A COMPENSATORY GENETIC ALGORITHM

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A COMPENSATORYGENETIC ALGORITHM

• Yuri R. Tsoy, Vladimir G. Spitsyn
• Computer Engineering Department,
• Tomsk Polytechnic University
• neuroevolution_at_mail.ru

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GENETIC ALGORITHMS

• Known as quite common and robust optimization
  concept
• Have problem of premature convergence
  (degeneration)

Degeneration Loss of diversity in genetic
representation of possible solutions
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ALLELE LOSS

• Prevalence of highly fitted schema involves loss
  of diversity
• Increase of population size and mutation
  probability weakens allele loss (De Jong, 1975)

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COMPENSATORY GENETIC ALGORITHM (CoGA)

• Proportional selection strategy
• One-point crossover
• No mutation
• Elitism strategy
• Compensatory strategy

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COMPENSATORY STRATEGY

• N' number of strings selected for reproduction
• a'ik value of loci k in the string i
• RB - random boolean

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COMPENSATORY STRATEGY

• Offsprings created in result of mate of
  compensatory string and random string selected
  for reproduction
• Best string and compensatory string are taken to
  the next generation
• Use of this strategy guarantees GA from premature
  convergence

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TEST FUNCTIONS

• ONEMAX (16 and 32 bits)
• Construction of string of 1s
• Sphere function (n30)
• 1 global minimum, no local optima
• Rastrigins function (n50)
• 1 global minimum, 1050-1 local optima

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TESTS CONDITIONS

• Compensatory algorithm was compared with
  canonical genetic algorithm (CGA)
• All runs were limited to 51200 object function
  evaluations
• Example Population of 512 strings allowed to
  evolve for 100 generations.

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RESULTS
ONEMAX 16 bits
ONEMAX 32 bits
cGA - Compensatory genetic algorithm CGA -
Canonical genetic algorithm
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RESULTS
Sphere function (CGA best 136.783, cGA worst
104.868)
Rastrigins function (CGA best215232, cGA
worst612.712)
cGA - Compensatory genetic algorithm CGA -
Canonical genetic algorithm
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DISCUSSION

• Performanse of compensatory algorithm decreases
  as population size growths. It seems like
  generations number plays more significant role.
• Additional research showed that speed of
  evolution in small populations is more than that
  of in larger populations.

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DISCUSSION INTERESTING SIDE EFFECT

• Problem of direct encoding
• 2n and 2n-1 numbers are correspondingly 100
  and 011.
• Use of compensatory strategy helps to solve this
  problem.
• Suggestion Compensatory algorithm can be
  effective against deceptive problems

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DISCUSSION WHY DOES COMPENSATORY GA WORK?

• Features of efficient genetic algorithm
• Balance between exploitation of found schemas and
  exploration for new ones.

• Compensatory genetic algorithm
• Exploitation via elitism.
• Exploration via compensatory strategy.

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CONCLUSION

• Advantages
• Nice searching abilities
• Effective with small populations
• Effective against premature convergence
• Can solve encoding problems
• Disadvantages
• Takes a lot of CPU time

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THANK YOU FORYOUR ATTENTION!