Lets Get Ready to Rumble: Crossover versus Mutation Head to Head

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Lets Get Ready to Rumble Crossover versus
Mutation Head to Head

• A review of Kumara Sastry and David E. Goldbergs
  2004 GECCO conference paper by David Cherba

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Overview of paper

• Compare the effectiveness of crossover versus
  mutation
• Effectiveness is measured in number of
  computations required for solution
• Two simple problems studied
• Onemax
• m k-trap
• Both meet the criterion that they can be solved
  exclusively with crossover or mutation

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Overview cont.

• Build a computational model for
  selectorecombinaitive (crossover)
• Population
• time to convergence
• s-wise tournament selection
• Build a computational model for
  Building-Block-Wise Mutation (BBMA)

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Overview Cont.

• Calculate classic speedup ratio
• But wait it didnt make crossover look better!!!!
• Add noise to problem
• Now crossover looks better!!
• Results plotted by size of problem for proof of
  scalability

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Abstract
This paper analyzes the relative advantages
between crossover and mutation on a class of
deterministic and stochastic additively separable
problems. This study assumes that the
recombination and mutation operators have the
knowledge of the building blocks (BBs) and
effectively exchange or search among competing
BBs. Facetwise models of convergence time and
population sizing have been used to determine the
scalability of each algorithm. The analysis shows
that for additively separable deterministic
problems, the BB-wise mutation is more efficient
than crossover, while the crossover outperforms
the mutation on additively separable problems
perturbed with additive Gaussian noise. The
results show that the speed-up of using BB-wise
mutation on deterministic problems is
, where k is the BB size, and m is the
number of BBs. Likewise, the speed-up of using
crossover on stochastic problems with fixed noise
variance is
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OneMax problem
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m k-trap
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Computational cost

• Selectorecombinative

Population
Convergence
k BB size m number of BBs d size signal
between the competing BBs, ?BB fitness variance
of a BB ? 1/m failure probability,
Total length of string
Selection pressure binary tournament
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Computational cost cont.

• BBMA

• Speedup

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For the m k-trap function
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Experimental results
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Experimental Result cont.
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But wait!!
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Add noise to the Problem
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Now the predicted results
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Conclusion

• That in a problem with noise the crossover is
  much better.
• This has been fair because of the problem is
  solvable by both operators
• Speedup is given by mutation/crossover cost for a
  problem with stochastic noise is