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GECCO'2007: Modeling Selection Pressure in XCS for Proportionate and Tournament Selection

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Albert Orriols-Puig

1. The document models the selection pressure and takeover time of the XCS learning algorithm under proportionate and tournament selection. Differential equations are derived and solved to obtain closed-form expressions for takeover time. 2. The models are validated experimentally on single-niche and multiple-niche problems. The results show the models accurately predict takeover time in general scenarios. 3. The models support previous findings that tournament selection is more robust than proportionate selection, and that sufficient fitness separation is needed for proportionate selection to identify the best classifier.

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Modeling Selection Pressure in XCS for Proportionate and Tournament Selection Albert Orriols-Puig 1,2 Kumara Sastry 2 Pier Luca Lanzi 1,3 David E. Goldberg 2 Ester Bernadó-Mansilla 1 1 Research Group in Intelligent Systems Enginyeria i Arquitectura La Salle, Ramon Llull University 2 Illinois Genetic Algorithms Laboratory Department of Industrial and Enterprise Systems Engineering University of Illinois at Urbana Champaign 3 Dipartamento di Elettronica e Informazione Politecnico di Milano
Motivation ,[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle
Motivation ,[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle
Aim ,[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle
Description of XCS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Description of XCS ,[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Description of XCS ,[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Description of XCS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle
Modeling Takeover Time ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Modeling Takeover Time ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Proportionate Selection ,[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions Num. ratio : n r = n 2 /n 1 Accuracy ratio: ρ = k 2 /k 1
Proportionate Selection ,[object Object],Enginyeria i Arquitectura la Salle ,[object Object],[object Object],[object Object],1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Proportionate Selection ,[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions P t = n 1 /n ,[object Object],[object Object],[object Object]
Proportionate Selection ,[object Object],Enginyeria i Arquitectura la Salle ,[object Object],[object Object],[object Object],[object Object],A higher separation between fitness enables a higher ability in identifying accurate rules, as announced by Karbat, Bull & Odeh, 2005. n 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions If ρ  1: t rws ≈ ∞ If ρ  0:
Tournament Selection ,[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Tournament Selection ,[object Object],Enginyeria i Arquitectura la Salle ,[object Object],[object Object],[object Object],1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Tournament Selection ,[object Object],Enginyeria i Arquitectura la Salle ,[object Object],[object Object],[object Object],[object Object],Tournament selection does not depend on the accuracy ratio between the best classifier and the others in the same [A], as pointed by Butz, Sastry & Goldberg, 2005 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions ,[object Object],[object Object],[object Object]
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle
Proportionate vs. Tournament ,[object Object],[object Object],Enginyeria i Arquitectura la Salle For P 0 = 0.01 and P = 0.99 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle
Design of Test Problems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Results on the Single-Niche Problem Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions Accuracy ratio: ρ = 0.01 RWS Tournament s=9 Tournament s=3 Tournament s=2
Results on the Single-Niche Problem Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions Accuracy ratio: ρ = 0.50 RWS Tournament s=9 Tournament s=3 Tournament s=2
Results on the Single-Niche Problem Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions Accuracy ratio: ρ = 0.90 RWS Tournament s=9 Tournament s=3 Tournament s=2
Design of Test Problems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Results on the Multiple-Niche Problem Enginyeria i Arquitectura la Salle ,[object Object],[object Object],[object Object],[object Object],1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions RWS ρ = 0.01 RWS ρ = 0.20 RWS ρ = 0.30 RWS ρ = 0.40 RWS ρ = 0.50
Results on the Multiple-Niche Problem Enginyeria i Arquitectura la Salle ,[object Object],[object Object],[object Object],1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions TS s = 2 TS s = 3 TS s = 9
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle
Modeling Generality ,[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Proportionate Selection ,[object Object],Enginyeria i Arquitectura la Salle ,[object Object],[object Object],[object Object],[object Object],[object Object],If cl 1 is either more accurate or more general than cl 2 , cl 1 will take over the population. 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Tournament Selection ,[object Object],Enginyeria i Arquitectura la Salle ,[object Object],[object Object],[object Object],[object Object],[object Object],For low ρ m or high s the right-hand logarithm goes to zero, so that the takeover time mainly depends on P 0 and P 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Results of the Extended Model on the one-niched Problem Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions RWS Tournament
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle
Conclusions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions
Modeling Selection Pressure in XCS for Proportionate and Tournament Selection Albert Orriols-Puig 1,2 Kumara Sastry 2 Pier Luca Lanzi 2 David E. Goldberg 2 Ester Bernadó-Mansilla 1 1 Research Group in Intelligent Systems Enginyeria i Arquitectura La Salle, Ramon Llull University 2 Illinois Genetic Algorithms Laboratory Department of Industrial and Enterprise Systems Engineering University of Illinois at Urbana Champaign

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GECCO'2007: Modeling Selection Pressure in XCS for Proportionate and Tournament Selection

  • 1. Modeling Selection Pressure in XCS for Proportionate and Tournament Selection Albert Orriols-Puig 1,2 Kumara Sastry 2 Pier Luca Lanzi 1,3 David E. Goldberg 2 Ester Bernadó-Mansilla 1 1 Research Group in Intelligent Systems Enginyeria i Arquitectura La Salle, Ramon Llull University 2 Illinois Genetic Algorithms Laboratory Department of Industrial and Enterprise Systems Engineering University of Illinois at Urbana Champaign 3 Dipartamento di Elettronica e Informazione Politecnico di Milano
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  • 24. Results on the Single-Niche Problem Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions Accuracy ratio: ρ = 0.01 RWS Tournament s=9 Tournament s=3 Tournament s=2
  • 25. Results on the Single-Niche Problem Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions Accuracy ratio: ρ = 0.50 RWS Tournament s=9 Tournament s=3 Tournament s=2
  • 26. Results on the Single-Niche Problem Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions Accuracy ratio: ρ = 0.90 RWS Tournament s=9 Tournament s=3 Tournament s=2
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  • 34. Results of the Extended Model on the one-niched Problem Enginyeria i Arquitectura la Salle 1. Description of XCS 2. Modeling Takeover Time 3. Comparing the two Models 4. Experimental Validation 5. Modeling Generality 6. Conclusions RWS Tournament
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  • 37. Modeling Selection Pressure in XCS for Proportionate and Tournament Selection Albert Orriols-Puig 1,2 Kumara Sastry 2 Pier Luca Lanzi 2 David E. Goldberg 2 Ester Bernadó-Mansilla 1 1 Research Group in Intelligent Systems Enginyeria i Arquitectura La Salle, Ramon Llull University 2 Illinois Genetic Algorithms Laboratory Department of Industrial and Enterprise Systems Engineering University of Illinois at Urbana Champaign

Editor's Notes

  1. In this work, we revisit the comparison between proportionate and tournament selection. In this case, under some assumptions, we derive a model of both selection schemes that permits us to compare them.