Genetic Algorithm and its applications

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Genetic Algorithm andits applications
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INTRODUCTION

• Looking at the world around us, we see a
  staggering diversity of life.
• There are millions of species, each with its own
  unique behavior patterns and characteristics and
  yet, all of these plants and creatures have
  evolved, and continue evolving, over millions of
  years

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• They have adapted themselves to a constantly
  shifting and changing environment in order to
  survive.
• The weaker members of a species tend to die away,
  leaving the stronger and fitter to mate, create
  offspring and ensure the continuing survival of
  the species.

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• The laws of natural selection and Darwinian
  evolution dictate their lives, and it is upon
  these ideas that Genetic Algorithm is based.

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Genetic Algorithm

• Genetic Algorithm starts with a population of
  randomly generated solutions, chromosomes, and
  advance toward better solutions by applying
  genetic operators, modeled on the genetic
  processes occurring in nature.

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• In these algorithms, we maintain a population of
  solutions for a given problem.
• This population undergoes evolution in a form of
  natural selection.

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• In each generation, relatively good solutions are
  reproduced to give offspring that replace the
  relatively bad solutions, which die.
• An evaluation of fitness function plays the role
  of the environment to distinguish between good
  and bad solutions.

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• Although there are many possible variants of the
  basic Genetic Algorithm.
• But, the fundamental mechanism operates on a
  population of chromosomes (representing possible
  solutions to the problem).

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• Genetic Algorithm is one of the stochastic search
  algorithms based on the mechanics of natural
  genetics.
• A solution variable for the problem is first
  represented using artificial chromosomes
  (strings).

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• In other words, the problem is encoded to strings
  that Genetic Algorithm can handle.
• A string represents one search point in the
  solution space.
• Genetic Algorithm uses a set (population) of
  strings (i.e. multiple search points).

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• Therefore, it can be a parallel search method.
• It modifies strings (searching points) using
  selection and genetic operators such as crossover
  and mutation.
• After convergence, strings are decoded to the
  original solution variables and the solutions are
  obtained.

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• Genetic Algorithm consists of three
  operations
• Evaluation of individual fitness
• Formation of a gene pool
• Recombination and mutation

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Basic Genetic Algorithm Operations

• The three basic operators found in every genetic
  algorithm.
• Reproduction
• Crossover
• Mutation
• One other GA operator
• Elitism

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• Though some algorithms may not employ the
  crossover operator, we refer to them as
  evolutionary algorithms rather than Genetic
  Algorithm.

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Reproduction

• The reproduction operator allows individual
  strings to be copied for possible inclusion in
  the next generation.
• The chance that a string will be copied is based
  on the string's fitness value, calculated from a
  fitness function.

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Reproduction

• For each generation, the reproduction operator
  chooses strings that are placed into a mating
  pool, which is used as the basis for creating the
  next generation.

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Example
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• From this table, it is obvious that the string
  10000 is the fittest, and should be selected for
  reproduction approximately 46 of the time.
• 01001 is the weakest, and should only be selected
  19 of the time.

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• There are many different types of reproduction
  operators.
• One always selects the fittest and discards the
  worst, statistically selecting the rest of the
  mating pool from the remainder of the population.

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• There are hundreds of variants of this scheme.
  None are right or wrong and in fact, some will
  perform better than others depending on the
  problem domain being explored.

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• Common reproduction method is the Roulette Wheel
  Method
• Chooses the strings in a statistical fashion
  based on the fitness values

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• When selecting the three strings that will be
  placed in the mating pool, the roulette wheel is
  spun three times, with the results indicating the
  string to be placed in the pool.
• It is obvious from the wheel that there's a good
  chance that string 10000 will be selected more
  than once.

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• Multiple copies of the same string can exist in
  the mating pool.
• This is even desirable, since the stronger
  strings will begin to dominate, eradicating the
  weaker ones from the population.
• There are difficulties with this, as it can lead
  to premature convergence on a local optimum.

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Crossover

• Once the mating pool is created, the next
  operator in the Genetic Algorithm's arsenal comes
  into play.
• Remember that crossover in biological terms
  refers to the blending of chromosomes from the
  parents to produce new chromosomes for the
  offspring.
• The analogy carries over to crossover in Genetic
  Algorithm.

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• The Genetic Algorithm selects two strings at
  random from the mating pool.
• The strings selected may be different or
  identical, it does not matter.
• The Genetic Algorithm then calculates whether
  crossover should take place using a parameter
  called the crossover probability.
• This is simply a probability value p and is
  calculated by flipping a weighted coin.
• The value of p is set by the user, and the
  suggested value is p0.6, although this value can
  be domain dependant.

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• If the Genetic Algorithm decides not to perform
  crossover, the two selected strings are simply
  copied to the new population (they are not
  deleted from the mating pool).
• They may be used multiple times during crossover.
  
• If crossover does take place, then a random
  splicing point is chosen in a string.
• The two strings are spliced and the spliced
  regions are mixed to create two (potentially) new
  strings.
• These child strings are then placed in the new
  population.

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• As an example, say that the strings 10000 and
  01110 are selected for crossover and the Genetic
  Algorithm decides to mate them.
• The Genetic Algorithm selects a splicing point at
  bit 3.
• The following then occurs

Example
100 00 100 10 011 10 011 00 Crossover in
Action
The newly created strings are 10010 and 01100.
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• Crossover is performed until the new population
  is created.
• Then the cycle starts again with selection.
• This iterative process continues until any user
  specified criteria is met (for example, fifty
  generations, or a string is found to have a
  fitness exceeding a certain threshold)

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Mutation

• Selection and crossover alone can obviously
  generate a staggering amount of differing
  strings.
• However, depending on the initial population
  chosen, there may not be enough variety of
  strings.
• To ensure the Genetic Algorithm sees the entire
  problem space or the Genetic Algorithm may find
  itself converging on strings that are not quite
  close to the optimum level it seeks, due to a bad
  initial population.

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• Some of these problems are overcomed by
  introducing a mutation operator into the Genetic
  Algorithm.
• The Genetic Algorithm has a mutation probability,
  m, which dictates the frequency at which mutation
  occurs.
• Mutation can be performed either during selection
  or crossover (though crossover is more usual).

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• For each string element, in each string in the
  mating pool, the Genetic Algorithm checks to see
  if it should perform a mutation.
• If it should, it randomly changes the element
  value to a new one. In our binary strings, ls
  are changed to 0s and 0s to 1s.

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For example, the Genetic Algorithm decides to
mutate bit position 4 in the string 10000
Example
10000 Mutate 10010
The resulting string is 10010 as the fourth bit
in the string is flipped.
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• The mutation probability should be kept very low
  (usually about 0.001).
• High mutation rate will destroy fit strings and
  degenerate the Genetic Algorithm into a random
  walk, with all the associated problems.

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• But mutation will help prevent the population
  from stagnating, adding "fresh blood", as it
  were, to a population.
• It must be taken note that Genetic Algorithm
  comes from the fact that it contains a rich set
  of strings of great diversity.
• Mutation helps to maintain that diversity
  throughout the Genetic Algorithm's iterations.

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Elitism

• There is also another important Genetic Algorithm
  operation that is called Elitism.
• When creating a new population by crossover and
  mutation, there is a large risk that we might
  loose the best chromosome.
• Elitism is the name of the method that first
  copies the best chromosome (or few best
  chromosomes) to the new population.

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• The rest of the population is constructed in ways
  described earlier, that are reproduction,
  crossover and mutation.
• Elitism can rapidly increase the performance of
  Genetic Algorithm, because it prevents a loss of
  the best-found solution.

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Simple Genetic Algorithms Optimization Algorithm
Fitness Value i fi ?f Fitness
Function for String i in the String Population

• Expression of the Fitness Function in a String
  Population

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Example Running GA using
y x2
1. Compute all the values in the table.
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2. With these selections, our mating pool now
looks like this
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3. Finally, the crossover probabilities need to
be calculated (two crossovers need to be
performed to create a new population of two).
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• 4. At the end of the first iteration, our new
  population looks like the following

Note these new strings would be added in the
mating pool now for the selection of strings in
the new population set for the next generation
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Traditional Optimization Methods vs. Genetic
Algorithm

• Traditional optimization techniques showing both
  their strengths and shortcomings when compared
  with GA
• Hill Climbing
• Enumerative
• Random Search Algorithms
• Randomized Search Techniques

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Hill Climbing

• Has its roots in the classical mathematics
  developed in the 18th and 19th centuries
• Finds an optimum by following the local gradient
  of the function
• Advantages
• searches multiple points in the problem space
• Disadvantages
• problem space being searched is continuous in
  nature meanwhile the real world problems are not
• takes the local optimum in the neighborhood of
  the current point

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Enumerative

• Technique is simple
• Finds optimum value in a problem space which is
  finite
• Disadvantages
• inefficient
• computational task is massive

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Random Search Algorithms

• Performs random walks of the problem space,
  recording the best optimum value
• Disadvantages
• inefficiency
• does not perform no better than the enumerative
  search
• does not use any knowledge gained from previous
  results and thus are both dumb and blind

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Randomized Search Techniques

• Random choice to guide itself through the problem
  search space
• Advantages
• not directionless
• knowledge gained from previous results in search,
  it combines them with some randomizing features
• can handle noisy, multimode search spaces with
  some relative efficiency
• most popular forms
• Simulated Annealing
• Genetic Algorithm

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Fuzzy with Genetic Algorithm

• Low mutation leads to premature convergence
• Fuzzy generates a proper mutation probability
• Example The air conditioning system
• These 5 values can be input sets for fuzzy
  systems that can be used to generate a mutation
  probability

very low Low (16 C - 19 C ) low Medium
(23 C) very high High (24 C to 30 C)
high
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Applications of Genetic Algorithm

• There are many applications of Genetic
  Algorithms.
• The two applications of Genetic Algorithm are
  following.
• Power Systems
• Computer Networks

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Power Systems

• Minimize power loss
• Whenever a power system network is reconfigured,
  there will be some power loss due to reverse of
  current or some other external factors. Genetic
  Algorithm approach can be used to minimize power
  loss.

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•  Find the best reconfigured network
• - The best-reconfigured network here means
  that, this reconfigured network has the most
  minimum power loss.

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•  
• Minimize time when network is reconfigured
• When a network is reconfigured, 200 generations
  of networks are produced. And to choose the best
  reconfiguration it takes a long time (maybe a few
  days to executed or compile the program). So, it
  is important to minimize the time taken to
  execute the program.

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Computer Networks

• Minimize time delay of packets that are forwarded
• In a normal computer network there will be
  some time delay (time taken to reach the
  particular node or branch). Genetic Algorithm
  approach can be used to minimize the time delay.

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• Find the best reconfigured network
• The best-reconfigured network here means that,
  this reconfigured network has the most minimum
  time delay.

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• Minimize time when network is reconfigured
• When a network is reconfigured, 200
  generations of networks are produced. To choose
  the best reconfiguration it takes a long time
  (maybe a few days to execute the program). It is
  important to minimize time taken to execute the
  program.

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The End
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Thank You