Coevolutionary Models

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Coevolutionary Models
A/Prof. Xiaodong Li School of Computer Science
and IT, RMIT University Melbourne,
Australia Email xiaodong.li_at_rmit.edu.au
April 2015
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Coevolution

• In biology, coevolution is "the change of a
  biological object triggered by the change of a
  related object. In other words, when changes in
  at least two species genetic compositions
  reciprocally affect each others evolution,
  coevolution has occurred.
• There is evidence for coevolution at the level of
  populations and species.
• The above is cited from wikipedia.

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Predators and preys
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Predator-prey population dynamics
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The Red Queen Effect

• The Red Queen Effect, is an evolutionary
  hypothesis which proposes that organisms must
  constantly adapt, evolve, and proliferate not
  merely to gain reproductive advantage, but also
  simply to survive while pitted against
  ever-evolving opposing organisms in an
  ever-changing environment.
• The Red Queen hypothesis intends to explain two
  different phenomena the constant extinction
  rates as observed in the paleontological record
  caused by co-evolution between competing species,
  and the advantage of sexual reproduction (as
  opposed to asexual reproduction) at the level of
  individuals (from Wikipedia).

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Competitive coevolution

• In competitive coevolution, individual fitness is
  evaluated through competition with other
  individuals in the population, rather than
  through an absolute fitness measure.
• In other words, fitness signifies only the
  relative strengths of solutions an increased
  fitness in one solution leads to a decreased
  fitness for another. Ideally, competing solutions
  will continually outdo one another, leading to an
  arms race of increasingly better solutions.

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Coevolving sorting networks

• A model of hosts and parasites to the evolution
  of sorting networks using a GA (Hillis, 1991).
• One species (the hosts) represents sorting
  networks, and the other species (the parasites)
  represents test cases in the form of sequences of
  numbers to be sorted.
• The interaction between the two species takes the
  form of complementary fitness functions. More
  specifically, a sorting network is evaluated on
  how well it sorts test cases, while the test
  cases are evaluated on how poorly they are
  sorted.

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Cooperative coevolution
Modelling an ecosystem consisting of two or more
species, collaborating cooperatively with one and
another. Fitness of an individual is evaluated
based on how well it cooperates with the
best-fit individuals from other species.
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Cooperative coevolutionary GA

1. A species represents a subcomponent of a
   potential solution
2. Complete solutions are obtained by assembling
   representative members of each of the species
   present
3. Credit assignment at the species level is defined
   in terms of the fitness of the complete solutions
   in which the species members participate
4. When required, the number of species
   (subpopulations) should itself evolve and
5. The evolution of each species (subpopulation) is
   handled by a standard GA.

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CCGA-1
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CCGA-1

• CCGA-1 begins by initializing a separate
  population of individuals for each function
  variable. The initial fitness of each
  subpopulation member is computed by combining it
  with a random individual from each of the other
  species and applying the resulting vector of
  variable values to the target function.
• After the startup phase, each of the individual
  subpopulations in CCGA-1 is coevolved in a
  round-robin fashion using a traditional GA. The
  fitness of a subpopulation member is obtained by
  combining it with the current best subcomponents
  of the remaining (temporarily frozen)
  subpopulations.

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CCGA-1 results on test functions
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CCGA-2

• Interacting variable (e.g., product terms) may
  present difficulties.
• To overcome this, the simple credit assignment
  scheme can be modified as follows each
  individual in a subpopulation is evaluated by
  combining it with the best known individual from
  each of the other species and with a random
  selection of individuals from each of the other
  species. The two resulting vectors are then
  applied to the target function and then the
  better of the two values is returned as the
  offsprings fitness.

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CCGA-1 and CCGA-2 results
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Evolving cascade networks
In cascade networks, all input units have direct
connections to all hidden units and to all output
units, the hidden units are ordered, and each
hidden unit sends its output to all downstream
hidden units and to all output units.
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Evolving cascade networks

• The network shown in Figure 8 (shown in the
  previous slide) is constructed incrementally as
  follows
• When the evolution of the network begins, there
  is only one species in the ecosystem, and its
  individuals represent alternatives for the output
  connection weights denoted by the three black
  boxes.
• Later in the networks evolution, the first
  hidden unit is added, and a second species is
  created to represent the new units input
  connection weights. In addition, a new connection
  weight is added to each individual of the first
  species. All of these new weights are denoted by
  gray boxes in the figure.
• The species creation event is triggered by
  evolutionary stagnation as described earlier.
  Later still, evolution again stagnates and the
  second hidden unit is added, a third species is
  created to represent the units connection
  weights, and the individuals of the first species
  are further lengthened. Further information
  refer to (Potter and De Jong, 2000).

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Further readings

• Mitchell A. Potter and Kenneth De Jong. A
  cooperative coevolutionary approach to function
  optimization. In Yuval Davidor, Hans-Paul
  Schwefel, and Reinhard Manner, editors, Parallel
  Problem Solving from Nature - PPSN III, pages
  249-257, Berlin, 1994. Springer.
• Mitchell A. Potter and Kenneth De Jong.
  Cooperative Coevolution An Architecture for
  Evolving Coadapted Subcomponents. Evolutionary
  Computation, 8(1) 1-29. MIT Press.