The Pareto fitness genetic algorithm: Test function study

Wei-Ming Chen2011.11.03

Outline

• The Pareto fitness genetic algorithm (PFGA)• Experimental results• Performance measures• Conclusion

PFGA

• Double ranking strategy (DRS)

• R’(i) : how many j that solution j performs better than solution i

• the DRS of solution i :

PFGA

PFGA

• Population size adaptive density estimation (PADE)

• The cell width on i-th dimension Wdi

• Wi : the width of the non-inferior cell

PFGA• Each dimension : pieces• Total : near N pieces

PFGA

• Fitness function :

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

PFGA

• Elitist external set : the set of non-dominated individuals

• updated at each generation

FPGA

Experimental results

Experimental results

Experimental results

Experimental results

Experimental results

Experimental results

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.

Performance measures

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

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.