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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.