8/19/2019 Lecture9a NSGA II

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O&!ecti'esThe objectie! o" thi! lect#re i! to$

•

%nder!tand the ba!ic conce&tand 'orking o" NSGA-II

• Adantage! and di!adantage!

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• (on)dominated sorting geneticalgorithm *II +as proposed &y De& etal. in ,---.

• (G/)II procedure has three features# – It uses an elitist principle

 – It emphasizes non)dominated solutions.

 – It uses an e0plicit di'ersity preser'ingmechanism

NSGA-II

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• NSGA-II

 1 2

 1 ,

ro!!oer

*#tation

NSGA-II

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• 3ro+ded tournament selection operator – / solution 0i +ins a tournament +ith another

solution 0 ! if any of the follo+ing conditions are true#

• If solution 0i has a &etter rank4 that is4 ri 5 r ! .

• If they ha'e the same rank &ut solution 0i  has a &etter

cro+ding distance than solution 0 !4 that is4 ri 6 r ! and di 7 d ! .

NSGA-II

+bjectie!&ace

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• 3ro+ding distance – To get an estimate of the density of solutions

surrounding a particular solution.

• 3ro+ding distance assignment procedure – Ste& $ et l 6 8984 9 is a set of solutions in a

front. et di 6 -4 i 6 24,4:4l.

 – Ste& $ 9or e'ery o&!ecti'e function m 624,4:4M4 sort the set in +orse order of f m or

"nd sorted indices 'ector# Im  6 sort;f m

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• tep =# 9or m 6 24,4:4M4 assign a largedistance to &oundary solutions4 i.e. setthem to > and for all other solutions ! 6 ,

to ;l)2

8/19/2019 Lecture9a NSGA II

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• /d'antages# – ?0plicit di'ersity preser'ation mechanism

 – O'erall comple0ity of (G/)II is at most

O;M(,< – ?litism does not allo+ an already found

Pareto optimal solution to &e deleted.

• Disad'antage# – 3ro+ded comparison can restrict the

con'ergence.

 – (on)dominated sorting on ,( size.

NSGA-II