Lecture 21

• Lecture 21
  • Video
  • Genetic Algos
  • Phases
    • Initial population
    • Fitness function
    • Naturak Selection - Select the best, discard the rest
    • Crossover
    • Mutation
  • Temination
  • Flow Chart
  • The algorithm
  • Mathematical Equality Problem

Video

link

Genetic Algos

• fittest among population..?
• search heuristic
• reflects process of natural selection where fittest individuals are selected for reproduction in order to produce offspring of next generation
• steps?
  • crossover
  • offsprings
  • mutation
• concepts?
  • population
  • attributes
  • fitness

Phases

• initial population
• fitness function
• selection
• crossover
• mutation

Initial population

• set of individuals = population
• each individ is soln to prob u wanna solve
• indiv is characterized by set of parameters(variables) known as geens
• genes are joined into a string to form chromosome(soln)

Fitness function

• detemines how fit an individual is (ability of an individ to compete with other individuals)
• softmax fn aayega
• gives a fitness score to each individual
• probability that an individual will be selected for reproduction is based on its fitness score

Naturak Selection - Select the best, discard the rest

• population size is fixed
• idea is to select fittest indiv and let them pass their genes to next gen
• population size is fixed always
  • 2 bacche banaye, toh 2 weakest hata bhi die

Crossover

• most significant phase in genetic algo
• for each pair of parents to be mated, a crossover point is chosen at random from within the genes

• offspring are created by exchanging genes of parent among themselves until the crossover point is reached

• popu size is fixed, so remove 2 literalls which are weakest

Mutation

• some of genes can be subjecte to mutation with low random prob
• implies that some bits in bit string can be flipped
• mutation occurs to maintain diversity within population and prevent premature convergence (converging to local maxima)

Temination

• algo terminates if populn converged
• i.e. does not produce offspring which are significantly diff from prev generation
• then we say it has provided set of solns to our prob

Flow Chart

The algorithm

Mathematical Equality Problem

• max one problem
  • 10 length string
  • n = 6 = individuals
  • 10 = attributes
  • how to generate population?
    • take a fair coin, toss it 60 times
    • f(s1) = number of 1s in s1, f(s2) = …
  • now selection?
    • on basis of f(i) i = 1..6
    • if sabki same f hai, would it matter kaunsa select kia? naah

• Our Problem

• Step 1

• Step 2

• Step 3

• now find probabilities = fitness[i] / sum (fitness i)

• c4 is highest prob wala

• Step 4

• pick 2 best and crossover kara de
• c4 and c6 hai best
• get 2 offspring, remove 2 weakest ones (c5, c1)

• and unme mutation

• after 1 iteration, 2 chromosomes (c1, and c5) ki values changed ho jayengi and baaki sab same rahenge