diversity maintenance behavior on evolutionary multi-objective o ptimization
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Diversity Maintenance Behavior on Evolutionary Multi-Objective
Optimization
Presenter : Tsung Yu Ho
2011.11.27 at TEILAB
Main Point of Today’s Presentation Introduction multi-objective problems (MOP)
Perato Front (non-dominated points)
Evolutionary multi-objective optimization (EMO) Perato dominance-based fitness
evaluation. Diversity maintenance Elitism
Diversity maintenance Want to observe diversity in high dimension
(D>4)
Related work Hisao Ishibuchi et.al. ,“A Many-Objective Test
Problem for Visually Examining Diversity Maintenance Behavior in a Decision Space”, GECCO 2011
A 2-D problems space is used for presenting many-objective problems.
Observer “diversity maintenance “ on current well-known EMO, such as NSGA-II, SPEA2
Multi-Objective Problems Perato Front (non-dominated points)
X
Y
Evolutionary multi-objective optimization (1) NSGA – II SPEA2
Fitness assignment
Density estimation
Y
X
Y
X
0
00
0
7
Evolutionary multi-objective optimization (2) SMS-EMOA
Hypervolume
What’s the problems Observe diversity maintenance
2-D is clear thinking.
Manny-objective problems is hardly observed by using figure.
Need to design a test functions to evaluate diversity maintenance.
It is easy to observe if the problems is mapped to 2-D space.
2-D distance minimization problems Buying a house nearest these location.
Convenience stores (Objective 1) MRT stations (Objective 2) School (Objective 3) Park (Objective 4)
2-D Decision Space : Perato Front A simple example
A
B C
Perato Front
Adjust Problems Observe diversity
Experiments
Real world application The region is the range of perato front
Real World Perato Front The number of perato front in three part.
What information that should be observed? Diversity maintenance
Number on difference region of Perato front
Small region of Perato front
Hypervolume
Experiment Results of distribution The number of solution in the smallest Pareto
region.
Experiment Results of diversity Observe with three points
Hypervolume The small value is worst.
The reference points : x {maximum value of each objective in perato front}
Conclusion A 2-D problems space is used for presenting
many-objective problems. Observe well-known EMO.
The 2-D distance minimization problems. Adjust the region of Perato front Can be utilized in the real world application
The observation measurement Hypervolume Number on difference region of Perato front Small region of Perato front
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