❝❧áss✐❝♦ ❞♦ s❡t♦r✱ ❞❡ ❢♦r♠❛ ❛ ❛✉♠❡♥t❛r ❛ ♣r♦❞✉t✐✈✐❞❛❞❡ ❞❛s ❡♠♣r❡s❛s ❞❛ ár❡❛✳

✶✳✸ ❖❜❥❡t✐✈♦s

✶✳✸✳✶ ❖❜❥❡t✐✈♦ ●❡r❛❧

❊st❡ tr❛❜❛❧❤♦ ♣♦ss✉✐ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❣❡r❛❧ ♣r♦♣♦r ✉♠ ♠♦❞❡❧♦ ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐✲ ♦❜❥❡t✐✈♦ ❡✜❝✐❡♥t❡✱ ❜❛s❡❛❞♦ ❡♠ ❞✐❢❡r❡♥t❡s ❢❡rr❛♠❡♥t❛s ❞❛ P❖✱ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ♦♣❡r❛❝✐♦♥❛❧ ❞❡ ❧❛✈r❛ ❡♠ ✉♠❛ ♠✐♥❛ ❛ ❝é✉ ❛❜❡rt♦ ❡ ✈❛❧✐❞á✲❧♦ ❛tr❛✈és ❞❡ ✉♠ ♠♦❞❡❧♦ ❞❡ s✐♠✉❧❛çã♦✳

✶✳✸✳✷ ❖❜❥❡t✐✈♦s ❊s♣❡❝í✜❝♦s

❖s ♦❜❥❡t✐✈♦s ❡s♣❡❝í✜❝♦s ❛ s❡r❡♠ ❛t✐♥❣✐❞♦s sã♦ ♦s s❡❣✉✐♥t❡s✿

✶✳ ❘❡❛❧✐③❛r ✉♠❛ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ s♦❜r❡ ♦ ❛ss✉♥t♦ ❡♠ ❡st✉❞♦❀

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✸✳ Pr♦♣♦r ✉♠ ❛❧❣♦r✐t♠♦ ❤❡✉ríst✐❝♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛❀

✹✳ ❉❡s❡♥✈♦❧✈❡r ✉♠ ♠♦❞❡❧♦ ❞❡ s✐♠✉❧❛çã♦ ❝♦♠♥♣✉t❛❝✐♦♥❛❧ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛❀

✺✳ ❱❛❧✐❞❛r ♦s ♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦ ❡ ❤❡✉ríst✐❝♦ ❞❡s❡♥✈♦❧✈✐❞♦s ♣♦r ♠❡✐♦ ❞❛ s✐♠✉✲ ❧❛çã♦❀

✻✳ ❉❡t❡r♠✐♥❛r ♦ s❡q✉❡♥❝✐❛♠❡♥t♦ ❞♦s ❝❛♠✐♥❤õ❡s ❛tr❛✈és ❞❛ s✐♠✉❧❛çã♦❀

✼✳ P♦ss✐❜✐❧✐t❛r ♠❛✐♦r ❡✜❝✐ê♥❝✐❛ ♥♦ ♣❧❛♥❡❥❛♠❡♥t♦ ♦♣❡r❛❝✐♦♥❛❧ ❞❛ ♣r♦❞✉çã♦ ❡♠ ❧❛✈r❛ ❡♠ ♠✐♥❛s ❛ ❝é✉ ❛❜❡rt♦✱ ❡ ❞❡♠❛✐s ❡t❛♣❛s ❞❛ ♣r♦❞✉çã♦❀

✽✳ ❈♦♥tr✐❜✉✐r ❝♦♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♠❡t♦❞♦❧♦❣✐❛s q✉❡ ❛t❡♥❞❛♠ ❝❛s♦s r❡❛✐s ❞❛ ✐♥❞ústr✐❛ ♠✐♥❡r❛❧ ❜r❛s✐❧❡✐r❛✳

✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦

P❛r❛ ❛ ❝♦♥❝r❡t✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦ ❢♦r❛♠ ❞❡t❡r♠✐♥❛❞♦s✱ ♥❡st❡ ♣r✐♠❡✐r♦ ❝❛♣ít✉❧♦✱ ♦s ♥♦rt❡❛❞♦r❡s ❞❛ ♣❡sq✉✐s❛ ❡ ✉♠❛ rá♣✐❞❛ ❝♦♥t❡①t✉❛❧✐③❛çã♦✱ q✉❡ sã♦ ♦s s❡❣✉✐♥t❡s✿ ✐♥tr♦❞✉çã♦✱ ❥✉st✐✜❝❛t✐✈❛ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞♦ tr❛❜❛❧❤♦ ❡ ♦❜❥❡t✐✈♦s ❛ s❡r❡♠ ❛❧❝❛♥ç❛❞♦s✳

❖ r❡st❛♥t❡ ❞❡st❡ tr❛❜❛❧❤♦ ❡stá ❡str✉t✉r❛❞♦ ❝♦♠♦ s❡❣✉❡✳

◆♦ ❝❛♣ít✉❧♦ ✷✱ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ♣r♦❜❧❡♠❛ ❡st✉❞❛❞♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ❡♠ ❞❡t❛❧❤❡s✱ ❜❡♠ ❝♦♠♦ s✉❛ ❛♣❧✐❝❛çã♦ ♥❛ ár❡❛ ❞❡ ▼✐♥❡r❛çã♦✳

◆♦ ❝❛♣ít✉❧♦ ✸ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ❡ ✉♠❛ ❢✉♥❞❛♠❡♥t❛✲ çã♦ t❡ór✐❝❛ ❞♦ tr❛❜❛❧❤♦✱ ❛❜♦r❞❛♥❞♦✲s❡ ♦s ❝♦♥❤❡❝✐♠❡♥t♦s r❡❧❛❝✐♦♥❛❞♦s à ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦✿ ♠ét♦❞♦s ❡①❛t♦s ❡ ❤❡✉ríst✐❝♦s❀ ❡ s✐♠✉❧❛çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧✳

◆♦ ❝❛♣ít✉❧♦ ✹ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ❢♦r♠✉❧❛çã♦ ❞❡ ♣r♦❣r❛♠❛çã♦ ♠❛t❡♠át✐❝❛ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✱ ♣r♦♣♦st♦ ✉♠ ❛❧❣♦r✐t♠♦ ❣❡♥ét✐❝♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ❡ ✉♠ ♠♦❞❡❧♦ ❞❡ s✐♠✉❧❛çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❝❛♣❛③ ❞❡ ✈❛❧✐❞❛r ♦s r❡s✉❧t❛❞♦s ❡ ❞❡t❡r♠✐♥❛r ♦ s❡q✉❡♥❝✐❛♠✲ ♥❡t♦ ❞♦s ❝❛♠✐♥❤õ❡s✳

◆♦ ❝❛♣ít✉❧♦ ✺ sã♦ ❛♣r❡s❡♥t❛❞♦s ❡ ❞✐s❝✉t✐❞♦s ♦s r❡s✉❧t❛❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ♦❜t✐❞♦s ❝♦♠ ❛ ❛♣❧✐❝❛çã♦ ❞❛ ❢♦r♠✉❧❛çã♦ ❞❡ ♣r♦❣r❛♠❛çã♦ ♠❛t❡♠át✐❝❛ ♣r♦♣♦st❛✱ ❞♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ❡ ❞♦ ♠♦❞❡❧♦ ❞❡ s✐♠✉❧❛çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧✳

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◆♦ ❝❛♣ít✉❧♦ ✻ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ❝♦♥❝❧✉sõ❡s s♦❜r❡ ♦ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✈✐❞♦ ❡ r❡❝♦♠❡♥❞❛çõ❡s ♣❛r❛ tr❛❜❛❧❤♦s ❢✉t✉r♦s✳

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❈❛♣ít✉❧♦ ✷

Pr♦❜❧❡♠❛ ❆❜♦r❞❛❞♦

❖ ♣r♦❜❧❡♠❛ ❡♠ ❡st✉❞♦ tr❛t❛ ❞♦ ♣❧❛♥❡❥❛♠❡♥t♦ ♦♣❡r❛❝✐♦♥❛❧ ❞❡ ❧❛✈r❛ ❞❡ ✉♠❛ ♠✐♥❛ ❛ ❝é✉ ❛❜❡rt♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛❧♦❝❛çã♦ ❞✐♥â♠✐❝❛ ❞❡ ❝❛♠✐♥❤õ❡s ✭P❖▲❆❉✮✳ ❈♦♠♦ ✈❡♠♦s ♥❛ ❋✐❣✳ ✷✳✶✱ ❡①tr❛í❞❛ ❞❡ ❙♦✉③❛ ❡t ❛❧✳ ✭✷✵✶✵✮✱ ♦ P❖▲❆❉ é ❝♦♠♣♦st♦ ♣♦r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❢r❡♥t❡s ❞❡ ❧❛✈r❛✱ ❞❡ ❡q✉✐♣❛♠❡♥t♦s ❞❡ ❝❛r❣❛ ❡ ❞❡ ❝❛♠✐♥❤õ❡s✳ ❋r❡♥t❡ ❞❡ ❧❛✈r❛ é ♦ ❧♦❝❛❧ ♥♦ q✉❛❧ ❡♥❝♦♥tr❛✲s❡ ♦ ♠❛t❡r✐❛❧ ❛ s❡r r❡t✐r❛❞♦ ✭❧❛✈r❛❞♦✮✱ ❡q✉✐♣❛♠❡♥t♦s ❞❡ ❝❛r❣❛ sã♦ ♦s ❡q✉✐♣❛♠❡♥t♦s r❡s♣♦♥sá✈❡✐s ♣❡❧❛ r❡t✐r❛❞❛ ❞♦ ♠❛t❡r✐❛❧ ❞❛ ❢r❡♥t❡ ❞❡ ❧❛✈r❛ ❡ ❝❛rr❡❣❛♠❡♥t♦ ❞♦s ❝❛♠✐♥❤õ❡s✳ ❖s ❝❛♠✐♥❤õ❡s sã♦ r❡s♣♦♥sá✈❡✐s ♣❡❧♦ tr❛♥s♣♦rt❡ ❞♦ ♠❛t❡r✐❛❧ ❛té s❡✉ ♣♦♥t♦ ❞❡ ❞❡s❝❛r❣❛ ✭❞❡st✐♥♦✮✳

◆❡ss❡ ♣r♦❜❧❡♠❛ ❞❡s❡❥❛✲s❡ s❡❧❡❝✐♦♥❛r ❛s ❢r❡♥t❡s ❞❡ ❧❛✈r❛ q✉❡ s❡rã♦ ✉t✐❧✐③❛❞❛s✱ ❛❧♦❝❛r ❡q✉✐♣❛♠❡♥t♦s ❞❡ ❝❛r❣❛ às ♠❡s♠❛s ❡ ❞❡t❡r♠✐♥❛r ♦ ♥ú♠❡r♦ ❞❡ ✈✐❛❣❡♥s ❞❡ ❝❛❞❛ ❝❛♠✐♥❤ã♦ ❛ ❡ss❛s ❢r❡♥t❡s✳ ❖s ♦❜❥❡t✐✈♦s ❞❡ss❡ ♣r♦❜❧❡♠❛ sã♦ ♠✐♥✐♠✐③❛r ♦s ❞❡s✈✐♦s ❡♠ r❡❧❛çã♦ às ♠❡t❛s ❞♦s t❡♦r❡s ❞♦s ♣❛râ♠❡tr♦s ❞❡ q✉❛❧✐❞❛❞❡ ❡ ❞❡ ♣r♦❞✉çã♦ ❞❡ ♠✐♥ér✐♦ ❡ ♦ ♥ú♠❡r♦ ❞❡ ❝❛♠✐♥❤õ❡s ✉t✐❧✐③❛❞♦s✳

P❛r❛ ❛ s❡❧❡çã♦ ❞❛s ❢r❡♥t❡s q✉❡ s❡rã♦ ❡①♣❧♦r❛❞❛s ♥❛ ❝♦♠♣♦s✐çã♦ ❞❛ ♠✐st✉r❛✱ é ♥❡❝❡ssár✐♦ ❧❡✈❛r ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛s ❡s♣❡❝✐✜❝❛çõ❡s ❞♦ ♠✐♥ér✐♦ q✉❡ ♥❡❧❛ s❡ ❡♥❝♦♥tr❛✱ t❛✐s ❝♦♠♦ ❛ ♣❡r❝❡♥t❛❣❡♠ ❞❡ ❞❡t❡r♠✐♥❛❞♦s ❡❧❡♠❡♥t♦s q✉í♠✐❝♦s✱ ✪❋❡ ❡ ✪❙✐❖2✱ ♣♦r

❡①❡♠♣❧♦✳ ➱ ✐♠♣♦rt❛♥t❡ ♦❜s❡r✈❛r q✉❡ t❛✐s ❡s♣❡❝✐✜❝❛çõ❡s ✈❛r✐❛♠ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❝❛❞❛ ❢r❡♥t❡ ❞❡ ❧❛✈r❛✳ ❆ss✐♠✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❡s♣❡❝✐✜❝❛çã♦ r❡q✉❡r✐❞❛ ♣❛r❛ ♦ ♣r♦❞✉t♦ ❞❡s❡❥❛❞♦✱ ✉♠❛ ❢r❡♥t❡ ❞❡✈❡ t❡r ♣r✐♦r✐❞❛❞❡ ❡♠ r❡❧❛çã♦ à ♦✉tr❛✳

P♦r ♦✉tr♦ ❧❛❞♦✱ ♣❛r❛ ❛ r❡t✐r❛❞❛ ❞❡ ♠✐♥ér✐♦ ❞❛s ❢r❡♥t❡s ❞❡ ❧❛✈r❛ sã♦ ✉t✐❧✐③❛❞❛s

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❋✐❣✉r❛ ✷✳✶✿ ■❧✉str❛çã♦ ❞♦ P❖▲❆❉

❝❛rr❡❣❛❞❡✐r❛s✳ ➚ ❝❛❞❛ ❝❛rr❡❣❛❞❡✐r❛ é ❛ss♦❝✐❛❞❛ ✉♠❛ ♣r♦❞✉çã♦ ♠á①✐♠❛ ❡ ✉♠❛ ♣r♦❞✉✲ çã♦ ♠í♥✐♠❛✳ ❆ ♣r♦❞✉çã♦ ♠á①✐♠❛ é ❞❡t❡r♠✐♥❛❞❛ ♣❡❧❛ ❝❛♣❛❝✐❞❛❞❡ ♠á①✐♠❛ ♣r♦❞✉t✐✈❛ ❞♦ ❡q✉✐♣❛♠❡♥t♦✱ ❡♥q✉❛♥t♦ ❛ ♣r♦❞✉çã♦ ♠í♥✐♠❛ é ❡st❛❜❡❧❡❝✐❞❛ ❞❡ ❢♦r♠❛ ❛ t♦r♥❛r ❛ ✉t✐❧✐③❛çã♦ ❞❛ ❝❛rr❡❣❛❞❡✐r❛ ❡❝♦♥♦♠✐❝❛♠❡♥t❡ ✈✐á✈❡❧✳

P❛r❛ ❞❡t❡r♠✐♥❛r ♦ ♥ú♠❡r♦ ❞❡ ✈✐❛❣❡♥s ❞❡ ❝❛❞❛ ❝❛♠✐♥❤ã♦ ❛ ❝❛❞❛ ❢r❡♥t❡ é ♣r❡❝✐s♦ ❝♦♥s✐❞❡r❛r q✉❛❧ ❛ ❝❛rr❡❣❛❞❡✐r❛ ❛❧♦❝❛❞❛ à ❢r❡♥t❡✱ ❛ t❛①❛ ❞❡ ✉t✐❧✐③❛çã♦ ♠á①✐♠❛ ❞♦ ❝❛♠✐♥❤ã♦ ❡ ❛s ♠❡t❛s ❞❡ ♣r♦❞✉çã♦ ❞❡ ♠✐♥ér✐♦ ❡ ❡stér✐❧✳ ❆ ❝❛rr❡❣❛❞❡✐r❛ ❛❧♦❝❛❞❛ à ❢r❡♥t❡ ❞❡✈❡ s❡r ♦♣❡r❛❝✐♦♥❛❧♠❡♥t❡ ❝♦♠♣❛tí✈❡❧ ❝♦♠ ♦ ❝❛♠✐♥❤ã♦✳ ❆❧é♠ ❞✐ss♦✱ ❛ t❛①❛ ❞❡ ✉t✐❧✐③❛çã♦ ♠á①✐♠❛ ❞♦ ❝❛♠✐♥❤ã♦ ❞❡✈❡ s❡r r❡s♣❡✐t❛❞❛✱ ❞❡ ❢♦r♠❛ ❛ ❧✐♠✐t❛r ♦ ♥ú♠❡r♦ ❞❡ ✈✐❛❣❡♥s ❞❡ ❝❛❞❛ ❝❛♠✐♥❤ã♦ ♥♦ ♣❡rí♦❞♦ ❞❡ ✉♠❛ ❤♦r❛✳ ❆ ♣r♦❞✉çã♦ ❞❡ ♠✐♥ér✐♦ ❞❡✈❡ r❡s♣❡✐t❛r ✉♠❛ ♣r♦♣♦rçã♦ ✜①❛ ❡♠ r❡❧❛çã♦ à q✉❛♥t✐❞❛❞❡ ❞❡ ❡stér✐❧ ✭r❡❧❛çã♦ ❡stér✐❧✴♠✐♥ér✐♦✮✱ ❜❡♠ ❝♦♠♦ ❛s ♠❡t❛s ❞❡ ♣r♦❞✉çã♦✳ ❆s ♠❡t❛s ❞❡ ♣r♦❞✉çã♦ ❡ s❡✉s ❧✐♠✐t❡s ✐♥❢❡r✐♦r ❡ s✉♣❡r✐♦r sã♦ ❞❡✜♥✐❞♦s ♣❡❧❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞❛ ✉s✐♥❛ ❞❡ ❜❡♥❡✜❝✐❛♠❡♥t♦ q✉❡ r❡❝❡❜❡rá ♦ ♠✐♥ér✐♦ ♣r♦❞✉③✐❞♦✳

❈♦♥s✐❞❡r♦✉✲s❡ ♥❡st❡ tr❛❜❛❧❤♦ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠❛ ❢r♦t❛ ❤❡t❡r♦❣ê♥❡❛ ❞❡ ❝❛✲ ♠✐♥❤õ❡s✱ ♦✉ s❡❥❛✱ q✉❡ ❡❧❡s ♣♦ss✉❡♠ ❞✐❢❡r❡♥t❡s ❝❛♣❛❝✐❞❛❞❡s ❞❡ ❝❛r❣❛✳ ❆❧é♠ ❞✐ss♦✱ ❛❞♦t♦✉✲s❡ ♦ ♠ét♦❞♦ ❞❡ ❛❧♦❝❛çã♦ ❞✐♥â♠✐❝❛✱ ♦ q✉❡ s✐❣♥✐✜❝❛ q✉❡ ✉♠ ♠❡s♠♦ ❝❛♠✐♥❤ã♦ ♣♦❞❡ s❡r ❛❧♦❝❛❞♦ ❛ ❞✐❢❡r❡♥t❡s ❢r❡♥t❡s ❛♣ós ❝❛❞❛ ❞❡s❝❛r❣❛ ❞❡ ♠❛t❡r✐❛❧✳ ❊ss❛ té❝♥✐❝❛ ❞✐♠✐♥✉✐ ♦ t❡♠♣♦ ❞❡ ✜❧❛ ❡ ❛✉♠❡♥t❛ ❛ t❛①❛ ❞❡ ✉t✐❧✐③❛çã♦ ❞♦s ❝❛♠✐♥❤õ❡s✳

❆♦ ❝♦♥trár✐♦ ❞❛ ♠❛✐♦r✐❛ ❞♦s tr❛❜❛❧❤♦s ❛♥t❡r✐♦r❡s ❡♥❝♦♥tr❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦ ❈♦st❛ ❡t ❛❧✳ ✭✷✵✵✹✮✱ ●✉✐♠❛r❛❡s ❡t ❛❧✳ ✭✷✵✵✼✮✱ ▼❡rs❝❤♠❛♥♥ ✭✷✵✵✷✮

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❡ ❙♦✉③❛ ❡t ❛❧✳ ✭✷✵✶✵✮✱ ❝♦♥s✐❞❡r❛♠♦s ❞♦✐s ♣♦♥t♦s ❞❡ ❞❡s❝❛r❣❛ ♣❛r❛ ♦ ♠❛t❡r✐❛❧ ❧❛✈r❛❞♦✱ s❡♥❞♦ ♦ ❜r✐t❛❞♦r ♣r✐♠ár✐♦ ♣❛r❛ ❞❡s❝❛r❣❛ ❞❡ ♠✐♥ér✐♦ ❡ ❛ ♣✐❧❤❛ ❞❡ ❡stér✐❧ ♣❛r❛ ❞❡s✲ ❝❛r❣❛ ❞❡ ❡stér✐❧✳ ■st♦ s❡ ❞❡✈❡ ❛♦ ❢❛t♦ ❞❡ q✉❡ ❛s tr❛❥❡tór✐❛s ❞♦s ❝❛♠✐♥❤õ❡s ❛té ❛ ♣✐❧❤❛ ❞❡ ❡stér✐❧ ❡stã♦ ❝❛❞❛ ✈❡③ ♠❛✐s ❞✐st❛♥t❡s✱ ❞❡✈✐❞♦ às ♥♦r♠❛s ❞❡ ♣r♦t❡çã♦ ❛♠❜✐❡♥t❛❧✱ s❡♥❞♦ s✐❣♥✐✜❝❛t✐✈❛ ❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦s t❡♠♣♦s ❞❡ ✈✐❛❣❡♠ ❞❛s ❢r❡♥t❡s ❛té ♦ ❜r✐t❛❞♦r ❡ ❞❛s ❢r❡♥t❡s ❛té ❛ ♣✐❧❤❛ ❞❡ ❡stér✐❧✳ ❚❛♠❜é♠ ❝♦♥s✐❞❡r❛♠♦s ♦ t❡♠♣♦ ❞❡ ❝✐❝❧♦ ❞♦s ❡q✉✐♣❛♠❡♥t♦s ❝♦♠♦ ✉♠❛ ✈❛r✐á✈❡❧ q✉❡ ❞❡♣❡♥❞❡ ❞❛ ❢r❡♥t❡ ❞❡ ❧❛✈r❛✱ ❞♦ t✐♣♦ ❞❡ ❡q✉✐✲ ♣❛♠❡♥t♦✱ ❡ ❞♦ t✐♣♦ ❞❡ ♠❛t❡r✐❛❧ tr❛♥s♣♦rt❛❞♦✳ ■st♦ é ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ q✉❡ ❝❛❞❛ t✐♣♦ ❞❡ ❝❛♠✐♥❤ã♦ ❞❡♠❛♥❞❛ ✉♠ t❡♠♣♦ ❞✐❢❡r❡♥t❡ ♣❛r❛ ♣❡r❝♦rr❡r ✉♠ ♠❡s♠♦ tr❛❥❡t♦ ❡ ❡st❡ t❡♠♣♦ t❛♠❜é♠ é ✐♥✢✉❡♥❝✐❛❞♦ ♣❡❧♦ t✐♣♦ ❞❡ ❝❛r❣❛ ✭♠✐♥ér✐♦ ♦✉ ❡stér✐❧✮✳

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❈❛♣ít✉❧♦ ✸

❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛

◆❡st❡ ❝❛♣ít✉❧♦ é ❢❡✐t❛ ✉♠❛ r❡✈✐sã♦ ❞♦s tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s ❛♦ ♣r♦❜❧❡♠❛ ❡♠ ❡st✉❞♦✳ ❚❛♠❜é♠ é ❛♣r❡s❡♥t❛❞❛ ❛ ❢✉♥❞❛♠❡♥t❛çã♦ t❡ór✐❝❛ ♥❛ q✉❛❧ ❡st❡ tr❛❜❛❧❤♦ s❡ ❛♣ó✐❛✳

✸✳✶ ❖t✐♠✐③❛çã♦ ▼✉❧t✐♦❜❥❡t✐✈♦

❉❡ ❛❝♦r❞♦ ❝♦♠ ❚✐❝♦♥❛ ✭✷✵✵✸✮✱ ❛ ♠❛✐♦r ♣❛rt❡ ❞♦s ♣r♦❜❧❡♠❛s r❡❛✐s ❡♥❝♦♥tr❛❞♦s ♥❛ ár❡❛ ❞❡ ♦t✐♠✐③❛çã♦ ❡♥✈♦❧✈❡ ❛ ♦❜t❡♥çã♦ ❞❡ ❞✐✈❡rs❛s ♠❡t❛s q✉❡ ❞❡✈❡♠ s❡r ❛t✐♥❣✐❞❛s s✐♠✉❧t❛♥❡❛♠❡♥t❡✳ ❊❧❛s ❣❡r❛❧♠❡♥t❡ sã♦ ❝♦♥✢✐t❛♥t❡s✱ ♦✉ s❡❥❛✱ ♥ã♦ ❡①✐st❡ ✉♠❛ s♦❧✉çã♦ ú♥✐❝❛ q✉❡ ♦t✐♠✐③❡ t♦❞❛s ❛♦ ♠❡s♠♦ t❡♠♣♦✳ P❛r❛ t❛❧ ❝❧❛ss❡ ❞❡ ♣r♦❜❧❡♠❛s ❞❡✈❡♠♦s ❜✉s❝❛r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ s♦❧✉çõ❡s ❡✜❝✐❡♥t❡s✳

Pr♦❜❧❡♠❛s ❞❡ss❛ ♥❛t✉r❡③❛ sã♦ ❝❤❛♠❛❞♦s ❞❡ ♣r♦❜❧❡♠❛s ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐✲ ♦❜❥❡t✐✈♦ ♣♦r ❡♥✈♦❧✈❡r❡♠ ♠✐♥✐♠✐③❛çã♦ ✭♦✉ ♠❛①✐♠✐③❛çã♦✮ s✐♠✉❧tâ♥❡❛ ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ♦❜❥❡t✐✈♦s s❛t✐s❢❛③❡♥❞♦ ❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ r❡str✐çõ❡s✳ ◆❡st❡ ❝❛s♦✱ ❛ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ s❡rá ❞❡ r❡s♣♦♥s❛❜✐❧✐❞❛❞❡ ❞♦ ❛♥❛❧✐st❛✱ q✉❡ ❞❡✈❡rá ♣♦♥❞❡r❛r ♦s ♦❜❥❡t✐✈♦s ❣❧♦✲ ❜❛✐s ❞♦ ♣r♦❜❧❡♠❛ ❡ ❡s❝♦❧❤❡r ✉♠❛ ❡♥tr❡ ❛s s♦❧✉çõ❡s ❞♦ ❝♦♥❥✉♥t♦ ❞❡ s♦❧✉çõ❡s ❡✜❝✐❡♥t❡s ✭❆rr♦②♦✱ ✷✵✵✷✮✳

❊st❡ é s❡♠ ❞ú✈✐❞❛ ✉♠ ✐♠♣♦rt❛♥t❡ tó♣✐❝♦ ❞❛ ♦t✐♠✐③❛çã♦✱ t❛♥t♦ ♣❛r❛ ♣❡s✲ q✉✐s❛❞♦r❡s q✉❛♥t♦ ♣❛r❛ ❡♥❣❡♥❤❡✐r♦s✱ ♥ã♦ só ♣♦r ❝❛✉s❛ ❞❡ s✉❛ ❛♣❧✐❝❛❜✐❧✐❞❛❞❡ ♥♦s ♣r♦❜❧❡♠❛s r❡❛✐s✱ ♠❛s t❛♠❜é♠ ♣❡❧❛s q✉❡stõ❡s ❛✐♥❞❛ ❡♠ ❛❜❡rt♦ ♥❡ss❛ ár❡❛ ✭❈♦❡❧❧♦✱ ✶✾✾✾❀ ❩✐t③❧❡r✱ ✶✾✾✾✮✳

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✸✳✶✳✶ ❈♦♥❝❡✐t♦s ❇ás✐❝♦s

P❛r❛ ❈♦❡❧❧♦ ✭✶✾✾✾✮✱ ❛ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ♣♦❞❡ s❡r ❞❡✜♥✐❞❛ ❝♦♠♦ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❛❝❤❛r ✉♠ ✈❡t♦r ❞❡ ✈❛r✐á✈❡✐s ❞❡ ❞❡❝✐sã♦ ❝✉❥♦s ❡❧❡♠❡♥t♦s r❡♣r❡s❡♥t❛♠ ❛s ❢✉♥çõ❡s ♦❜✲ ❥❡t✐✈♦s✳ ❊ss❛s ❢✉♥çõ❡s ❢♦r♠❛♠ ✉♠❛ ❞❡s❝r✐çã♦ ♠❛t❡♠át✐❝❛ ❞♦ ❝r✐tér✐♦ ❞❡ ♦t✐♠❛❧✐❞❛❞❡ q✉❡ ❡stã♦ ❡♠ ❝♦♥✢✐t♦ ✉♠❛s ❝♦♠ ❛s ♦✉tr❛s✳ ◆❡st❡ ❝❛s♦✱ ♦ t❡r♠♦ ✏♦t✐♠✐③❛r✑ s✐❣♥✐✜❝❛ ❡♥❝♦♥tr❛r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ s♦❧✉çõ❡s q✉❡ ♥ã♦ ♣♦❞❡♠ s❡r ♠❡❧❤♦r❛❞❛s s✐♠✉❧tâ♥❡❛♠❡♥t❡ ♣❛r❛ ♦ ❛♥❛❧✐st❛✳

❋♦r♠❛❧♠❡♥t❡✱ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ♣♦❞❡ s❡r ❢♦r♠✉❧❛❞♦ ❝♦♠♦✿

minimizar z =f(x) = (f1(x), f2(x),· · ·, fOB(x)) ✭✸✳✶✮

s✉❥❡✐t♦ ❛: g(x) = (g1(x), g2(x), g3(x),· · · , gr(x))≤b ✭✸✳✷✮ x= (x1, x2, x3,· · · , xn)∈X ✭✸✳✸✮ z = (z1, z2, z3,· · ·, zr)∈Z ✭✸✳✹✮

♥❛ q✉❛❧ x é ♦ ✈❡t♦r ❞❡ ❞❡❝✐sã♦✱ OB ♦ ♥ú♠❡r♦ ❞❡ ♦❜❥❡t✐✈s✱ z é ♦ ✈❡t♦r ♦❜❥❡t✐✈♦✱ X

❞❡♥♦t❛ ♦ ❡s♣❛ç♦ ❞❡ ❜✉s❝❛ ❞❡ ❞❡❝✐sõ❡s✱ ❡ z = f(x) é ❛ ✐♠❛❣❡♠ ❞❡ X✱ ❞❡♥♦♠✐♥❛❞❛

❡s♣❛ç♦ ♦❜❥❡t✐✈♦✳

❖ ❝♦♥❥✉♥t♦ ❞❡ r❡str✐çõ❡s g(x) ≤ b | b ∈ R+ ❡ ♦ ❡s♣❛ç♦ X ❞❡t❡r♠✐♥❛♠ ♦

❝♦♥❥✉♥t♦ ❞❛s s♦❧✉çõ❡s ✈✐á✈❡✐s ♦✉ ❢❛❝tí✈❡✐s✿ X∗ ={x∈X |g(x)≤b}✳

P♦rt❛♥t♦✱ ♦ ♣r♦❜❧❡♠❛ ♠✉❧t✐♦❜❥❡t✐✈♦ ♣♦❞❡ s❡r ❡s❝r✐t♦ ❞❛ ❢♦r♠❛✿

minimizar z = (f1(x), f2(x),· · · , fr(x)) ✭✸✳✺✮

s✉❥❡✐t♦ ❛: x∈X∗ ✭✸✳✻✮

❆ ✐♠❛❣❡♠ ❞❡ X∗ é ❞❡♥♦♠✐♥❛❞❛ ❡s♣❛ç♦ ♦❜❥❡t✐✈♦ ❢❛❝tí✈❡❧ ❡ é ❞❡♥♦t❛❞❛ ♣♦r Z∗ =f(X∗) ={f(x)|x∈X∗}✳

❊♥q✉❛♥t♦ q✉❡ ♥❛ ♦t✐♠✐③❛çã♦ ♠♦♥♦✲♦❜❥❡t✐✈♦ ✉♠❛ s♦❧✉çã♦ ót✐♠❛ é ❝❧❛r❛♠❡♥t❡

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✐❞❡♥t✐✜❝❛❞❛✱ ♣♦✐s ♦ ❡s♣❛ç♦ ❞❡ s♦❧✉çã♦ é ♦r❞❡♥❛❞♦✱ ♥❛ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦✱ ♣♦r ♦✉tr♦ ❧❛❞♦✱ ❤á ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❛❧t❡r♥❛t✐✈❛s✱ ❣❡r❛❧♠❡♥t❡ ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ s♦❧✉çõ❡s P❛r❡t♦✲ót✐♠❛s✱ q✉❡✱ ♣❛r❛ ❋♦♥s❡❝❛ ❡ ❋❧❡♠✐♥❣ ✭✶✾✾✺✮✱ t❛♠❜é♠ ♣♦❞❡♠ s❡r ❞❡♥♦♠✐♥❛❞❛s ❝♦♠♦ s♦❧✉çõ❡s ❡✜❝✐❡♥t❡s✱ ♦✉ ❝♦♥❥✉♥t♦ ❛❞♠✐ssí✈❡❧ ❞♦ ♣r♦❜❧❡♠❛✳

❙❡❣✉♥❞♦ P❛r❡t♦ ✭✶✽✾✻✮✱ ♦ ❝♦♥❝❡✐t♦ ❞❡ P❛r❡t♦✲ót✐♠♦ ❝♦♥st✐t✉✐ ❛ ♦r✐❣❡♠ ❞❛ ❜✉s❝❛ ♥❛ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦✳ P❡❧❛ ❞❡✜♥✐çã♦✱ ✉♠ ✈❡t♦rz é P❛r❡t♦✲ót✐♠♦ s❡ ♥ã♦

❡①✐st❡ ✉♠ ♦✉tr♦ ✈❡t♦r ✈✐á✈❡❧z∗ q✉❡ ♣♦ss❛ ♠❡❧❤♦r❛r ❛❧❣✉♠ ♦❜❥❡t✐✈♦✱ s❡♠ ❝❛✉s❛r ✉♠❛

♣✐♦r❛ ❡♠ ♣❡❧♦ ♠❡♥♦s ✉♠ ♦✉tr♦ ♦❜❥❡t✐✈♦✳ ❊♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ ✉♠ ✈❡t♦r s♦❧✉çã♦ z

♣❡rt❡♥❝❡ ❛♦ ❝♦♥❥✉♥t♦ ❞❡ s♦❧✉çõ❡s P❛r❡t♦✲ót✐♠♦ s❡ ♥ã♦ ❡①✐st❡ ♥❡♥❤✉♠ ✈❡t♦r s♦❧✉çã♦

z∗ q✉❡ ❞♦♠✐♥❡ z

❈♦♥s✐❞❡r❛♥❞♦ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ♠✐♥✐♠✐③❛çã♦✱ t❡♠♦s✿

• z ❞♦♠✐♥❛z∗ s❡✱ ❡ s♦♠❡♥t❡ s❡✱ z

j ≤z∗j ∀j ❡zj < z∗j ♣❛r❛ ❛❧❣✉♠ j❀

• z ❡z∗ sã♦ ✐♥❞✐❢❡r❡♥t❡s ♦✉ ♣♦ss✉❡♠ ♦ ♠❡s♠♦ ❣r❛✉ ❞❡ ❞♦♠✐♥â♥❝✐❛ s❡✱ ❡ s♦♠❡♥t❡

s❡✱ z ♥ã♦ ❞♦♠✐♥❛ z∗ ❡ z∗ ♥ã♦ ❞♦♠✐♥❛z✳

◆❡st❡ ú❧t✐♠♦ ❝❛s♦✱ ❛s s♦❧✉çõ❡s ♥ã♦ ♣♦❞❡♠ s❡r ✐❞❡♥t✐✜❝❛❞❛s ❝♦♠♦ ♠❡❧❤♦r q✉❡ ❛s ♦✉tr❛s✱ ❛ ♠❡♥♦s q✉❡ ✐♥❢♦r♠❛çõ❡s ❞❡ ♣r❡❢❡rê♥❝✐❛ ❡♠ r❡❧❛çã♦ ❛♦s ♦❜❥❡t✐✈♦s s❡❥❛♠ ✐♥❝❧✉í❞❛s✳

❙❡❣✉♥❞♦ ❋♦♥s❡❝❛ ❡ ❋❧❡♠✐♥❣ ✭✶✾✾✺✮✱ ❛ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ❞✐✈❡r❣❡ ❞❛ ♦t✐♠✐③❛çã♦ ♠♦♥♦✲♦❜❥❡t✐✈♦✱ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ r❛r❛♠❡♥t❡ ❛❞♠✐t✐r ✉♠❛ s✐♠♣❧❡s s♦❧✉çã♦✳ P♦r ✐ss♦✱ ❛ s♦❧✉çã♦ é ❝♦♠♣♦st❛ ♣♦r ✉♠❛ ❢❛♠í❧✐❛ ❞❡ s♦❧✉çõ❡s ♣❛r❡t♦✲❡✜❝✐❡♥t❡s ✭♦✉ ♣❛r❡t♦✲ót✐♠❛s✮ q✉❡ ❞❡✈❡♠ s❡r ❝♦♥s✐❞❡r❛❞♦s ❡q✉✐✈❛❧❡♥t❡s✱ ❡♠ ✈✐st❛ ❞❛ ❛✉sê♥❝✐❛ ❞❡ ✐♥❢♦r♠❛çã♦ r❡❢❡r❡♥t❡ à ✐♠♣♦rtâ♥❝✐❛ ❞❡ ❝❛❞❛ ♦❜❥❡t✐✈♦✳

❉❡ ❛❝♦r❞♦ ❝♦♠ P❡r❡✐r❛ ✭✷✵✵✹✮✱ à ♠❡❞✐❞❛ q✉❡ s❡ ❛✉♠❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ♦❜❥❡✲ t✐✈♦s ❛ s❡r❡♠ ♦t✐♠✐③❛❞♦s✱ ❡ t❛♠❜é♠✱ ♣♦♥❞❡r❛❞♦s ♦s ♦❜❥❡t✐✈♦s ♠❡♥♦s ✏❜❡♠ ❝♦♠♣♦r✲ t❛❞♦s✑✱ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❜✉s❝❛r ✉♠❛ s♦❧✉çã♦ ♣❛r❡t♦✲ót✐♠❛ t♦r♥❛✲s❡ ❝♦♠♣❧❡①♦ ❞❡ ❢♦r♠❛ rá♣✐❞❛ ❡ ♣r♦❣r❡ss✐✈❛✳

❊♠ ❛❧❣✉♥s ❝❛s♦s✱ ❛s ❢✉♥çõ❡s ♦❜❥❡t✐✈♦s ♣♦❞❡r✐❛♠ s❡r ♦t✐♠✐③❛❞❛s s❡♣❛r❛❞❛✲ ♠❡♥t❡✱ ✉♠❛ ❛ ✉♠❛ ❜✉s❝❛♥❞♦ ✉♠ ❣❛♥❤♦ ♥♦ t❡♠♣♦ ❝♦♠♣✉t❛❝✐♦♥❛❧✳ P♦ré♠✱ s♦❧✉çõ❡s

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s❛t✐s❢❛tór✐❛s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❣❧♦❜❛❧ r❛r❛♠❡♥t❡ ♣♦❞❡r✐❛♠ s❡r ❛❝❤❛❞❛s ♥❡st❡ s❡♥t✐❞♦✳ ❖✉ s❡❥❛✱ ✉♠❛ s♦❧✉çã♦ ót✐♠❛ ❡♠ ✉♠ ♦❜❥❡t✐✈♦✱ s❡ t❛❧ ót✐♠♦ ❡①✐st❡✱ ❝♦♠✉♠❡♥t❡ ✐♠✲ ♣❧✐❝❛ ❞❡s❡♠♣❡♥❤♦ ✐♥❛❝❡✐tá✈❡❧ ❡♠ ✉♠ ♦✉ ♠❛✐s ❞♦s ♦✉tr♦s ♦❜❥❡t✐✈♦s✱ r❡s✉❧t❛♥❞♦ ♥❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡ ❢❛③❡r ✉♠ ❛❥✉st❡✳

P❛r❛ ❛❧❣✉♥s ❛✉t♦r❡s✱ ❝♦♠♦ P❡r❡✐r❛ ✭✷✵✵✹✮✱ ♦s ♠ét♦❞♦s ❞❡ ♦t✐♠✐③❛çã♦ ❝♦♥✲ ✈❡♥❝✐♦♥❛❧✱ ❝♦♠♦ ♦s ❜❛s❡❛❞♦s ♥♦ ●r❛❞✐❡♥t❡ ❡ ♥♦ ❙✐♠♣❧❡①✱ ❛❞❛♣t❛❞♦s ❛♦s ♣r♦❜❧❡♠❛s ♠✉❧t✐♦❜❥❡t✐✈♦ ❛♣r❡s❡♥t❛♠ r❡str✐çõ❡s ❡ t♦r♥❛♠✲s❡ ✐♥❡✜❝✐❡♥t❡s✳ ◆❡st❡ ❝❛s♦✱ ❞❡✈❡♠♦s ❜✉s❝❛r ♥♦✈♦s ♠ét♦❞♦s ❞❡ ♦t✐♠✐③❛çã♦ ♣❛r❛ ❡st❛ ❣❛♠❛ ❞❡ ♣r♦❜❧❡♠❛s✳

✸✳✶✳✷ ▼ét♦❞♦s ❞❡ ❖t✐♠✐③❛çã♦ ▼✉❧t✐♦❜❥❡t✐✈♦

❊♠ ✈✐st❛ ❞❛ ❡①✐stê♥❝✐❛ ❞❡ ♦❜❥❡t✐✈♦s ❝♦♥✢✐t❛♥t❡s✱ ❡♥❝♦♥tr❛r s♦❧✉çõ❡s ✈✐á✈❡✐s q✉❡ ♦t✐✲ ♠✐③❡♠ s✐♠✉❧t❛♥❡❛♠❡♥t❡ t♦❞♦s ♦s ♦❜❥❡t✐✈♦s é ♦ ♠❛✐♦r ❞❡s❛✜♦ ❞❛ ♦t✐♠✐③❛çã♦ ♠✉❧t✐✲ ♦❜❥❡t✐✈♦✳

❙❡❣✉♥❞♦ ❍♦r♥ ✭✶✾✾✼✮✱ ♥❛ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ♠✉❧t✐♦❜❥❡t✐✈♦s✱ ❞♦✐s ♣r♦❜❧❡✲ ♠❛s ♣♦❞❡♠ s❡r ✐❞❡♥t✐✜❝❛❞♦s✿ ❜✉s❝❛ ❞❡ s♦❧✉çõ❡s ❡ t♦♠❛❞❛ ❞❡ ❞❡❝✐sõ❡s✳

❖ ♣r✐♠❡✐r♦ r❡❢❡r❡✲s❡ ❛♦ ♣r♦❝❡ss♦ ❞❡ ♦t✐♠✐③❛çã♦ ♥♦ q✉❛❧ ♦ ❝♦♥❥✉♥t♦ ❞❡ s♦❧✉✲ çõ❡s ✈✐á✈❡✐s✱ ♦✉ ❢❛❝tí✈❡✐s✱ ❞❡✈❡ s❡r ❣✉✐❛❞♦ ♣❛r❛ ♦ ❡♥❝♦♥tr♦ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ s♦❧✉çõ❡s P❛r❡t♦✲Ót✐♠❛s✳

❖ s❡❣✉♥❞♦ ♣r♦❜❧❡♠❛✱ ❞❡ t♦♠❛❞❛ ❞❡ ❞❡❝✐sõ❡s✱ ❝♦♥s✐st❡ ♥❛ s❡❧❡çã♦ ❞❡ ✉♠ ❝r✐tér✐♦ ❛♣r♦♣r✐❛❞♦ ♣❛r❛ ❛ ❡s❝♦❧❤❛ ❞❡ ✉♠❛ s♦❧✉çã♦ ❞♦ ❝♦♥❥✉♥t♦ P❛r❡t♦✲Ót✐♠♦✳ ❊st❡ ❝r✐tér✐♦ s❡rá ✉t✐❧✐③❛❞♦ ♣❡❧♦ r❡s♣♦♥sá✈❡❧✱ ♦✉ ❞❡❝✐s♦r✱ ♣❛r❛ ❛ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦✱ ♦✉ s❡❥❛✱ ❡❧❡ ♣♦❞❡rá ♣♦♥❞❡r❛r ❡♥tr❡ ❛s ❞✐❢❡r❡♥t❡s s♦❧✉çõ❡s ❝♦♥✢✐t❛♥t❡s✳

P❛r❛ ♠✉✐t♦s ❛✉t♦r❡s✱ ❝♦♠♦ ❩✐t③❧❡r ✭✶✾✾✾✮✱ ❱❡❧❞❤✉✐③❡♥ ❡ ▲❛♠♦♥t ✭✷✵✵✵✮✱ ❋♦♥s❡❝❛ ❡ ❋❧❡♠✐♥❣ ✭✶✾✾✺✮ ❡ ❆rr♦②♦ ✭✷✵✵✷✮✱ ♦s ♠ét♦❞♦s ❞❡ ♦t✐♠✐③❛çã♦ ♠✉❧t✐♦❜❥❡t✐✈♦ ♣♦❞❡♠ s❡r ❝❧❛ss✐✜❝❛❞♦s ❞❡♥tr♦ ❞❡ três ❝❛t❡❣♦r✐❛s✿

• ▼ét♦❞♦ ❛✲♣r✐♦r✐ ♦✉ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ ❛♥t❡s ❞❛ ❜✉s❝❛✳ • ▼ét♦❞♦ ❛✲♣♦st❡r✐♦r✐ ♦✉ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ ❞❡♣♦✐s ❞❛ ❜✉s❝❛✳ • ▼ét♦❞♦ ✐t❡r❛t✐✈♦ ♦✉ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ ❞✉r❛♥t❡ ❛ ❜✉s❝❛✳

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