1. Diversity Maintenance Behavior on Evolutionary Multi-Objective Optimization Presenter : Tsung Yu Ho 2011.11.27 at TEILAB

2. 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)

3. 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

4. Multi-Objective Problems  Perato Front (non-dominated points) X Y

5. Evolutionary multi-objective optimization (1)  NSGA – II SPEA2 Fitness assignment Density estimation Y X Y X 0 0 0 0 7

6. Evolutionary multi-objective optimization (2)  SMS-EMOA  Hypervolume

7. 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.

8. 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)

9. 2-D Decision Space : Perato Front  A simple example A B C Perato Front

10. Adjust Problems  Observe diversity

11. Experiments

12. Real world application  The region is the range of perato front

13. Real World Perato Front  The number of perato front in three part.

14. What information that should be observed?  Diversity maintenance  Number on difference region of Perato front  Small region of Perato front  Hypervolume

15. Experiment Results of distribution  The number of solution in the smallest Pareto region.

16. Experiment Results of diversity  Observe with three points

17. Hypervolume

18. 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