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Introduction to Genetic Algorithms

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Introduction to Genetic Algorithms Genetic Algorithms What are they? Evolutionary algorithms that make use of operations like mutation, recombination, and selection Uses? – PowerPoint PPT presentation

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Title: Introduction to Genetic Algorithms


1
Introduction toGenetic Algorithms
2
Genetic Algorithms
  • What are they?
  • Evolutionary algorithms that make use of
    operations like mutation, recombination, and
    selection
  • Uses?
  • Difficult search problems
  • Optimization problems
  • Machine learning
  • Adaptive rule-bases

3
Theory of Evolution
  • Every organism has unique attributes that can be
    transmitted to its offspring
  • Offspring are unique and have attributes from
    each parent
  • Selective breeding can be used to manage changes
    from one generation to the next
  • Nature applies certain pressures that cause
    individuals to evolve over time

4
Evolutionary Pressures
  • Environment
  • Creatures must work to survive by finding
    resources like food and water
  • Competition
  • Creatures within the same species compete with
    each other on similar tasks
  • Rivalry
  • Different species affect each other by direct
    confrontation (e.g. hunting) or indirectly by
    fighting for the same resources

5
Natural Selection
  • Creatures that are not good at completing tasks
    like hunting have fewer chances of having
    offspring
  • Creatures that are successful in completing basic
    tasks are more likely to transmit their
    attributes to the next generation since there
    will be more creatures born that can survive and
    pass on these attributes

6
Genetics
  • Genome (class)
  • Sequence of genes describing the overall
    structure of the genetic for a particular species
  • Genomics
  • Study of the meaning of the genes for a
    particular species
  • Alleles
  • Values that can be assigned to a given gene
  • Genotype (instance)
  • Sequence of alleles

7
Physical Properties
  • Phenetics
  • Study of physical properties and morphology of
    creatures independent of genetic information
  • Phenome
  • General structure of creatures body and
    attributes
  • Phenotype
  • Particular instance of phenome realized as a
    unique creature
  • Product of genotype and environment forces

8
Conversions
  • In real-world mapping between genotypes and
    phenotypes is hard
  • In AI work it can be done by defining a
    convenient function or even designing encodings
    by hand
  • It is often easier to adapt genetic operators to
    work with the evolutionary data structure used to
    represent the phenotype than to encode and decode
    phenotypes

9
Genetic Algorithmic Process
  • Potential solution for problem domains are
    encoded using machine representation (e.g. bit
    strings) that supports variation and selection
    operations
  • Mating and mutation operations produce new
    generation of solutions from parent encodings
  • Fitness function judges the individuals that are
    best suited (e.g. most appropriate problem
    solution) for survival

10
Initialization
  • Initial population must be a representative
    sample of the search space
  • Random initialization can be a good idea (if the
    sample is large enough)
  • Random number generator can not be biased
  • Can reuse or seed population with existing
    genotypes based on algorithms or expert opinion
    or previous evolutionary cycles

11
Evaluation
  • Each member of the population can be seen as
    candidate solution to a problem
  • The fitness function determines the quality of
    each solution
  • The fitness function takes a phenotype and
    returns a floating point number as its score
  • It is problem dependent so can be very simple
  • It can be a bottleneck if it is not carefully
    thought out (there are magic ways to create them)

12
Selection
  • Want to give preference to better individuals
    to add to mating pool
  • If entire population ends up being selected it
    may be desirable to conduct a tournament to order
    individuals in population
  • Would like to keep the best in the mating pool
    and drop the worst (elitism)
  • Elitism is trade-off with search space
    completeness

13
Crossover
  • In sexual reproduction the genetic codes of both
    parents are combined to create offspring
  • A sexual crossover has no impact on the mating
    pool
  • Would like to keep 60/40 split between parent
    contributions
  • 95/5 splits negate the benefits of crossover

14
Crossover
  • If we have selected two strings
  • A 11111 and B 00000
  • We might choose a uniformly random site (e.g.
    position 3) and trade bits
  • This would create two new strings
  • A 11100 and B 00011
  • These new strings might then be added to the
    mating pool if they are fit

15
Mutation
  • Mutations happen at the genome level (rarely and
    not good) and the genotype level (better for the
    GA process)
  • Mutation is important for maintaining diversity
    in the genetic code
  • In humans, mutation was responsible for the
    evolution of intelligence
  • Example The occasional (low probably) alteration
    of a bit position in a string

16
Operators
  • Selection and mutation
  • When used together give us a genetic algorithm
    equivalent of to parallel, noise tolerant, hill
    climbing algorithm
  • Selection, crossover, and mutation
  • Provide an insurance policy against losing
    population diversity and avoiding some of the
    pitfalls of ordinary hill climbing

17
Replacement
  • Determine when to insert new offspring into the
    mating pool and which individuals to drop out
    based on fitness
  • Steady state evolution calls for the same number
    of individuals in the population, so each new
    offspring processed one at a time so fit
    individuals can remain a long time
  • In generational evolution, the offspring are
    placed into a new population with all other
    offspring (genetic code only survives in kids)

18
Genetic Algorithm
  • Set time t 0
  • Initialize population P(t)
  • While termination condition not met
  • Evaluate fitness of each member of P(t)
  • Select members from P(t) based on fitness
  • Produce offspring from the selected pairs
  • Replace members of P(t) with better offspring
  • Set time t t 1

19
Why use genetic algorithms?
  • They can solve hard problems
  • Easy to interface genetic algorithms to existing
    simulations and models
  • GAs are extensible
  • GAs are easy to hybridize
  • GAs work by sampling, so populations can be
    sized to detect differences with specified error
    rates
  • Use little problem specific code

20
Traveling Salesman Problem
  • To use a genetic algorithm to solve the traveling
    salesman problem we could begin by creating a
    population of candidate solutions
  • We need to define mutation, crossover, and
    selection methods to aid in evolving a solution
    from this population
  • At random pick two solutions and combine them to
    create a child solution, then a fitness function
    is used to rank the solutions

21
Traveling Salesman Problem
  • For crossover we might take two paths (P1 and P2)
    break them at arbitrary points and define new
    solutions Left1Right2 and Left2Right1
  • For mutation we might randomly switch two cites
    in an existing path

22
Evolve Algorithm for TSP
  • Set up initial population
  • For G generations
  • Create M mutations and add them to the population
  • Subject mutations to population constraints and
    determine their relative fitness
  • Create C crossovers and add them to the
    population
  • Subject crossovers to population constraints and
    determine their relative fitness

23
Solving TSP using GA
  • Steps
  • Create group of random tours
  • Stored as sequence of numbers (parents)
  • Choose 2 of the better solutions
  • Combine and create new sequences (children)
  • Problems here
  • City 1 repeated in Child 1
  • City 5 repeated in Child 2

24
Modifications Needed
  • Algorithm must not allow repeated cities
  • Also, order must be considered
  • 12345 is same as 32154
  • Based upon these considerations, a computer model
    for N cities can be created
  • Gets quite detailed

25
Genetic Algorithm Example
Parent A
Parent B
A
A
B
B
C
E
E
C
D
D
26
Genetic Algorithm Example
Combined Path
B
A
B
A
A
B
A
B
E
B
C
A
A
B
D
27
Genetic Algorithm Example
Child
B
A
B
A
B
E
C
A
B
D
28
Mutations
Chance of 1 in 50 to introduce a mutation to the
next generation (the child if it replaces a
parent, or the first parent)
R1
R2
E
B
F
D
G
A
C
E
A
G
D
F
B
C
29
Premature Convergence
  • Occasionally a gene takes over because it is so
    much fitter than all others (genetic drift)
  • If this is the best solution, that may be OK (if
    not you may never find the optimal solution if
    this happens too soon)
  • Large populations genetic drift is less likely to
    happen
  • Using higher mutation rates can combat genetic
    drift

30
Premature Convergence
  • High levels of randomness are not always helpful
    to GA
  • To prevent genetic drift
  • You might have several small populations and
    cross-breed individuals from them
  • Take game of life approach, pretend individuals
    live on 2D grid and only allow breeding between
    neighbors (spatial organizational structure)

31
Slow Convergence
  • Some GA will simply fail to converge
  • Similar to plateau problem in hill climbing (need
    to add noise to fitness values to make them
    converge)
  • Can increase elitism to encourage fitter
    individuals to spread their genes (at the risk of
    premature convergence)
  • Increasing level of random mutations sometimes
    helps

32
Parameters
  • Require lots of parameters (mutation rate,
    crossover type, population size, fitness scaling
    policy)
  • Can make use of a hierarchy of GAs with a master
    GA setting the parameters for an ordinary GA
  • Parameterless GA have default values chosen for
    parameters so that human interaction is not
    needed for fine tuning

33
Domain Knowledge
  • GA do not exploit domain knowledge unless the KE
    designs special policies and operators
  • During initialization there can be a bias toward
    certain genotypes selected by the domain expert
  • Can use gene dependent mutation rates and
    heuristic crossover split points
  • The choice of representation can affect the size
    and search efficiency of the problem space

34
GA Strengths
  • Do well at avoiding local minima and can often
    times find near optimal solutions since search is
    not restricted to small search areas
  • Easy to extend by creating custom operators
  • Perform well for global optimizations
  • Work required to to choose representations and
    conversion routines is acceptable

35
GA Weaknesses
  • Do not take advantage of domain knowledge
  • Not very efficient at local optimization (fine
    tuning solutions)
  • Randomness inherent in GA make them hard to
    predict (solutions can take a long time to
    stumble upon)
  • Require entire populations to work (takes lots of
    time and memory) and may not work well for
    real-time applications

36
Evolvee
  • Uses existing representations (like Neural Net)
  • Realism is relatively poor
  • Attack simple tasks (e.g. attack behaviors) do
    not pose any problems for it
  • (not found in current archive)

37
Actions and Parameters
  • Limited action set needed
  • Look parameter direction
  • Single value up, ahead, down
  • Move parameter weights
  • Vector (projectile, collision point, impact
    location)
  • Fire parameter
  • Jump parameter

38
Sequences
  • Contained in simple arrays of actions and times
  • Times can be associated with actions in two ways
  • Time offset relative to previous action
  • Absolute time since start of sequence
  • The order of sequences in an array is not
    important (this allows symmetric solutions but
    avoids the cost of sorting actions before
    evolution is complete)

39
Random Generation
  • Time offset will be a randomly generated values
    within maximum sequence length
  • Action type can be encoded as a symbol randomly
    chosen from set of all possible actions
  • Parameters values are action specific and need to
    be chosen after action is selected and given in
    range values

40
Random Generation
  • The length of all action sequences can also be
    generated randomly (with an maximum upper bound)
  • The sequences of actions will be housed in a
    dynamic array
  • Start time of first action in a sequence can be
    reset to zero

41
Crossover
  • Simple one point crossover
  • Randomly split two move sequences from parents
    and swap sub-arrays to create two new children
  • Fairly easy to program using arrays

42
Mutation
  • A low probability mutation might be to change the
    length of a sequence
  • Empty spaces can be filled with random action
  • Excess actions are simply ignored
  • A low probability mutation might be to replace
    individual actions within existing sequences
  • Gene storage time follows normal distribution

43
Evolution
  • Population size will remain constant
  • Evolution happens on request
  • If individual unassigned fitness exists chose it
    otherwise choose two parents with probabilities
    proportional to their fitness for
    crossover/mutation
  • Individuals are removed from the population using
    random selection based on inverse fitness
  • To diversify the population remove the poorer of
    two similar behaviors

44
Object for Defensive Tactics
  • In combat game terms, defensive tactics is the
    sequence of actions carried out by an object to
    protect itself when it comes under attack
  • This is a natural choice for learning behavior by
    genetic algorithm, because the object is in a
    highly competitive situation with a survival
    mandate
  • It should be possible to decide on the fittest
    behaviors and select for them in the evolving
    sequence of actions
  • To keep things simple, we will focus on only two
    behaviors dodging enemy fire and rocket jumping
  • But the method could be extended to include other
    defensive moves, such as weaving and seeking
    cover

45
Computing FitnessRocket Jumping
  • Assign rewards only for upward movement when
    object is not touching the floor, to avoid
    rewarding running up the stairs
  • Reward high jump a lot more than lower jumps

46
Computing FitnessDodging Fire
  • Provide 0 reward when hit and high reward when
    object escapes with no damage
  • Must include distance of dodging movement away
    from point of impact to avoid rewarding standing
    still
  • Damage to object must also be measured and
    subtracted from fitness value
  • Use time as a 4th dimension to resolve ties

47
For the Game
  • Make use of genetic algorithm
  • Learn its jumping and dodging behaviors during
    the game
  • Fitness function provides rewards on a per jump
    or per dodge basis

48
Evaluation
  • Learns to jump fairly quickly
  • Multiple jumps are no problem
  • Dodging behavior is also learned quickly
  • Any balanced combination of vector weights
    (estimated point of impact, closest collision
    point, project attributes) that causes movement
    to safety work well
  • Approach is sub-optimal but acceptable

49
Evaluation
  • Continuous fitness values are more helpful to the
    genetic algorithm than Boolean success indicators
  • Scheme reveals how well it is possible to evolve
    behaviors using genetic operators
  • The representation is better suited to modeling
    sequences than either decision trees or fuzzy
    rules
  • Representation is incompatible with rule-based
    schemes

50
Related Technologies
  • Genetic Programming
  • Existing programs are combined to breed new
    programs
  • Artificial Life
  • Using cellular automata to simulate population
    growth
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