The Adaptive Hierarchical Fair Competition HFC Model for EAs

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The Adaptive Hierarchical Fair Competition (HFC)
Model for EAs

• Jianjun Hu, Erik D. Goodman
• Kisung Seo, Min Pei
• Genetic Algorithm Research Applications Group
  (GARAGe)
• Department of Computer Science Engineering
• Department of Electrical and Computer
  Engineering
• Michigan State University
• Presented at GECCO, 2002, New York

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Outline of this talk

• Motivation of Adaptive HFC model
• HFC Metaphor from Societal and Biological
  Systems
• HFC Algorithm
• Limitations of HFC
• Adaptive HFC toward autonomous EAs
• AHFC with adaptive admission thresholds
• Experiments
• Conclusion and future work

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Motivation for Adaptive HFC Model

• The Holy Grail of EC Autonomous EC
• Algorithm parameters adaptive to problem space
• Algorithm structure adaptive to problem space
• Efficient and robust
• AHFC- an Adaptive Parallel (multi-population) EA
  model

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Motivation for HFC Model Fighting Premature
Convergence.

• Why how premature convergence occurs?
• Exploiting best individuals ? loss of diversity ?
  reduced ability to explore
• Higher average fitness ? harder to explore
• High rates of mutation (crossover, too, in GP) ?
  unproductive diversity
• New (or random) individuals with quite different
  genetic makeup usually have low fitness and
  produce few offspring ?less chance to explore and
  exploit new peaks ? premature convergence!

Our conclusion unfair competition leads to
premature convergence.
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HFC Metaphor from Societal Systems

• Q how to protect new but promising individuals
  with low fitness?
• A fair competition mechanism in sports, chess,
  education systems
• Competition allowed only among candidates with
  comparable capabilities
• Competition organized into hierarchical levels
• Child prodigies recognized, advanced
• Protects young candidates, reduces unfair
  competition

Our solution Fair Competition by levels.
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HFC Model for EAs

• Main Points
• Ensure fair competition among individuals
• Protect young (low-fitness) individuals while
  exploiting higher-fitness ones
• Stratify the individuals into a hierarchy of
  fitness levels
• Export individuals by moving out, not copying
• Introduce random individuals continually

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HFC Structure of the Algorithm

• Multi-population
• Multiple fitness levels with
• admission thresholds
• export thresholds
• Each level may have one or more subpopulations
• Admission buffers allows asynchronous HFC
• Migration by moving individuals to the level
  whose fitness range includes their fitness
• Random individuals imported to base level
  continually

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Adaptation in HFC Model

• Adaptive topologies assigning subpopulations to
  levels using
• Sliding subpopulation(s)
• Topology metamorphosis
• Adaptive number of levels
• Adaptive admission thresholds
• Difficult to set good thresholds before searching
• Too high admission threshold gap may make HFC get
  stuck.
• separation of individuals should depend on
  relative fitnesses

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AHFC HFC with adaptive thresholds
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AHFC Pseudocode

• Determine normal EA parameters and
• nLevel Number of levels of the hierarchy
• nCalibGen Number of generations for initial
  calibration of thresholds
• nUpdateGen Number of generations between
  admission threshold updates
• nExch Number of generations between admission
  process exchanges
• 1. During calibration stage
• Run EA without migration.
• 2. At the end of calibration stage
• Compute the mean fitness of whole
  population,
• Compute std dev of the whole population,
• Find the max fitness of whole population,
• Distribute the admission thresholds even
  between
• and
• 3. At threshold update stage
• Compute mean fitness std dev of highest
  level, and
• Find the max fitness of highest level,
• Distribute the admission thresholds even
  between
• and

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Experiment Eigenvalue Problem Dynamic System
Synthesis by GP

• Eigenvalue problem --- difficult synthesis
  problem requiring simultaneous search of
  topology and parameters
• Synthesize a dynamic system (for example,
  electrical circuit) such that the eigenvalues of
  the state equation are at the target values.
• Problem instances with different degrees of
  difficulty
• 6- to 12-eigenvalue problems

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AHFC, HFC Parameter Settings
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Results for 6-, 8-Eigenvalue Problems
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Results for 10-, 12-Eigenvalue Problems
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Observations Conclusions

• Both HFC and AHFC do much better than single
  population GP and standard multi-population GP
  with little additional computation effort
• For simpler problems, AHFC can outperform the HFC
  version that uses admission thresholds determined
  based on our experience with the problem space
• For more difficult problems, AHFC can approximate
  the static HFC performance, but is a little less
  effective
• For difficult problems, more levels are highly
  preferred
• HFC and AHFC are well suited for difficult
  problems

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Future Work

• Adaptive determination of number of levels
• Performance monitoring mechanism to decide
  migrations
• More sophisticated admission threshold adaptation
  mechanism based on qualification ratio
• Multi-processor parallel implementation of HFC
  and testing on huge problems.

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Acknowledgements

• National Science Foundation, Design, Manufacture,
  and Industrial Innovation Program, grant number
  DMI-0084934
• Our NSF GP/Bond Graph research group
  collaborators
• Prof. Ronald C. Rosenberg
• Zhun Fan
• More information
• Google search keywords
• MSU, HFC