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