On population size and neutrality: facilitating the evolution of evolvability

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On population size and neutrality facilitating
the evolution of evolvability

• Richard Downing
• University of Birmingham
• rmd_at_cs.bham.ac.uk

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Introduction

• Evolutionary search traditionally depicted as
  taking place on a multi-modal landscape.
  Difficulties
• Sensitivity to the starting configuration.
• Diversity maintenance.
• The neutralist depiction
• Neutral networks alleviate local optima (Ebner et
  al.).
• Search tolerant of diversity loss (Harvey
  Thomson).
• What is the role of population diversity in a
  search space in which neutral networks have
  completely alleviated local optima?

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Findings

• Population diversity, in conjunction with
  neutrality, facilitates the evolution of
  evolvability.
• Neutral mutation decouples fitness variation from
  evolvability variation.
• Population diversity facilitates evolvability
  exploration, whilst restraining its loss to
  drift.
• Selection acts indirectly on evolvability,
  propagating favourable evolvability traits
  (increased fitness is by-product of better
  evolvability traits).
• Context Barnett (2001) argued that a variety of
  hill-climber was optimal. Smith et al (2001)
  nothing useful happening as a result of neutral
  evolution.
• Evolvability defn The heritable potential of a
  genotype to acquire increased fitness through
  random mutation.

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Overview

• Genotypic representation Ordered Binary Decision
  Diagrams (OBDDs)
• Evolving BDDS with Inherent Neutrality (EBDDIN)
• Experiments
• Identify a property of the genotype that is
  indicative of evolvability.
• Evidence for conclusions.
• Summary and discussion.

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Ordered Binary Decision Diagrams

• Rooted, DAG representation for Boolean functions.
• The variable ordering, p x, y, z, restricts
  the appearance of variables along any path.
• Reducible to unique ROBDD form by recursively
• removing redundant tests
• merging equivalencies

e.g. (x y) z
OBDD
ROBDD
OBDD


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For many functions, ROBDD complexity is very
sensitive to p.
6-bit parity
6-bit mux
for all p
Parity complexity is 2n-1, invariant in
complexity for all p.
sensitive
insensitive
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Some terminology

• For a given p and target function, the Implied
  Solution Complexity (ISC) is the complexity
  (number of nonterminals) of the ROBDD
  representation of the target using that p.

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EBDDIN mutations
p unaffected
dynamic p
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Evolvability is dependant on ISC

• Fixed p (no N3).
• There is a a correlation between ISC and
  evolvability.

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Emergent p using N3 mutation

• 11-mux, (7,12) ES, initialised to worst p.

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Effects of diversity loss

• Compare how diversity loss influences
  performance
• Diverse
• Clones
• Periodically converge every 50 generations
• Loss of diversity has modest performance impact.
• Search is highly independent of the starting
  configuration

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Conserving fitness with Greedy Selection

• Individual i is a parent if fitness(i)
  gt fitnessmax(pop).
• Denote GS by setting µ 0 fitness distribution
  determines the number of parents.
• Breeding lesser fitness phenotypes not effective.
• Use steady-state also to avoid generation lag
  and facilitate viable comparison of population
  sizes using AES.

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Comparing population sizes
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Neutrality population diversity

• Small population loses evolvability to neutral
  drift.
• Larger population maintains evolvability and
  better tolerates neutrality induced exploration.

• Low variance in AES.
• More neutrality leads to better exploration
  generally.

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Summary

• Temporary loss of diversity is benign
• Greedy, steady-state selection
• Always breeds optimal phenotype
• Viable comparison of population sizes using AES.
• Too small a population loses evolvability to
  drift.
• A larger population allows evolvability to emerge
  and be maintained.

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Conclusion and future work

• Evolvability can evolve, and can be facilitated
  by a modest amount of diversity working in
  conjunction with neutrality, enabling strong
  selection.
• Rather than attempting to generate and maintain
  gross diversity on highly modal/deceptive
  landscapes, it may better to transform a search
  space, with neutrality, into one more susceptible
  to gradual evolution.
• Future work will focus on understanding why low
  ISC p exhibit better evolvability.