introduction to niching methods

1
introduction to niching methods

• consider the following possibilities
• on a landscape comprising peaks of equal size one
  might expect the population to distribute itself
  approximately evenly across all peaks
• on a landscape comprising peaks of differing size
  one might expect the population to distribute
  itself approximately proportional to the height
  of the peaks
• unless specific steps are taken, neither of above
  situations will occur
• small finite populations, genetic drift and
  stochastic errors in sampling will cause
  convergence to a single peak
• this might not be the global optimum
• niching methods are incorporated into a genetic
  algorithm to encourage the formation of stable
  sub-populations on multiple optima
• the number of sustainable peaks is limited by the
  population size
• may be beneficial in multi-modal optimisation
• useful in the context of classification and
  machine learning
• in nature, a species is limited in size by the
  resources available within its niches and its
  ability to exploit them

2

• niching methods generally fall into one of two
  categories
• selection and/or replacement steps that
  incorporate a similarity or distance metric
• e.g. crowding and variations (probabilistic,
  deterministic), restricted tournament selection
• those that modify fitness scores according to the
  size of the niche
• e.g. genotypic and phenotypic sharing, sequential
  niching, clustering
• generally, sharing schemes offer the strongest
  niching
• there is a trade-off between the number of
  sustainable peaks and the accuracy of the
  optimisation of each peak
• in general, the more peaks, the less accurate the
  optimisation
• crowding was introduced to counter poor
  performance of an elitist strategy on a
  multimodal problem
• speciation is forced by controlling the
  replacement of individuals
• a new sample is compared to a randomly selected
  number of individuals
• the number of individuals is called the crowding
  factor (typically a small value such as 2 or 3)
• the most similar individual is replaced
• more recent variants include probabilistic
  crowding and deterministic crowding

3

• restricted tournament selection
• tournament selection usually involves selecting
  the most fit individual from a randomly selected
  pool
• restricted tournament selection (strictly, this
  is actually a replacement mechanism) selects two
  individuals, x and y, at random
• these are subject to recombination and mutation
  to form two offspring, x and y
• for each of these, w individuals are drawn from
  the population at random (with replacement)
• from each respective group, the closest
  individuals to x and y are identified
• they compete in a binary tournament - if
  successful, x and/or y will take their place
• some distance metric is required
• genotypic or phenotypic sharing
• reduces the fitness of each individual according
  to the size of its niche - the larger the niche,
  the less fit it will appear
• requirements
• a distance metric (based on genotype or
  phenotype)
• some method for determining membership of a niche
• some method for determining the fitness reduction
• wide range of variations on the basic scheme, for
  example, using cluster analysis to identify niches

4

• a sharing function is defined to determine the
  neighbourhood and degree of sharing for each
  individual
• the sharing function considers the distance
  between individuals and assigns a share of the
  unmodified fitness
• if they are close the share is near or equal to
  one
• if they are far the share is near or equal to
  zero
• a suitable cut-off point (sshare) must be
  determined
• each individual is assigned the unmodified
  fitness divided by the sum of shares

1
share, s(dij)
0
sshare
distance, dijd(pi, pj)
0
5

• sequential niching
• when the fitness of an individual reaches a set
  threshold, the fitness function is modified by
  composition with a derating function to reduce
  the fitness of that area of the search space
• elimination of peaks in this way forces the
  population to explore other areas of the search
  space
• as peaks are removed one by one it is possible to
  discover a large number of peaks
• the radius of influence of the derating function
  is the critical parameter
• if too small, peaks might not be fully removed
• if too large, neighbouring peaks might also be
  removed
• domain knowledge, or empirical study is required
  to determine suitable parameters
• mating restrictions may be applied when using
  sharing schemes
• reproduction between niches has a high
  probability of producing lethals
• various schemes have been suggested, including
  those based on distance metrics and templates/tag
  bits
• typically restrict reproduction to similar
  parents, but allow for some reproduction between
  niches
• if there is no reproduction between niches then
  new peaks are unlikely to be discovered after
  niches have formed

6

• mating restrictions between similar individuals
  may also be applied
• reproduction between similar parents tends to
  produce similar offspring
• reduces useful diversity and constrains the
  search
• sharing schemes maintain diversity due to the
  reduction of fitness of overcrowded peaks
• in algorithms without sharing, reproduction
  between similar parents can be restricted to
  support the production of diverse offspring
• schemes may involve a simple distance metric and
  threshold, or involve examination of the ancestry
  of mating pairs
• mating restrictions based on distance metrics are
  computationally expensive
• an alternative is to add a tag or template to the
  chromosome
• this is subject to the usual genetic operators
• generally, individuals selected for reproduction
  have matching tags
• occasional interaction may be permitted between
  non-matching individuals, e.g. by mutation of the
  tag
• adaptation of both the solution and the ideal
  mating group can occur simultaneously
• when deciding which approach to take, consider
  the trade-off between maintaining diversity /
  number of peaks and the accuracy of optimisation