The CHC Adaptive Search Algorithm Larry J' Eshelman

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The CHC Adaptive Search Algorithm Larry J.
Eshelman

• Presented by Sam Talaie

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What is the paper about?

• Completely different selection
• No mutation during reproduction and recombination
• Different type of crossover
• Motivation for CHC
• Diversity with traditional GA larger pop size
• CHC Achieve same diversity with smaller pop size

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What is CHC?

• Crossover using generational elitist selection
• Heterogeneous recombination
• Cataclysmic mutation
• Best individuals are preserved
• Aggressive recombination, no incest
• If diverging, keep best candidate, and start
  over.

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Elitist Selection

• Randomly selected with no emphasis on fitness
• Implicit Parallelism exponential growth
• Elitist selection exhibits Weak Implicit
  Parallelism grow at least as fast as
• leads to exponential growth
• Requires selection operator that is not strongly
  biased against better schemata?

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Half Uniform Crossover

• Crossover ½ of non-matching bits randomly
• Highly disruptive
• Guarantees exploration, diversity
• CHC prefers low order schema, while traditional
  GA prefer short defining length schema

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Avoiding Incest

• Hamming Distance
• If ½ of the Hamming Distance between parents
  doesnt meet a threshold, they cant mate
• If no children produced for next generation,
  threshold is decremented
• Slows pace of convergence

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Mutation and Restarts

• No mutation in reproduction-recombination cycle
• Mutation in CHC is not as effective as in
  traditional GA
• When search has converged
• Use best individual as a template
• create new members by changing a fixed portion of
  best individual (i.e. 35)
• Keep a copy of best individual

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Recap
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Results

• Tested on 10 functions (F1-F10)
• F1-F5 De Jong functions
• F6-F10 Several multimodal functions
• Traditional GA, For each function, used 5 best
  parameter sets
• CHC outperformed traditional GA on 9 functions
• When both functions found results on all 50 runs
• 5/6 times the CHC did it in less evaluations
• On remaining 4 functions, CHC found optimum more
  often

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Deceptive Problems

• Functions easy for a robust hill climber
• Tightly Ordered (benign) deceptive Functions
• Bits of the deceptive sub-problems are adjacent
• Incest prevention slows convergence too much
• Traditional GAs positional bias leads to
  favoring schemata of short defining length gives
  it an advantage over CHC.

• Goldberg 40,000 for opt. tightly ordered
  sub-problems
• CHC 20960 (div. rate 0.15)
• If HUX is replaced by 2-point reduced surrogate
  cross over w/ div rate of 0.5 performance is
  significantly improved. (3162 for Goldberg
  problem)

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Permutation Problems

• Binary to integer
• Crossover and Mutation changed
• Operate on edges
• Only one child is produced
• Whenever an individual is created, use a
  hill-climber to improve tour
• Performance improved when limitations are placed
  on edge swapping by hill climber

• Padbergs 532-city TSP.
• 10 Runs
• Pop 50
• Divergence rage 30
• Optimum 27686
• Achieved 27710 in under 3 hours on a SINGLE
  processor
• Padburg 27702 3 hours, 64 processors

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Conclusion

• Outperforms traditional GA as function optimizer
• Smaller population size needed to maintain same
  diversity as traditional GA
• Very effective for parameter optimization (Darrel
  Whitley)

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