On the Optimization Of a Class of Blackbox Optimization Algorithms

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On the Optimization Of a Class of Blackbox
Optimization Algorithms

• Gang Wang, Erik Goodman and William Punch
• Presented By Jeff Clune

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Experimental Results

• Sherri has told you the Grand Idea

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Experimental Results

• Sherri has told you the Grand Idea
• Raising the perennial question

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Experimental Results

• Sherri has told you the Grand Idea
• Raising the perennial question
• Did you do it, does it work?

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Experimental Results

• Note
• The first part of the paper uses formal notation
  to describe the idea
• In the interest of time, we press on to the data

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Experimental Results

• Test problems
• Counting Ones
• Royal Road

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Counting Ones

• Fitness Function
• Number of ones in the genome

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Counting Ones

• Parameters

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Counting Ones

• Parameters
• Chromosome length 900
• Population size 400 (each)

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Counting Ones

• Control
• Simulated Simple GA (SGA)
• Used DAGA2 to simulate
• Level 1 parameters static
• Single population was used

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Counting Ones

• Control SGA

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Counting Ones

• Control SGA

- Mutation rate is too high
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Counting Ones

• Control II SGA

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Counting Ones

• Control II SGA

- Selection pressure too light progress, but slow
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Counting Ones

• DAGA2

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Counting Ones

• DAGA2
• Available Selection Type
• Tournament selection, roulette wheel selection,
  stochastic remainder sampling, stochastic
  universal sampling
• Available Crossover Type
• Single-point, Two-point, uniform
• Mutation Bitwise
• Crossover Rate .5, 1
• Mutation Rate .001, .01

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Counting Ones

• DAGA2
• Level-2 fitness function
• Increase in average fitness since last cycle
• Current average fitness

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Counting Ones

• DAGA2
• Level-2 fitness function
• Increase in average fitness since last cycle
• Current average fitness
• Note that it includes both a raw and delta
  component

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Counting Ones

• DAGA2

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Counting Ones

• DAGA2

-This one is JUST RIGHT!
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Counting Ones

• How did it do it?

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Counting Ones

• Selection Selection

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Counting Ones

• Selection Selection

-Indicates Level-2 Evolution
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Counting Ones

• Crossover Selection

-Some trends, but more ambiguous
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Counting Ones

• Crossover Rate Selection

-Seemingly consistent trend
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Counting Ones

• Mutation Rate Selection

-Obviously consistent trend, but not to the floor
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Counting Ones

• Testing the discoveries

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Counting Ones

• Testing the discoveries

-Not surprisingly, this outperforms all others
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Counting Ones

• Quick Recap
• Definitely seeing level-2 evolution
• Level-2 evolution honing in on appropriate
  parameters
• Meta-GA unnecessary on simple problems, but that
  is not the point.

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Royal Road

• Royal road with potholes - Holland 93
• GA must
• complete the assembly of building blocks to
  level 3 (the penultimate level) of a level-4
  problem
• i.e., to generate a chromosome with either the
  first eight or last eight blocks set
  appropriately (Wang et al, 1997)

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Royal Road

• First experiment
• Fitness functions
• offspring with fitness gt parents this cycle
• Fitness of best individual/number function
  evaluations
• No. 1/function evals

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Royal Road

• First experiment
• Fitness functions
• offspring with fitness gt parents this cycle
  (4/20)
• Fitness of best individual/number function
  evaluations (19/20)
• No. 1/function evals (20/20)

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Royal Road

• First experiment
• Fitness functions
• offspring with fitness gt parents this cycle
  (4/20)
• Fitness of best individual/number function
  evaluations (19/20)
• No. 1/function evals (20/20) - use this one for
  the rest

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Royal Road

• Second experiment
• Reducing crossover
• rate range
• Experiments 6,7,8 vs. 5
• Negative effect, but still pretty good
• Note that 7 poses no bound

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Royal Road

• Second experiment
• Reducing crossover
• rate range
• Experiments 6,7,8 vs. 5
• Negative effect, but still pretty good
• Note that 7 poses no bound
• Conclude Level-2 parameters are sensitive, but
  too much

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Royal Road

• Third experiment
• Increasing cycle length
• Experiment 9
• Negative effect, but still pretty good at 75
• Similar conclusion

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Royal Road

• Fourth experiment
• Reduce migrants
• Experiment 10
• Slight negative effect, but could be chance
• Similar conclusion

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Conclusions

• DAGA2 demonstrates evolution of level-2
  parameters to appropriate settings

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Conclusions

• DAGA2 demonstrates evolution of level-2
  parameters to appropriate settings
• Shows less sensitivity to parameter settings than
  at level-1

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Future Work

• More replicates, statistical significance

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Future Work

• More replicates, statistical significance
• Get a free lunch!
• Show two test problems that DAGA2 solves, but no
  individual parameter setting would solve

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Future Work

• More replicates, statistical significance
• Get a free lunch!
• Show two test problems that DAGA2 solves, but no
  individual parameter setting would solve
• Show a problem that clearly is solved better by
  changes in parameters over time