SLIDE 1
Theoretical Foundations of SBSE Xin Yao CERCIA, School of Computer - - PowerPoint PPT Presentation
Theoretical Foundations of SBSE Xin Yao CERCIA, School of Computer - - PowerPoint PPT Presentation
Theoretical Foundations of SBSE Xin Yao CERCIA, School of Computer Science University of Birmingham Some Theoretical Foundations of SB SE Xin Yao and Many Others CERCIA, School of Computer Science University of Birmingham
SLIDE 2
SLIDE 3
▼♦t✐✈❛t✐♦♥ ❢♦r t❤❡♦r❡t✐❝❛❧ ❛♥❛❧②s✐s ♦❢ ❊❆s
❊❆s ❤❛✈❡ ♠❛♥② ❛ttr❛❝t✐✈❡ ❢❡❛t✉r❡s
■ ❡❛s❡ ♦❢ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ■ ❛♣♣❧✐❝❛❜❧❡ ✐♥ ❛ ✇✐❞❡ r❛♥❣❡ ♦❢ ❞♦♠❛✐♥s ■ r❡s✉❧ts ♦❢t❡♥ ❝♦♠♣❡t✐t✐✈❡ ✇✐t❤ tr❛❞✐t✐♦♥❛❧ t❡❝❤♥✐q✉❡s✱
❜✉t t❤❡ ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ ❤♦✇ ❊❆s r❡❛❧❧② ✇♦r❦ ✐s ✐♥❝♦♠♣❧❡t❡
■ ❝❛♥ ❜❡ ❤✐❣❤❧② s❡♥s✐t✐✈❡ t♦ ❝❤♦✐❝❡ ♦❢ ♣❛r❛♠❡t❡r s❡tt✐♥❣s ■ ❡①♣❡r✐♠❡♥t❛❧ ♣❛r❛♠❡t❡r t✉♥✐♥❣ ❡①♣❡♥s✐✈❡ ■ ✐♥ ♠♦st ❝❛s❡s✱ r✉♥ ❊❆ ❛♥❞ s❡❡ ✇❤❛t ❤❛♣♣❡♥s ■ ✳✳✳
SLIDE 4
❚r❛❞✐t✐♦♥❛❧ ■♥✈❡st✐❣❛t✐♦♥ ♦❢ ❊❆s
❘✉♥ ❛❧❣♦r✐t❤♠✭s✮ ♦♥ ❭r❡❛❧ ✇♦r❧❞✧ ♣r♦❜❧❡♠ ✐♥st❛♥❝❡✭s✮✳ ❆♥❛❧②s❡ r❡s✉❧ts ✇✐t❤ s♦♠❡ st❛t✐st✐❝❛❧ ♠❡t❤♦❞♦❧♦❣②✳ ❍♦✇ r❡♣r❡s❡♥t❛t✐✈❡ ❛r❡ t❤❡ r❡s✉❧ts❄
■ ❈❛♥ ✇❡ ♠❛❦❡ ❛♥② ❣✉❛r❛♥t❡❡ ❛❜♦✉t ♣❡r❢♦r♠❛♥❝❡❄ ■ ❲❤❛t ❤❛♣♣❡♥s ♦♥ ♦t❤❡r ✐♥st❛♥❝❡s❄ ■ ❲❤❛t ❤❛♣♣❡♥s ❢♦r ❧❛r❣❡r ✐♥st❛♥❝❡ s✐③❡s❄ ■ ❲❤❛t ❤❛♣♣❡♥s ❢♦r ♦t❤❡r ♣❛r❛♠❡t❡r s❡tt✐♥❣s❄
❍♦✇ ❝❛♥ t❤❡ r❡s✉❧ts ❜❡ ❡①♣❧❛✐♥❡❞❄
■ ❲❤② ❞♦❡s✴❞♦❡s ♥♦t t❤❡ ❛❧❣♦r✐t❤♠ ✇♦r❦❄ ■ ❈❛♥ t❤❡ ❛❧❣♦r✐t❤♠ ❜❡ ✐♠♣r♦✈❡❞❄
❂ ✮ ❲❤② ♥♦t ❛tt❡♠♣t t❤❡ ✇❡❧❧ ❡st❛❜❧✐s❤❡❞ ♠❡t❤♦❞♦❧♦❣② t❤❛t ❡①✐sts ❢♦r ❛♥❛❧②s✐♥❣ ❝❧❛ss✐❝❛❧ ❛❧❣♦r✐t❤♠s❄
SLIDE 5
❊✈♦❧✉t✐♦♥❛r② ❆❧❣♦r✐t❤♠s ❛r❡ ❆❧❣♦r✐t❤♠s
❈r✐t❡r✐❛ ❢♦r ❡✈❛❧✉❛t✐♥❣ ❛❧❣♦r✐t❤♠s ✶✳ ❈♦rr❡❝t♥❡ss✳
■ ❉♦❡s t❤❡ ❛❧❣♦r✐t❤♠ ❛❧✇❛②s ❣✐✈❡ t❤❡ ❝♦rr❡❝t ♦✉t♣✉t❄
✷✳ ❈♦♠♣✉t❛t✐♦♥❛❧ ❈♦♠♣❧❡①✐t②✳
■ ❍♦✇ ♠✉❝❤ ❝♦♠♣✉t❛t✐♦♥❛❧ r❡s♦✉r❝❡s ❞♦❡s
t❤❡ ❛❧❣♦r✐t❤♠ r❡q✉✐r❡ t♦ s♦❧✈❡ t❤❡ ♣r♦❜❧❡♠❄
❙❛♠❡ ❝r✐t❡r✐❛ ❛❧s♦ ❛♣♣❧✐❝❛❜❧❡ t♦ s❡❛r❝❤ ❤❡✉r✐st✐❝s ✶✳ ❈♦rr❡❝t♥❡ss✳
■ ❉✐s❝♦✈❡r ❣❧♦❜❛❧ ♦♣t✐♠✉♠ ✐♥ ☞♥✐t❡ t✐♠❡❄
✷✳ ❈♦♠♣✉t❛t✐♦♥❛❧ ❈♦♠♣❧❡①✐t②✳
■ ❚✐♠❡ ✭♥✉♠❜❡r ♦❢ ❢✉♥❝t✐♦♥ ❡✈❛❧✉❛t✐♦♥s✮
♠♦st r❡❧❡✈❛♥t ❝♦♠♣✉t❛t✐♦♥❛❧ r❡s♦✉r❝❡✳
SLIDE 6
❲♦rst ❈❛s❡ ❈♦♠♣✉t❛t✐♦♥❛❧ ❈♦♠♣❧❡①✐t②
❭r❡❛❧ ✇♦r❧❞✧ ✐♥st❛♥❝❡ ❤❛r❞ ✐♥st❛♥❝❡ r✉♥t✐♠❡ ✐♥st❛♥❝❡s
❭❘❡❛❧ ✇♦r❧❞✧ r✉♥t✐♠❡✿ ❘✉♥t✐♠❡ ♦♥ ❭r❡❛❧ ✇♦r❧❞✧ ✐♥st❛♥❝❡s
■ ❆r❡ t❤❡s❡ ✐♥st❛♥❝❡s st✐❧❧ r❡❧❡✈❛♥t ✐♥ ✶✵ ②❡❛rs❄ ■♥ ✶✵✵ ②❡❛rs❄
❆✈❡r❛❣❡ ❝❛s❡ r✉♥t✐♠❡✿ ❘✉♥t✐♠❡ ❛✈❡r❛❣❡❞ ♦✈❡r ✐♥st❛♥❝❡s
■ ❲❤❛t ✐s ❛♥ ❛✈❡r❛❣❡ ✐♥♣✉t ✭❡✳❣✳ ❛✈❡r❛❣❡ ❋❙▼✮❄
❲♦rst ❝❛s❡ r✉♥t✐♠❡✿ ❘✉♥t✐♠❡ ♦♥ ❤❛r❞❡st ✐♥st❛♥❝❡
■ ❙tr♦♥❣ ❣✉❛r❛♥t❡❡ ❛❜♦✉t ♣❡r❢♦r♠❛♥❝❡ ♦❢ ❛♥ ❛❧❣♦r✐t❤♠✳ ■ ▲♦✇❡r ❜♦✉♥❞s ♦❜t❛✐♥❡❞ ❜② ❛♥❛❧②s✐♥❣ r✉♥t✐♠❡
♦♥ s♣❡❝✐☞❝ ❤❛r❞ ♣r♦❜❧❡♠ ✐♥st❛♥❝❡✳
SLIDE 7
❈♦♠♣✉t❛t✐♦♥❛❧ ❈♦♠♣❧❡①✐t② ♦❢ ❙❡❛r❝❤ ❍❡✉r✐st✐❝s
50 100 10000 Instance Size Runtime
Pr❡❞✐❝t✐♦♥ ♦❢ r❡s♦✉r❝❡s ♥❡❡❞❡❞ ❢♦r ❛ ❣✐✈❡♥ ✐♥st❛♥❝❡✳ ❯s✉❛❧❧② r✉♥t✐♠❡ ❛s ❢✉♥❝t✐♦♥ ♦❢ ✐♥st❛♥❝❡ s✐③❡✳ ◆✉♠❜❡r ♦❢ ☞t♥❡ss ❡✈❛❧✉❛t✐♦♥s ❜❡❢♦r❡ ☞♥❞✐♥❣ ♦♣t✐♠✉♠✳
■ ❊①♣♦♥❡♥t✐❛❧ r✉♥t✐♠❡ ❂
✮ ■♥❡✍❝✐❡♥t ❛❧❣♦r✐t❤♠✳
■ P♦❧②♥♦♠✐❛❧ r✉♥t✐♠❡ ❂
✮ ❭❊✍❝✐❡♥t✧ ❛❧❣♦r✐t❤♠✳ ❆s②♠♣t♦t✐❝ ♥♦t❛t✐♦♥ ❤✐❞❡s ❭✉♥✐♠♣♦rt❛♥t✧ ❞❡t❛✐❧s ❛❜♦✉t r✉♥t✐♠❡✳
SLIDE 8
❙❡❛r❝❤ ❍❡✉r✐st✐❝ ❛r❡ ❘❛♥❞♦♠✐s❡❞ ❆❧❣♦r✐t❤♠s
❊❬❚♥❪ ❢✭♥✮ ❊❬❚♥❪ ❢✭♥✮ ♥ ■♥st❛♥❝❡ ❙✐③❡
❙❡❛r❝❤ ❤❡✉r✐st✐❝s ❞❡♣❡♥❞ ♦♥ r❛♥❞♦♠ ✐♥♣✉ts
■ ❘✉♥t✐♠❡ ❞✐☛❡rs ❜❡t✇❡❡♥ r✉♥s✳
❊①♣❡❝t❡❞ r✉♥t✐♠❡
■ ❘✉♥t✐♠❡ ❛✈❡r❛❣❡❞ ♦✈❡r ♣♦ss✐❜❧❡ r❛♥❞♦♠ ✐♥♣✉ts✳
❙✉❝❝❡ss ♣r♦❜❛❜✐❧✐t②
■ Pr♦❜❛❜✐❧✐t② ♦❢ ☞♥✐s❤✐♥❣ ✇✐t❤✐♥ ❛ s♣❡❝✐☞❡❞ t✐♠❡ ❢✭♥✮✳
SLIDE 9
❘❡s❡❛r❝❤ ❖❜❥❡❝t✐✈❡s ❛♥❞ ❙tr❛t❡❣②
❘✉♥t✐♠❡ ❛♥❛❧②s✐s ♦❢ s❡❛r❝❤ ❤❡✉r✐st✐❝s ♦♥ s♦❢t✇❛r❡ t❡st✐♥❣
■ ❯♥❞❡rst❛♥❞ ❜❡❤❛✈✐♦✉r ♦❢ ❛❧❣♦r✐t❤♠ ■ ❘✉♥t✐♠❡ ✐♠♣❛❝t ♦❢ ♦♣❡r❛t♦rs ❛♥❞ ♣❛r❛♠❡t❡r s❡tt✐♥❣s ■ ❘✉♥t✐♠❡ ✐♠♣❛❝t ♦❢ ♣r♦❜❧❡♠ ✐♥st❛♥❝❡ ❝❤❛r❛❝t❡r✐st✐❝s
❘❡s❡❛r❝❤ str❛t❡❣②
■ ❙t❛rt ❜② ❛♥❛❧②s✐♥❣ s✐♠♣❧❡ ♣r♦❜❧❡♠s ❛♥❞ ❛❧❣♦r✐t❤♠s ■ Pr♦❝❡❡❞ ✇✐t❤ ♠♦r❡ ❝♦♠♣❧❡① s❝❡♥❛r✐♦s ■ ❋✐♥❞ ❛♣♣r♦♣r✐❛t❡ ♠❛t❤❡♠❛t✐❝❛❧ t❡❝❤♥✐q✉❡s ♦♥ t❤❡ ✇❛②
SLIDE 10
❈♦♥❢♦r♠❛♥❝❡ t❡st✐♥❣ ❛♥❞ ❯■❖s
❈♦♥❢♦r♠❛♥❝❡ t❡st✐♥❣ ✐♥✈♦❧✈❡s t❤❡ st❛t❡ ✈❡r✐☞❝❛t✐♦♥ ♣r♦❜❧❡♠✱ ✇❤✐❝❤ ❝❛♥ ❜❡ s♦❧✈❡❞ ✉s✐♥❣ ✉♥✐q✉❡ ✐♥♣✉t ♦✉t♣✉t ✭❯■❖✮ s❡q✉❡♥❝❡s✳
s✸ s✹ s✷ s✶ ✶❂❛ ✵❂❜ ✵❂❜ ✶❂❜ ✵❂❜ ✵❂❛ ✶❂❜ ✶❂❜
❉❡☞♥✐t✐♦♥
❆ ✉♥✐q✉❡ ✐♥♣✉t ♦✉t♣✉t s❡q✉❡♥❝❡ ❢♦r ❛ st❛t❡ s ✐s ❛ s❡q✉❡♥❝❡ ① st✳
■ ✽t ✻❂ s✱ ✕✭s❀ ①✮ ✻❂ ✕✭t❀ ①✮✱
✇❤❡r❡
■ ✕✭s❀ ①✮ ✐s ♦✉t♣✉t ♦❢ ❋❙▼
♦♥ ✐♥♣✉t ①✱ st❛rt✐♥❣ ✐♥ st❛t❡ s✳
❊①❛♠♣❧❡
■ ✶ ✐s ❛ ❯■❖ ❢♦r st❛t❡ s✸✳ ■ ✶ ✐s ♥♦t ❛ ❯■❖ ❢♦r st❛t❡ s✶✳
❯■❖✭①✮ ✿❂ ❥❢t ✷ ❙ ❥ ✕✭s❀ ①✮ ✻❂ ✕✭t❀ ①✮❣❥
SLIDE 11
Pr❡✈✐♦✉s ✇♦r❦
❯■❖s ❛r❡ ❢✉♥❞❛♠❡♥t❛❧ ✐♥ ❝♦♥❢♦r♠❛♥❝❡ t❡st✐♥❣ ♦❢ ❋❙▼s✳
■ ❯s❡❞ t♦ s♦❧✈❡ t❤❡ st❛t❡ ✈❡r✐☞❝❛t✐♦♥ ♣r♦❜❧❡♠✳
❚❤❡♦r❡t✐❝❛❧ ❛s♣❡❝ts
■ ◆P✲❤❛r❞ t♦ ❝❤❡❝❦ ✇❤❡t❤❡r ❛ st❛t❡ ❤❛s ❛ ❯■❖
❬▲❡❡ ❛♥❞ ❨❛♥♥❛❦❛❦✐s✱ ✶✾✾✹❪✳
■ ❙❤♦rt❡st ❯■❖s ❝❛♥ ❜❡ ❡①♣♦♥❡♥t✐❛❧❧② ❧♦♥❣
✭❡♠♣✐r✐❝❛❧ r❡s✉❧ts s✉❣❣❡st t❤❡② ❛r❡ ♦❢t❡♥ s❤♦rt✮✳ ❊①♣❡r✐♠❡♥t❛❧ ❝♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ r❛♥❞♦♠ s❡❛r❝❤ ❛♥❞ ●❆ ❬●✉♦ ❡t ❛❧✳✱ ✷✵✵✹❪ ❛♥❞ ❬❉❡r❞❡r✐❛♥ ❡t ❛❧✳✱ ✷✵✵✻❪
■ ▼✐♥✳ ❧❡♥❣t❤✱ ♠❛①✳ ♥✉♠❜❡r ♦❢ ❞✐☛❡r❡♥t ♦✉t♣✉ts✳ ■ ❙✐♠✐❧❛r ♣❡r❢♦r♠❛♥❝❡ ♦♥ s♠❛❧❧ ❋❙▼s✳ ■ ●❆ ❜❡tt❡r t❤❛♥ r❛♥❞♦♠ s❡❛r❝❤ ♦♥ ❧❛r❣❡r ❋❙▼s✱
❡s♣❡❝✐❛❧❧② ✇❤❡♥ ❧♦♥❣ ❯■❖s ❛r❡ ♥❡❡❞❡❞
SLIDE 12
✭✶✰✶✮ ❊✈♦❧✉t✐♦♥❛r② ❆❧❣♦r✐t❤♠
✭✶✰✶✮ ❊❆
❈❤♦♦s❡ ① ✉♥✐❢♦r♠❧② ❢r♦♠ ❢✵❀ ✶❣♥✿ ❘❡♣❡❛t ①✵ ✿❂ ①✳ ❋❧✐♣ ❡❛❝❤ ❜✐t ♦❢ ①✵ ✇✐t❤ ♣r♦❜❛❜✐❧✐t② ✶❂♥✳ ■❢ ❢✭①✵✮ ✕ ❢✭①✮✱ t❤❡♥ ① ✿❂ ①✵✳
SLIDE 13
❍❛r❞ ✐♥st❛♥❝❡ ❝❧❛ss ✲ ❋❙▼ ❈♦♠❜✐♥❛t✐♦♥ ▲♦❝❦
❚❤❡♦r❡♠
❖♥ t❤❡ ✐♥st❛♥❝❡ ❝❧❛ss ❜❡❧♦✇
■ ❚❤❡ ♣r♦❜✳ t❤❛t ✭✶✰✶✮ ❊❆ ✭♦r ❘❙✮ ☞♥❞s t❤❡ ❯■❖ ❢♦r
st❛t❡ s✶ ✇✐t❤✐♥ ❡❝✁♥ ✐t❡r❛t✐♦♥s ✐s ❡①♣♦♥❡♥t✐❛❧❧② s♠❛❧❧✳
s✶ s✷ s✸ s♥✶ s♥ ✵❂❛ ✵❂❛ ✵❂❛ ✵❂❜ ✶❂❛ ✶❂❛ ✶❂❛ ✶❂❛ ✶❂❛
♥
Pr♦♦❢ ✐❞❡❛ ❢♦r ✭✶✰✶✮ ❊❆✿
■ ❆❧❧ st❛t❡s ❭❝♦❧❧❛♣s❡✧ ✐♥t♦ s✶ ♦♥ ✐♥♣✉t ✵✳ ■ Pr♦❜❧❡♠ ✐♥st❛♥❝❡ ✐s ❛ ❭♥❡❡❞❧❡ ✐♥ t❤❡ ❤❛②st❛❝❦✧✳ ■ ❙✉❝❝❡ss ♣r♦❜❛❜✐❧✐t② ❜♦✉♥❞❡❞ ❜② ❞r✐❢t ❛♥❛❧②s✐s✳
❬▲❡❤r❡ ❛♥❞ ❨❛♦✱ ✷✵✵✼❪
SLIDE 14
❊❛s② ✐♥st❛♥❝❡ ❝❧❛ss ✲ ❋❙▼ ❈♦✉♥t❡r
❚❤❡♦r❡♠
❖♥ t❤❡ ✐♥st❛♥❝❡ ❝❧❛ss ❜❡❧♦✇✱
■ ✭✶✰✶✮ ❊❆ ☞♥❞s t❤❡ ❯■❖ ❢♦r s✶ ✐♥ ❡①♣✳ t✐♠❡ ❖✭♥ ❧♦❣ ♥✮✳ ■ ❚❤❡ ♣r♦❜✳ t❤❛t r❛♥❞♦♠ s❡❛r❝❤ ☞♥❞s ❛ ❯■❖ ❢♦r s✶
✇✐t❤✐♥ ❡❝✁♥ ✐t❡r❛t✐♦♥s ✐s ❡①♣♦♥❡♥t✐❛❧❧② s♠❛❧❧ ❡✡✭♥✮✳
s✶ s✷ s✸ s♥✶ s♥ ✵❂❛ ✵❂❛ ✵❂❛ ✵❂❛ ✶❂❛ ✶❂❛ ✶❂❛ ✶❂❛ ✶❂❜
♥
Pr♦♦❢ ✐❞❡❛✿ ❚❤❡ ♣r♦❜❧❡♠ ✐♥st❛♥❝❡ ✐s ❡ss❡♥t✐❛❧❧② ❖♥❡▼❛①✳
❬▲❡❤r❡ ❛♥❞ ❨❛♦✱ ✷✵✵✼❪
SLIDE 15
(1+1) EA? Are you kidding?
- What about populations?
- Well, large populations might not help.
– J. He and X. Yao, ‘From an Individual to a Population: An Analysis of the First Hitting Time
- f Population-Based Evolutionary Algorithms,”
IEEE Transactions on Evolutionary Computation, 6(5):495-511, October 2002. – T. Chen, K. Tang, G. Chen and X. Yao, “A Large Population Size Can Be Unhelpful in Evolutionary Algorithms,” Theoretical Computer Science, accepted on 8/2/2011.
SLIDE 16
Operator Interaction
- We are often concerned about which operators to
- use. In fact, interactions among operators can be
- essential. E.g.,
– P. K. Lehre and X. Yao, “On the Impact of Mutation- Selection Balance on the Runtime of Evolutionary Algorithms,” IEEE Transactions on Evolutionary Computation, accepted in January 2011.
- Even parameter settings.
– T. Chen, J. He, G. Chen and X. Yao, ``Choosing Selection Pressure for Wide-gap Problems,'' Theoretical Computer Science, 411(6):926-934, February 2010.
SLIDE 17
Insight into Problems
- Search algorithms can help us in gaining
insight into a problem, e.g., we can use EDAs (Estimation of Distribution Algorithms) to find a near optimum while learning a model of the underlying problem --- a wonderful idea!
- However,
– . Chen, K. Tang, G. Chen and X. Yao, ``Analysis
- f Computational Time of Simple Estimation of
Distribution Algorithms,'' IEEE Transactions on Evolutionary Computation, 14(1):1-22, 2010.
SLIDE 18
❋✉t✉r❡ ❲♦r❦
❘❡s❡❛r❝❤ ◗✉❡st✐♦♥s
■ ❘❡❧❛t✐♦♥s❤✐♣s ❜❡t✇❡❡♥ ♣r♦❜❧❡♠s ❛♥❞ ❤❡✉r✐st✐❝s✳ ■ ❆♥❛❧②s✐s ♦❢ ♦t❤❡r ♠❡t❛✲❤❡✉r✐st✐❝s✳ ■ ❆♥❛❧②s✐s ♦❢ ❜r♦❛❞❡r ♣r♦❜❧❡♠ ❝❧❛ss❡s✳ ■ ❆♣♣r♦①✐♠❛t✐♦♥ q✉❛❧✐t② ♦❢ s❡❛r❝❤ ❤❡✉r✐st✐❝s✳
▼❡t❤♦❞♦❧♦❣②
■ ■♠♣r♦✈❡ ♠❛t❤❡♠❛t✐❝❛❧ t❡❝❤♥✐q✉❡s✳
SLIDE 19
More Practical Considerations
- Dynamic optimisation: The objective function may change;
Fitness evaluation may be noisy; Variable values may be inaccurate
- P. Rohlfshagen and X. Yao, ``Dynamic Combinatorial Optimisation
Problems: An Analysis of the Subset Sum Problem,'' Soft Computing. Available online.
- Robust optimisation: The optimised solution is robust
against minor perturbations of the decision variables
- H. Handa, L. Chapman and Xin Yao, ``Robust route optimisation for
gritting/salting trucks: A CERCIA experience,'' IEEE Computational Intelligence Magazine, 1(1):6-9, February 2006.
- ROOT (robust optimisation over time)
- X. Yu, Y. Jin, K. Tang and X. Yao, ``Robust Optimization over Time --- A
New Perspective on Dynamic Optimization Problems,'' Proc. of the 2010 IEEE Congress on Evolutionary Computation (CEC2010), Barcelona, Spain, 18-23 July 2010, pp.3998-4003.
SLIDE 20
More Practical Considerations
- Scenario: Given a fixed time budget (say one day),
what is the best solution you can generate using whatever algorithms at your disposal?
- Should I select one algorithm and allocate all the
time to it? Should I divide the time budge among mutiple algorithms? How to allocate the time resources?
– F. Peng, K. Tang, G. Chen and X. Yao, ``Population- based Algorithm Portfolios for Numerical Optimization,'' IEEE Transactions on Evolutionary Computation, 14(5):782-800, October 2010.
SLIDE 21
More Practical Considerations
- Multi-objective formulation can sometimes
solve a problem better, even by measuring a single objective only.
– K. Praditwong, M. Harman and X. Yao, ``Software Module Clustering as a Multi- Objective Search Problem,'' IEEE Transactions
- n Software Engineering, 37(2):264-282,