1. The Pareto fitness genetic algorithm: Test function study Wei-Ming Chen 2011.11.03

2. Outline The Pareto fitness genetic algorithm (PFGA) Experimental results Performance measures Conclusion

3. PFGA Double ranking strategy (DRS) R’(i) : how many j that solution j performs better than solution i the DRS of solution i :

4. PFGA

5. Population size adaptive density estimation (PADE) The cell width on i-th dimension Wdi Wi : the width of the non-inferior cell

6. PFGA Each dimension : pieces Total : near N pieces

7. PFGA Fitness function :

8. PFGA Selection operation “binary stochastic sampling without replacement” Normalizing the fitness of each considered individual by dividing it by the total fitness Generate R1 => find which individual is there Generate R2 => find another individual

9. PFGA Elitist external set : the set of non-dominated individuals updated at each generation

10. FPGA

11. Experimental results

17. Performance measures some quantitative measures are used to evaluate the trade-off surface fronts (E. Zitzler, K. Deb, L. Thiele, Comparison of multi- objective evolutionary algorithms) – The convergence to the Pareto optimal front. – The distribution and the number of non- dominated solutions found. – The spread of the given set.

18. Performance measures

19. Conclusion A new MOEA design was proposed in this paper!! a modified ranking strategy, a promising sharing procedure and a new fitness function design a relatively good performance when dealing with different Pareto front features

20. Conclusion Although the MOEA comparison may be useful, we think that the aim of the multi-objective optimization is not to decide which algorithm outperforms the other but how to deal with difficult problems, which genetic operator may be more suitable for which algorithm to solve a given kind of problems, how to extract the best features from the existing approaches and why not to hybridize some of them to provide better problems’ solutions.