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Genetic Algorithms


Genetic Algorithms Sources Jaap Hofstede Beasly, Bull, Martin Introduction to Evolutionary Computation Evolutionary Computation is the field of study devoted to the ... – PowerPoint PPT presentation

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Title: Genetic Algorithms

Genetic Algorithms
  • Jaap Hofstede
  • Beasly, Bull, Martin

Introduction to Evolutionary Computation
  • Evolutionary Computation is the field of study
    devoted to the design, development, and analysis
    is problem solvers based on natural selection
    (simulated evolution).
  • Evolution has proven to be a powerful search
  • Evolutionary Computation has been successfully
    applied to a wide range of problems including
  • Aircraft Design,
  • Routing in Communications Networks,
  • Tracking Windshear,
  • Game Playing (Checkers Fogel)

Introduction to Evolutionary Computation(Applicat
ions cont.)
  • Robotics,
  • Air Traffic Control,
  • Design,
  • Scheduling,
  • Machine Learning,
  • Pattern Recognition,
  • Job Shop Scheduling,
  • VLSI Circuit Layout,
  • Strike Force Allocation,

Introduction to Evolutionary Computation(Applicat
ions cont.)
  • Theme Park Tours (Disney Land/World)
  • Market Forecasting,
  • Egg Price Forecasting,
  • Design of Filters and Barriers,
  • Data-Mining,
  • User-Mining,
  • Resource Allocation,
  • Path Planning,
  • Etc.

Example of Evolutionary Algorithm
  • An Example Evolutionary Computation
  • Procedure EC
  • t 0
  • Initialize Pop(t)
  • Evaluate Pop(t)
  • While (Not Done)
  • Parents(t) Select_Parents(Pop(t))
  • Offspring(t) Procreate(Parents(t))
  • Evaluate(Offspring(t))
  • Pop(t1) Replace(Pop(t),Offspring(t))
  • t t 1

Candidate Solutions CS
  • In an Evolutionary Computation, a population of
    candidate solutions (CSs) is randomly generated.
  • Each of the CSs is evaluated and assigned a
    fitness based on a user specified evaluation
  • The evaluation function is used to determine the
    goodness of a CS.
  • A number of individuals are then selected to be
    parents based on their fitness.
  • The Select_Parents method must be one that
    balances the urge for selecting the best
    performing CSs with the need for population

Parents and Generations
  • The selected parents are then allowed to create a
    set of offspring which are evaluated and assigned
    a fitness using the same evaluation function
    defined by the user.
  • Finally, a decision must be made as to which
    individuals of the current population and the
    offspring population should be allowed to
  • Typically, in EC , this is done to guarantee that
    the population size remains constant.
  • The study of ECs with dynamic population sizes
    would make an interesting project for this course

Selecting and Stopping
  • Once a decision is made the survivors comprise
    the next generation (Pop(t1)).
  • This process of selecting parents based on their
    fitness, allowing them to create offspring, and
    replacing weaker members of the population is
    repeated for a user specified number of cycles.
  • Stopping conditions for evolutionary search could
  • The discovery of an optimal or near optimal
  • Convergence on a single solution or set of
    similar solutions,
  • When the EC detects the problem has no feasible
  • After a user-specified threshold has been
    reached, or
  • After a maximum number of cycles.

A Brief History of Evolutionary Computation
  • The idea of using simulated evolution to solve
    engineering and design problems have been around
    since the 1950s (Fogel, 2000).
  • Bremermann, 1962
  • Box, 1957
  • Friedberg, 1958
  • However, it wasnt until the early 1960s that we
    began to see three influential forms of EC emerge
    (Back et al, 1997)
  • Evolutionary Programming (Lawrence Fogel, 1962),
  • Genetic Algorithms (Holland, 1962)
  • Evolution Strategies (Rechenberg, 1965
    Schwefel, 1968),

A Brief History of Evolutionary
  • The designers of each of the EC techniques saw
    that their particular problems could be solved
    via simulated evolution.
  • Fogel was concerned with solving prediction
  • Rechenberg Schwefel were concerned with solving
    parameter optimization problems.
  • Holland was concerned with developing robust
    adaptive systems.

A Brief History of Evolutionary
  • Each of these researchers successfully developed
    appropriate ECs for their particular problems
  • In the US, Genetic Algorithms have become the
    most popular EC technique due to a book by David
    E. Goldberg (1989) entitled, Genetic Algorithms
    in Search, Optimization Machine Learning.
  • This book explained the concept of Genetic Search
    in such a way the a wide variety of engineers and
    scientist could understand and apply.

A Brief History of Evolutionary
  • However, a number of other books helped fuel the
    growing interest in EC
  • Lawrence Davis, Handbook of Genetic
    Algorithms, (1991),
  • Zbigniew Michalewicz book (1992), Genetic
    Algorithms Data Structures Evolution
  • John R. Kozas Genetic Programming (1992), and
  • D. B. Fogels 1995 book entitled, Evolutionary
    Computation Toward a New Philosophy of Machine
  • These books not only fueled interest in EC but
    they also were instrumental in bringing together
    the EP, ES, and GA concepts together in a way
    that fostered unity and an explosion of new and
    exciting forms of EC.

A Brief History of Evolutionary ComputationThe
Evolution of Evolutionary Computation
  • First Generation EC
  • EP (Fogel)
  • GA (Holland)
  • ES (Rechenberg, Schwefel)
  • Second Generation EC
  • Genetic Evolution of Data Structures
  • Genetic Evolution of Programs (Koza)
  • Hybrid Genetic Search (Davis)
  • Tabu Search (Glover)

A Brief History of Evolutionary ComputationThe
Evolution of Evolutionary Computation (cont.)
  • Third Generation EC
  • Artificial Immune Systems (Forrest)
  • Cultural Algorithms (Reynolds)
  • DNA Computing (Adleman)
  • Ant Colony Optimization (Dorigo)
  • Particle Swarm Optimization (Kennedy Eberhart)
  • Memetic Algorithms
  • Estimation of Distribution Algorithms
  • Fourth Generation ????

Introduction to Evolutionary ComputationA
Simple Example
  • Lets walk through a simple example!
  • Lets say you were asked to solve the following
  • Maximize
  • f6(x,y) 0.5 (sin(sqrt(x2y2))2 0.5)/(1.0
  • Where x and y are take from -100.0,100.0
  • You must find a solution that is greater than
    0.99754, and you can only evaluate a total of
    4000 candidate solutions (CSs)
  • This seems like a difficult problem.
  • It would be nice if we could see what it looks
  • This may help us determine a good algorithm for
    solving it.

Introduction to Evolutionary ComputationA
Simple Example
  • A 3D view of f6(x,y)

Introduction to Evolutionary ComputationA
Simple Example
  • If we just look at only one dimension f6(x,1.0)

Introduction to Evolutionary ComputationA
Simple Example
  • Lets develop a simple EC for solving this
  • An individual (chromosome or CS)
  • ltxi,yigt
  • fiti f6(xi,yi)

Introduction to Evolutionary ComputationA
Simple Example
  • Procedure simpleEC
  • t 0
  • Initialize Pop(t) / of P individuals /
  • Evaluate Pop(t)
  • while (t lt 4000-P)
  • Select_Parent(ltxmom,ymomgt) / Randomly /
  • Select_Parent(ltxdad,ydadgt) / Randomly /
  • Create_Offspring(ltxkid,ykidgt)
  • xkid rnd(xmom, xdad) Nx(0,?)
  • ykid rnd(ymom, ydad) Ny(0,?)
  • fitkid Evaluate(ltxkid,ykidgt)
  • Pop(t1) Replace(worst,kid)Pop(t)-worst?
  • t t 1

Introduction to Evolutionary ComputationA
Simple Example
  • To simulate this simple EC we can use the applet
  • http//

Introduction to Evolutionary ComputationA
Simple Example
  • To get a better understanding of some of the
    properties of ECs lets do the in class lab
    found at http//

Hill climbing
Introduction 1
  • Inspired by natural evolution
  • Population of individuals
  • Individual is feasible solution to problem
  • Each individual is characterized by a Fitness
  • Higher fitness is better solution
  • Based on their fitness, parents are selected to
    reproduce offspring for a new generation
  • Fitter individuals have more chance to reproduce
  • New generation has same size as old generation
    old generation dies
  • Offspring has combination of properties of two
  • If well designed, population will converge to
    optimal solution

  • Generate initial population
  • Compute fitness of each individual
  • REPEAT / New generation /
  • FOR population_size / 2 DO
  • Select two parents from old generation
  • / biased to the fitter ones /
  • Recombine parents for two offspring
  • Compute fitness of offspring
  • Insert offspring in new generation
  • UNTIL population has converged
  • END

Example of convergence
Introduction 2
  • Reproduction mechanism has no knowledge of the
    problem to be solved
  • Link between genetic algorithm and problem
  • Coding
  • Fitness function

Basic principles 1
  • Coding or Representation
  • String with all parameters
  • Fitness function
  • Parent selection
  • Reproduction
  • Crossover
  • Mutation
  • Convergence
  • When to stop

Basic principles 2
  • An individual is characterized by a set of
    parameters Genes
  • The genes are joined into a string Chromosome
  • The chromosome forms the genotype
  • The genotype contains all information to
    construct an organism the phenotype
  • Reproduction is a dumb process on the
    chromosome of the genotype
  • Fitness is measured in the real world (struggle
    for life) of the phenotype

  • Parameters of the solution (genes) are
    concatenated to form a string (chromosome)
  • All kind of alphabets can be used for a
    chromosome (numbers, characters), but generally a
    binary alphabet is used
  • Order of genes on chromosome can be important
  • Generally many different codings for the
    parameters of a solution are possible
  • Good coding is probably the most important factor
    for the performance of a GA
  • In many cases many possible chromosomes do not
    code for feasible solutions

Example of coding for TSP
  • Travelling Salesman Problem
  • Binary
  • Cities are binary coded chromosome is string of
  • Most chromosomes code for illegal tour
  • Several chromosomes code for the same tour
  • Path
  • Cities are numbered chromosome is string of
  • Most chromosomes code for illegal tour
  • Several chromosomes code for the same tour
  • Ordinal
  • Cities are numbered, but code is complex
  • All possible chromosomes are legal and only one
    chromosome for each tour
  • Several others

  • Crossover
  • Two parents produce two offspring
  • There is a chance that the chromosomes of the two
    parents are copied unmodified as offspring
  • There is a chance that the chromosomes of the two
    parents are randomly recombined (crossover) to
    form offspring
  • Generally the chance of crossover is between 0.6
    and 1.0
  • Mutation
  • There is a chance that a gene of a child is
    changed randomly
  • Generally the chance of mutation is low (e.g.

  • One-point crossover
  • Two-point crossover
  • Uniform crossover

One-point crossover 1
  • Randomly one position in the chromosomes is
  • Child 1 is head of chromosome of parent 1 with
    tail of chromosome of parent 2
  • Child 2 is head of 2 with tail of 1

Randomly chosen position
Parents 1010001110 0011010010 Offspring
0101010010 0011001110
One-point crossover 2
Two-point crossover
  • Randomly two positions in the chromosomes are
  • Avoids that genes at the head and genes at the
    tail of a chromosome are always split when

Randomly chosen positions
Parents 1010001110 0011010010 Offspring
0101010010 0011001110
Uniform crossover
  • A random mask is generated
  • The mask determines which bits are copied from
    one parent and which from the other parent
  • Bit density in mask determines how much material
    is taken from the other parent (takeover

Mask 0110011000 (Randomly
generated) Parents 1010001110 0011010010 Offsp
ring 0011001010 1010010110
Problems with crossover
  • Depending on coding, simple crossovers can have
    high chance to produce illegal offspring
  • E.g. in TSP with simple binary or path coding,
    most offspring will be illegal because not all
    cities will be in the offspring and some cities
    will be there more than once
  • Uniform crossover can often be modified to avoid
    this problem
  • E.g. in TSP with simple path coding
  • Where mask is 1, copy cities from one parent
  • Where mask is 0, choose the remaining cities in
    the order of the other parent

Fitness Function
  • Purpose
  • Parent selection
  • Measure for convergence
  • For Steady state Selection of individuals to die
  • Should reflect the value of the chromosome in
    some real way
  • Next to coding the most critical part of a GA

Parent selection
  • Chance to be selected as parent proportional to
  • Roulette wheel
  • To avoid problems with fitness function
  • Tournament
  • Not a very important parameter

Roulette wheel
  • Sum the fitness of all chromosomes, call it T
  • Generate a random number N between 1 and T
  • Return chromosome whose fitness added to the
    running total is equal to or larger than N
  • Chance to be selected is exactly proportional to
  • Chromosome 1 2 3 4 5 6
  • Fitness 8 2 17 7 4 11
  • Running total 8 10 27 34 38 49
  • N (1 ? N ? 49) 23
  • Selected 3

  • Binary tournament
  • Two individuals are randomly chosen the fitter
    of the two is selected as a parent
  • Probabilistic binary tournament
  • Two individuals are randomly chosen with a
    chance p, 0.5ltplt1, the fitter of the two is
    selected as a parent
  • Larger tournaments
  • n individuals are randomly chosen the fittest
    one is selected as a parent
  • By changing n and/or p, the GA can be adjusted

Problems with fitness range
  • Premature convergence
  • ?Fitness too large
  • Relatively superfit individuals dominate
  • Population converges to a local maximum
  • Too much exploitation too few exploration
  • Slow finishing
  • ?Fitness too small
  • No selection pressure
  • After many generations, average fitness has
    converged, but no global maximum is found not
    sufficient difference between best and average
  • Too few exploitation too much exploration

Solutions for these problems
  • Use tournament selection
  • Implicit fitness remapping
  • Adjust fitness function for roulette wheel
  • Explicit fitness remapping
  • Fitness scaling
  • Fitness windowing
  • Fitness ranking

Fitness scaling
  • Fitness values are scaled by subtraction and
    division so that worst value is close to 0 and
    the best value is close to a certain value,
    typically 2
  • Chance for the most fit individual is 2 times the
  • Chance for the least fit individual is close to 0
  • Problems when the original maximum is very
    extreme (super-fit) or when the original minimum
    is very extreme (super-unfit)
  • Can be solved by defining a minimum and/or a
    maximum value for the fitness

Example of Fitness Scaling
Fitness windowing
  • Same as window scaling, except the amount
    subtracted is the minimum observed in the n
    previous generations, with n e.g. 10
  • Same problems as with scaling

Fitness ranking
  • Individuals are numbered in order of increasing
  • The rank in this order is the adjusted fitness
  • Starting number and increment can be chosen in
    several ways and influence the results
  • No problems with super-fit or super-unfit
  • Often superior to scaling and windowing

Other parameters of GA 1
  • Initialization
  • Population size
  • Random
  • Dedicated greedy algorithm
  • Reproduction
  • Generational as described before (insects)
  • Generational with elitism fixed number of most
    fit individuals are copied unmodified into new
  • Steady state two parents are selected to
    reproduce and two parents are selected to die
    two offspring are immediately inserted in the
    pool (mammals)

Other parameters of GA 2
  • Stop criterion
  • Number of new chromosomes
  • Number of new and unique chromosomes
  • Number of generations
  • Measure
  • Best of population
  • Average of population
  • Duplicates
  • Accept all duplicates
  • Avoid too many duplicates, because that
    degenerates the population (inteelt)
  • No duplicates at all

Example run
  • Maxima and Averages of steady state and
    generational replacement

Introduction to Evolutionary ComputationReading
  • Bäck, T., Hammel, U., and Schwefel, H.-P. (1997).
    Evolutionary Computation Comments on the
    History and Current State, IEEE Transactions on
    Evolutionary Computation, VOL. 1, NO. 1, April
  • Spears, W. M., De Jong, K. A., Bäck, T., Fogel,
    D. B., and de Garis, H. (1993). An Overview of
    Evolutionary Computation, The Proceedings of the
    European Conference on Machine Learning, v667,
    pp. 442-459. (http//
  • De Jong, Kenneth A., and William M. Spears
    (1993). On the State of Evolutionary
    Computation, The Proceedings of the Int'l
    Conference on Genetic Algorithms, pp. 618-623.