Analysis of Mixing in Genetic Algorithms: A Survey

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    Analysis of Mixing in Genetic Algorithms: A Survey - Presentation Transcript

    1. Survey of Recombination- Operator Modeling Kumara Sastry Illinois Genetic Algorithms Laboratory (IlliGAL) Department of General Engineering 117 Transporation Bldg., UIUC http://www-illigal.ge.uiuc.edu Ksastry@uiuc.edu
    2. Background Design decomposition Goldberg, Deb, & Clark (1992) BB mixing is critical to GA success Mixing issue usually overlooked Success with fixed recombination operators Fixed recombination operators fail Thierens & Goldberg (1993) Problem specific crossovers Survey of Mixing Models February 12, 2002 GE 493DEG Course Presentation Sastry, K.
    3. Why Study Mixing? Facetwise models assume tight linkage A priori knowledge of building blocks (BBs) We don’t have tight linkage Incorporate BB mixing into GA dynamics First analyze fixed crossover operators Modeling mixing More effective GA designs Need to know what studies exist Survey of Mixing Models February 12, 2002 GE 493DEG Course Presentation Sastry, K.
    4. Overview Mixing Problem Classification of Models Crossover as a mixer Crossover as a BB disruptor Crossover as an innovator Summary & Conclusions Survey of Mixing Models February 12, 2002 GE 493DEG Course Presentation Sastry, K.
    5. The Mixing Problem Goldberg, Thierens, & Deb, 1993 How well fixed crossover operators solve GA-easy problems GA-hard problems An expanded view Studies on modeling recombination operator Survey of Mixing Models February 12, 2002 GE 493DEG Course Presentation Sastry, K.
    6. Models of Recombination Role of crossover operator Crossover as a mixer Motivations from population genetics Crossover as a schema disruptor Motivations from Schema theorem Crossover as an innovator All in one models Survey of Mixing Models February 12, 2002 GE 493DEG Course Presentation Sastry, K.
    7. Crossover As A Mixer Motivation from quantitative genetics Robbin’s equilibrium (1918) Geiringer’s theorem (1944), Models predict Linkage disequilibrium (Christiansen, 1989) Rate of convergence to equilibrium (Rabani, Rabinovich, & Sinclair, 1998) Marginal recombination distributions (Booker, 1993) Survey of Mixing Models February 12, 2002 GE 493DEG Course Presentation Sastry, K.
    8. Relaxation Time Rate of convergence to equilbrium Rabani, Rabinovich, & Sinclair, 1998 Prugel-Bennett, 2001 Uniform crossover: 2log2l One-point crossover: llnl Two-point crossover: 0.5llnl Survey of Mixing Models February 12, 2002 GE 493DEG Course Presentation Sastry, K.
    9. Crossover As A Disrupter Motivations from schema theorem Syswerda (1989) Schema survival rate De Jong and co-workers De Jong (1975), Spears & De Jong (1991) Multi-point crossover analysis Does not incorporate mixing Survey of Mixing Models February 12, 2002 GE 493DEG Course Presentation Sastry, K.
    10. Crossover As An Innovator Goldberg, Thierens & Deb, 1993 Allele-wise mixing (GA-easy problem) Mixing time: tx = (npcpl)-1 Control map: s vs. pc Selection time, drift time, cross-competition Large sweet-spot for GA easy problems Fixed crossover operators are good! Survey of Mixing Models February 12, 2002 GE 493DEG Course Presentation Sastry, K.
    11. Crossover As An Innovator II Thierens & Deb, 1993; Thierens, 1995 What about GA-hard problems: BB mixing Two BBs, extend to m BBs. Mixing time: 2 µk 2 m 2 µk 2 m , n ln n > c tx = c ln s 5/ 2 5/ 2 npc m npc m Population size grows exponentially! Sweet-spot shrinks exponentially! Survey of Mixing Models February 12, 2002 GE 493DEG Course Presentation Sastry, K.
    12. All In One Models Exact difference equations Markov-chain models Statistical mechanics models Coarse grain analysis Mixing info hidden in complex formulation Not very useful to design GAs Survey of Mixing Models February 12, 2002 GE 493DEG Course Presentation Sastry, K.
    13. Summary & Conclusions Mixer models: Uniform crossover is best Disrupter models: n-point crossover is best Innovation models: Fixed crossover operators are not enough All in one models: Accurate, does not help in GA design Survey of Mixing Models February 12, 2002 GE 493DEG Course Presentation Sastry, K.

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