The Genetic Algorithm vs. Simulated Annealing

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Finding Global Minimum/Maximum

• The Genetic Algorithm vs. Simulated Annealing

Charles Barnes PHY 327
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Finding the min/max of a function

• The genetic algorithm and simulated annealing
  processes are used for determining the global
  minimum and maximum of a selected range for any
  given function.

Global minimum
The function E(x) is equivalent to the internal
energy of the system.
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Genetic Algorithm

• The genetic algorithm is a computer-performed
  optimization method that mimics the process of
  natural evolution.
• An initial population is generated A(0)(A1(0),
  A2(0), An(0)
• Each individual in a population is assigned a
  fitness function.
• There are three types of operators for genetic
  algorithm
• Reproduction (Selection)
• Crossover
• Mutation

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Reproduction

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Crossover

• The crossover operator randomly recombines pairs
  through mating.

Parents P1 P2
1001 0111 0111
1110 0111 1111
Child
1110 0100 1111
Parents P1,2 P3
1110 0111 1111
1010 0111 0001
Child
1010 1101 0001
etc.
This is a genetic operator and evolutionary
algorithm known as crossover.
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Mutation

• The mutation operator is a sudden change of
  chromosome.

001100101001011101
001100101101011101
001100101101001101
A number is randomly switched in the code.
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Genetic Algorithm - Parameters

• There are three main parameters that can be
  changed in the function of the genetic algorithm
• M the population of a specific farm
• N the length of an individuals binary string
• k the temperature interval
• In addition to these, the function can also
  itself be changed.
• The research done on the genetic algorithm was to
  find which parameters, if any, influenced the
  production of accurate results.

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Functions Used in Genetic Algorithm
 
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Results Genetic Algorithm

• The genetic algorithm proved quite accurate on
  each experiment, producing exceptional results
  entirely independent of the function.
• When the variables M, N, and k were changed,
  little to no effect on the global min/max was
  observed.
• The genetic algorithm had no problem finding the
  minimum and maximum on any type of function.

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Simulated Annealing

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The Simulated Annealing Process

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Results Finding the Global Max

• Finding the global maximum of a function
  typically produced a graph as follows

The graph displays how the solutions converge.
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Results Finding the Global Min

• Finding the global minimum of a function
  typically produced a graph as follows

The graph displays how the solutions converge.
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Results Changing Parameters

• The algorithm used for finding the maximum
  function was generally more accurate than the
  minimum algorithm, producing similar graphs with
  similar maximums each time.
• e.g.

100 Calculations
10,000 Calculations
It is interesting to note that the more
calculations done by the algorithm, the faster
the convergence is to the solution.
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Results Accuracy

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Graph 2 (x-2)23
Graph 1 (x-2)23
Max1 Min2
Results of the Algorithms
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Max13 at x2
Min25.04 at x0.57
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Findings Simulated Annealing

• Accurate results for both the maximum and minimum
  simulated annealing algorithms were dependent on
  functions, as more complicated functions
  (typically those with powers or exponentials) had
  trouble producing accurate results
• In general, the more iterations the algorithm
  would undergo, the more accurate the final data
  would be for simpler functions.
• Finding the maximum via simulated annealing is
  much more accurate than finding the minimum,
  though not usually typically accurate.

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Conclusion

• As observed, the genetic algorithm seems to be
  the most accurate method of the two to find both
  the maximum and minimum of any function.
• The simulated annealing process seems to have
  trouble finding the maximum and minimum of more
  complicated functions.

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Future Research

• To understand why the simulated annealing
  algorithm was not accurate, especially at finding
  the global minimum of a function