Evolutionary- Algorithms by chandrapro


									        Introduction to Evolutionary
• 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 process.

• 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
            (Applications cont.)
•   Robotics,
•   Air Traffic Control,
•   Design,
•   Scheduling,
•   Machine Learning,
•   Pattern Recognition,
•   Job Shop Scheduling,
•   VLSI Circuit Layout,
•   Strike Force Allocation,
  Introduction to Evolutionary Computation
             (Applications 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));
      Pop(t+1)= Replace(Pop(t),Offspring(t));
      t = t + 1;

        Candidate Solutions CS

1. In an Evolutionary Computation, a population of candidate
   solutions (CSs) is randomly generated.

2. Each of the CSs is evaluated and assigned a fitness based on a
   user specified evaluation function.
   1.   The evaluation function is used to determine the „goodness‟ of a CS.

3. A number of individuals are then selected to be parents based on
   their fitness.

4. 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
1. 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.

2. Finally, a decision must be made as to which individuals
   of the current population and the offspring population
   should be allowed to survive.
   1.   Typically, in EC , this is done to guarantee that the population
        size remains constant.
   2.    [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

• 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 be:
    •   The discovery of an optimal or near optimal solution
    •   Convergence on a single solution or set of similar solutions,
    •   When the EC detects the problem has no feasible solution,
    •   After a user-specified threshold has been reached, or
    •   After a maximum number of cycles.

 A Brief History of Evolutionary
• The idea of using simulated evolution to solve
  engineering and design problems have been around
  since the 1950‟s (Fogel, 2000).
   •   Bremermann, 1962
   •   Box, 1957
   •   Friedberg, 1958

• However, it wasn‟t until the early 1960‟s that we began
  to see three influential forms of EC emerge (Back et al,
   •   Evolutionary Programming (Lawrence Fogel, 1962),
   •   Genetic Algorithms (Holland, 1962)
   •   Evolution Strategies (Rechenberg, 1965 & Schwefel, 1968),
A Brief History of Evolutionary Computation

• 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.                                   9
A Brief History of Evolutionary Computation

• 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 Computation
• However, a number of other books helped fuel the
  growing interest in EC:
   •   Lawrence Davis’, “Handbook of Genetic Algorithms”,
   •   Zbigniew Michalewicz’ book (1992), “Genetic Algorithms
       + Data Structures = Evolution Programs.
   •   John R. Koza’s “Genetic Programming” (1992), and
   •   D. B. Fogel’s 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 Computation:
 The Evolution of Evolutionary Computation

   • First Generation EC
      •   EP (Fogel)
      •   GA (Holland)
      •   ES (Rechenberg, Schwefel)

   • Second Generation EC
      •   Genetic Evolution of Data Structures (Michalewicz)
      •   Genetic Evolution of Programs (Koza)
      •   Hybrid Genetic Search (Davis)
      •   Tabu Search (Glover)

  A Brief History of Evolutionary Computation:
The 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
             A Simple Example
• Let‟s walk through a simple example!

• Let‟s say you were asked to solve the following problem:
   •   Maximize:
   •   f6(x,y) = 0.5 + (sin(sqrt(x2+y2))2 – 0.5)/(1.0 + 0.001(x2+y2))2
   •   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 like!
   •   This may help us determine a good algorithm for solving it.
    Introduction to Evolutionary Computation:
                A Simple Example
•   A 3D view of f6(x,y):

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

 Introduction to Evolutionary Computation:
             A Simple Example
• Let‟s develop a simple EC for solving this

• An individual (chromosome or CS)
  •   <xi,yi>
  •   fiti = f6(xi,yi)

 Introduction to Evolutionary Computation:
             A Simple Example
Procedure simpleEC{
    t = 0;
    Initialize Pop(t); /* of P individuals */
    Evaluate Pop(t);
    while (t <= 4000-P){
      Select_Parent(<xmom,ymom>); /* Randomly */
      Select_Parent(<xdad,ydad>); /* Randomly */
         xkid = rnd(xmom, xdad) + Nx(0,);
         ykid = rnd(ymom, ydad) + Ny(0,);
      fitkid = Evaluate(<xkid,ykid>);
      Pop(t+1) = Replace(worst,kid);{Pop(t)-{worst}}{kid}
      t = t + 1;
    Introduction to Evolutionary Computation:
                A Simple Example
•   To simulate this simple EC we can use the applet at:
•   http://www.eng.auburn.edu/~gvdozier/GA.html

 Introduction to Evolutionary Computation:
             A Simple Example

• To get a better understanding of some of
  the properties of ECs let‟s do the „in class‟
  lab found at:

Hill climbing

                    Introduction 1
• Inspired by natural evolution
• Population of individuals
   •   Individual is feasible solution to problem
• Each individual is characterized by a Fitness function
   •   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
• Offspring has combination of properties of two parents
• If well designed, population will converge to optimal
  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
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:
• 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
• 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 bits
        Most chromosomes code for illegal tour
        Several chromosomes code for the same tour
• Path
   •   Cities are numbered; chromosome is string of integers
        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. 0.001)

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

        One-point crossover 1
• Randomly one position in the chromosomes is chosen
• 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
    1          2     1          2

2          1        2       1
         Two-point crossover
• Randomly two positions in the chromosomes are chosen
• Avoids that genes at the head and genes at the tail of a
  chromosome are always split when recombined

           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 parameter)

 Mask:         0110011000        (Randomly   generated)

 Parents:      1010001110        0011010010

 Offspring: 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
   •   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
• 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 fitness
• 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 fitness

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,
       0.5<p<1, 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
   •   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 fitness
   •   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 average
   •   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
   •   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 fitness
• 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 generation
   •   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

45        St_max

40        St_av.
     0             5     10         15         20

     Introduction to Evolutionary Computation:
                    Reading List
1.     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

2.     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.

3.     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.


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