Evolutionary Algorithms

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Evolutionary Algorithms
Nicolas Kruchten 4th Year Engineering
Science Infrastructure Option
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What are they?

• EAs are stochastic techniques used to search
  multidimensional spaces for points, according to
  some criteria.
• They operate by mimicking reproduction
  selection processes
• More on this in a bit

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What are they good for?

• EAs are used to solve optimization problems of
  various types
• Find the vector x such that f(x) is min or max
• A huge variety of engineering or science problems
  can be reduced to, or expressed as, optimization
  problems

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A black-box example

• Say you have a black box, with n knobs, and a
  light bulb, what set of knob positions will make
  the bulb glow brightest?

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What if

• n1? n10000?
• knobs are continuous? discrete? mixed?
• some combinations are invalid? (i.e. knob 1 must
  be less than knob 2)
• an analytical expression exists?

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Traditional methods

• Direct Calculus
• Gradient descent or hill climbing
• Frank Wolfe (!)
• Simplex
• Simulated Annealing
• SPSA
• Etc.

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Unfortunately they

• Sometimes simply dont apply
• Only work for specific problems
• Dont scale well (NP-Hard, NP-Complete)
• Get trapped in local optima

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EAs

• Dont have all of these problems
• Scale reasonably well
• Work for a huge variety of problems
• Dont require gradients but can use them

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How EAs work

• Pick a population of feasible points
• Generate new points from the better ones
• Throw out the worse ones
• Thats one generation rinse repeat
• Lo and behold! The points in your population are
  getting better and better!

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Back to our example

• Our feasible points were sets of knob positions,
  we call these chromosomes
• Individual knob positions are genes
• The brightness we call the fitness, were
  looking for chromosomes with good fitness

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How to get new points

• This is where the genetic comes in
• Given some parent chromosomes, how do we mix
  them up and get a child?
• Various schemes are possible depending on how we
  represent the parents (binary, real, integer etc)

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Mutation

• If we only ever blend or mix and match genes, we
  can only ever explore combinations of our initial
  gene pool
• To explore new parts and find new optima, we
  periodically change, or mutate, genes.
• Again, various processes are possible.

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Which parents to use

• Various schemes exist for selection
• Pick the best ones
• Pick random ones
• Pick them based on relative fitness
• Pick them based on relative rank
• Pick them based on how different they are
• etc

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Which points to keep

• Various schemes exist to decide which children
  and/or parents to keep at each generation
• Keep only the children
• Select from a pool of children and parents
• Best
• Random
• Rank
• Fitness, etc

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When to stop

• You can stop an EA whenever is appropriate, but
  typical convergence criteria include
• A number of generations
• A given standard deviation of fitnesses
• A period of time
• Total convergence
• Etc.

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Putting it all together
Let t 0 Initialize P(t)
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EA Limitations

• EAs are extremely flexible, but they have their
  own problems
• Can be very slow, requiring many potentially long
  evaluations
• Are tough to design and configure, many many
  parameters
• No guarantee of global optimum

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Some history

• You may have heard of GAs, which are a subset of
  EAs
• Much confusion and conflicting terminology exists
• A huge body of operators, combinations and
  approaches have been proposed

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Evolutionary Programming

• Traditional
• Credited to Fogel, US, published in 66
• Single parents (so not genetic)
• Basically pure mutation
• Since then
• EP approaches themselves mutated independently
  towards general EA practice

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Evolutionary Strategies

• Traditional
• Credited to Rechenberg and Schwefel, Switzerland,
  published in 73
• Tiny populations (1 or 2)
• Sophisticated adaptive mutation scheme
• Since then
• Adaptive mutation has gone mainstream

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Genetic Algorithms

• Traditional
• Credited to Holland, US, published in 72
• Binary coding
• Keep only the children
• Since then
• Has grown to be loosely interchangable with EA,
  with real-coded GA, crowding GA etc

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State of the art

• No hard and fast rules about the best EA flavour
  for a given problem
• Some heuristics exist
• EAs have been successfully applied to many
  problems in various fields, but with few general
  results

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Advanced EAs

• Parallelization
• Distribution
• Master/Slave
• Peered Demes (see parallelization)
• Hybrid
• Hybridization

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ITS Applications

• Model calibration is a great example of a
  challenging transportation-related optimization
• Minimize an error term byvarying some model
  parameters

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ITS Example GAID

• Genetic Adaptive Incident Detection
• Use of a GA to train a neural network perfect
  example of ANN EA ITS
• The problem automatically detecting incidents on
  the freeway, using traffic loop data

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GAID Basics

• GAID uses a probabilistic neural network (PNN)
  which takes 16d vectors and classifies them into
  two piles
• Traffic loop data -gt incident/normal
• The PNN is defined by 16 parameters

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GAID Diagram
EA
16 Parameters
Incident
PNN f(parameters)
Loop Data
Normal
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GAID Fitness

• Fitness correct classifications/number of
  vectors
• We quiz the PNN with known data to score it
• We are looking for the set of 16 real parameters
  which make GAID the most accurate

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GAID Initialization

• Initialization
• Pick population size 50
• Pick 50 random sets of 16 real parameters between
  0 and 1000
• Score the chromosomes

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GAID Generation

• Generation
• Pick the child population (generation) size 50
• Select 2 parents at random
• Each child gene is either mom or dads
• Mutate every gene add some uniformly distributed
  random number between -50 and 50
• Score the children

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GAID 2d view
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GAID 2d view
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GAID 2d view
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One alternative
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GAID Assembly

• Assembly of children and parents
• Choose the 50 best from the combined pool of
  children and parents
• Convergence repeat, stopping when the STD is
  less than 0.005

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GAID Summary

• Real representation, 16 genes
• Popsize Gensize 50
• Random Initialization
• 2 parents, random selection
• real crossover, creep mutation on all genes
• Crowding assembly, best selection
• STD convergence