# Selection

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```					                                          Logistics
   Assignments
Selection and Fitness                            Checkpoint 1 -- Problem
   Checkpoint 2 --Framework
   Checkpoint 3 -- Genotype / Phenotype
   Due tonight
   Checkpoint 4 -- Selection / Fitness
   Given today
   Due October 17

Final exam date                           Project Presentation
   Final exam date has been announced:      12 Projects
   Presentations:
   Dates:
Week 10
Friday, November 16th


   Monday, November 5
   2:45pm - 4:45pm                                    Wednesday, November 7

   70-1445                                  15 minutes / presentation
   Schedule now on Web
   Please send me choice of time/day
   However…
   Code, Report, and Grad Survey
   DUE FRIDAY, NOV 9th

Plan for today                            Evolutionary Algorithms
   1st half: Selection                      An EA uses some mechanisms inspired by biological
evolution: reproduction, mutation, recombination,
   2nd half: fitness / CP4                   natural selection and survival of the fittest.
   Candidate solutions to the optimization problem play
the role of individuals in a population, and the cost
function determines the environment within which
the solutions "live".
   Evolution of the population then takes place after the
   Questions before we start                 repeated application of the above operators.

1
Evolutionary Computation
process                                                                   Evolutionary Algorithms
   To use evolutionary algorithms your must:
Initialize
population
Select individuals for
crossover (based on                              Define your genotype
fitness function
   Define the genotype -> phenotype translation
Mutation
   Define crossover and mutation operators
Insert new offspring
into population                                  Define fitness
Are stopping criteria
satisfied?
   Determine selection criteria
   Set population parameters
Finish

Selection                                                                 Selection
Generation k                                         Generation k+1
   Process of determining individuals of
generation i+1 from generation i.

   Basic process
Selection                                           Choose parents from generation i.
   Have chosen parents produce offspring
   Add these offspring to population
   Choose individuals from population to survive in
generation i+1.

Selection                                                                 Selection methods
   Two processes:                                                           Deterministic
   Parent selection                                                         Each individual is assigned how many times it will
   Survival selection                                                        be chosen.
   Stochastic
   Categories:                                                                  Each individual is assigned a probability of being
   Non-overlapping generational models                                       chosen and choice is made stochastically.
Parents live only one generation
Can be applied to both parent and survival


   Overlapping generational models
   Parents can live multiple generations                            selection.
   Parents can compete with offspring for survival.

2
Stochastic Selection Methods                                          Stochastic Selection Methods
   Roulette Wheel selection                                             Roulette Wheel selection
Each individual is assigned a probability of being
http://www.geatbx.com/docu/algindex-

chosen                                                            

   Individuals are mapped to contiguous segments of                      02.html#P399_25658
a line
   Length of segment proportional to probability of being
chosen.
   A random number is generated for each individual
to be selected.
   The individual whose segment spans the random
number is selected.

Stochastic Selection Methods                                          Stochastic Selection Methods
   Stochastic Universal Selection                                       Stochastic Universal Selection
Each individual is assigned a probability of being
Like Roulette Wheel except, a single


chosen
random number which specifies equal                                  Individuals are mapped to contiguous segments of
distance between selection values is                                  a line
chosen.                                                                   Length of segment proportional to probability of being
chosen.
   A single random number between 1 - 1/n is
chosen (sample distance)
   N is the number of individuals to be selected.
   n selection values determined based on sample
distance .

Stochastic Selection Methods                                          Stochastic selection methods
   Stochastic universal selection                                       Stochastic Remainder selection
   http://www.geatbx.com/docu/algindex-                                 Expected number of selections per
02.html#P452_27492                                                    individual determined based on probability
   e = prob * n ( n = number to be chosen)
   Individual are selected based on the
integral part of e.
   Fractional part of e used as probabilities for
a roulette wheel selection for remaining
slots.

3
Common Selection
Questions                                           Mechanisms
   Generational selection mechanisms
   Truncation Selection
   Ranking Selection
   Tournament Selection
   Fitness-Proportional Selection

Truncation Selection                                Ranking Selection
   To chose k individuals from a                      aka Rank-Proportional Selection
population of m individuals                        To choose k individuals from a
   Rate each individual via fitness                population of m individuals
   k best individuals are chosen                      Rate each individual (fitness)
   Sort individual by fitness
   Define probability of selection as a function
of rank (position in list)
   Actual selection performed stochastically

Ranking Selection                                   Ranking Selection
   Least fit = rank 1                                 Linear rank selection.
   Most fit = rank n (for population of size                      #                 r "1&
n)                                                        pi = %2 " sp + 2(sp "1) i (
\$                 n "1'
   Where
   pi = prob of individual i
!          ri = rank of individual i
   sp = selective pressure = prob of best individuals
being chosen compared to average indivdual.

4
Ranking Selection                                            Tournament Selection
   Exponential ranking                                         Randomly choose k individuals from the
pool.
1
pi =     (1" e1"ri )                            Most fit individual “wins” the
c
tournament and is selected.
   Where
!     c is a normalization factor

   Probabilty of selecting worst individual = 0.

   Probabilities of selection directly                         One member of population is replaced
proportional to fitness.                                     per iteration.
   Use stochastic selection mechanism                          Replacement mechanisms:
directly.                                                       Replace worst
   Replace random
   Stochastically using negative fitness

   Questions?

Reproduction                                                 Crossover and Mutation
   Crossover or Mutation?                                      Increase crossover rate
   Crossover rate                                              increases recombination of building blocks
   probability of being chosen for crossover              increases the disruption of good strings.
Percentage of individuals to be chosen for


crossover
   Increase mutation rate
   Mutation rate                                               transform the genetic search into a random
search
   Probably of mutation of a given gene within a
genome.                                                Helps reintroduce lost genetic material.

5
Crossover, Mutation, and Population Size        Crossover and Mutation
   Increase population size                       Optimal crossover/mutation rates fitness
dependent
   Increases diversity
   Typical schemes (for GAs)
   Reduces probability of premature               Large Population / low rates:
convergence                                         Crossover rate: 0.6
Mutation rate: 0.001
   Takes longer to converge                         

   Population size: 100
   Small Population / larger rates
   Crossover rate: 0.9
   Mutation rate: 0.01
   Population size: 30

Crossover and Mutation                          Measuring selection effectiveness
   Is crossover necessary?                        How does one measure effectiveness of selection
mechanism
   Towards a random search                        Selective pressure
   tendency to select the most fit individuals in a generation.
   Probability of best individual being chosen for selection
(compared to prob of average individual)
   Is mutation necessary?                             Diversity
Tendency for a generation to consists of a variety of individuals
   Assumes initial population is diverse            

   Inverse relationship
enough
   Challenge is to maintain balance.

Growth Ratio                                    Growth Ratio
   Rate of growth (w.r.t fitness) from            Fitness Proportional Selection
generation to generation.                          Growth ratio --> high when max fitness is
low
Growth ratio --> low when max fitness is
   Must balance your growth ratio                  

high.
   Too high --> premature convergence
   Too low --> too long to converge
   Scaled fitness.

6
Growth Ratio                                            Measuring selection effectiveness
   Linear Ranking and Binary Tournament                   For complete analysis
   Early Growth Ratios between 1 - 2                      See [Goldberg, Deb]
   Late Growth Ratios between 1-1.5                       See [Blicke, Thiele]

Reality Check
   In choosing a selection scheme
   Overlapping or non-overlapping?
   Selection mechanism for parents
   Selection mechanisms for survival
   Determine rates for crossover / mutation.

   Goal: Maintain good balance between selective
pressure and diversity.
   Questions?
   Break.

7

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