Genetic Algorithms

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Genetic Algorithms

• Motivation and overview
• Efficient and robust search technique in vast and
  complex search areas.
• Finds optimal or near optimal solutions to
  problems.
• Based on the mechanics of natural selection and
  genetics. ie survival of the fittest. Many of
  the terms used come from evolution/genetics.
• Rather than working with a single solution to a
  problem at a time, a number of solutions are
  evaluated simultaneously referred to as a
  population
• Each solution is evaluated for its fitness. The
  better the solution the greater its chance of
  survival.
• Uses an iterative process, with better solutions
  normally evolving over time

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Genetic Algorithms

• Application areas
• Genetic Algorithms are used for optimization
  problems. These problems usually involve
  maximizing or minimizing some parameters, for
  example minimizing cost or time, maximizing
  usage or a combination of these. For example
• Scheduling
• Design
• Financial Management

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Genetic Algorithms

• Problem formulation
• the problem is formulated as a string of binary
  digits (sometimes referred to as a chromosome)
• a chromosome consists of a series of genes
• both the value of the gene and the position of
  the gene in the chromosome are important
• the value represents some problem variable
• the position represents some problem variable

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Genetic Algorithms

• Example (1)
• A very simple timetabling problem
• there are four subjects to be timetabled into
  eight time slots.
• two variables subject four different values,
  slot eight different values
• one possibility
• gene value -gt a subject
• gene position -gt a time slot
• four different subjects ie four gene values -gt a
  2 bit gene

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Genetic Algorithms

• Example (1)
• i.e.
• binary decimal meaning
• 00 0 subject 1
• 01 1 subject 2
• 10 2 subject 3
• 11 3 subject 4
• We require 8 positions one for each time slot,
  in other words 8 genes

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Genetic Algorithms

• Example (1)
• An example of a timetable represented in this way
  would be
• 00 01 01 11 00 11 01 01
• or
• 0001011100110101
• This chromosome is composed of eight two bit
  genes
• i.e a 16 bit chromosome
• Note as a decimal string it would be
• 0 1 1 3 0 3 1 1

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Genetic Algorithms

• Example (1)
• 00 01 01 11 00 11 01 01
• How might you interpret this?
• subject 1 (00) timetabled into slot 1
• subject 2 (01) timetabled into slot 2
• subject 2 (01) timetabled into slot 3
• subject 4 (11) timetabled into slot 4
• subject 1 (00) timetabled into slot 5
• subject 4 (11) timetabled into slot 6
• subject 2 (01) timetabled into slot 7
• subject 2 (01) timetabled into slot 8
• and subject 3 (10) does not appear at all

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Genetic Algorithms

• Example (1)
• 00 01 01 11 00 11 01 01
• Note at this stage there are no constraints on
  these timetables
• i.e. no concept of a valid or invalid timetable,
  no concept of one time table being better' than
  another.
• How many possible timetables are there?
• 65 538 (216)

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Genetic Algorithms

• Example (1)
• An alternative formulation?
• use the position to represent the subject and the
  gene value to represent the time slot
• Now we only have four genes there are only four
  subjects, but we need a three bit gene to
  generate eight different values, for the time
  slots
• 000 0 slot 1
• 001 1 slot 2
• 010 2 slot 3
• 011 3 slot 4
• 100 4 slot 5
• 101 5 slot 6
• 110 6 slot 7
• 111 7 slot 8

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Genetic Algorithms

• Example (1)
• An alternative formulation?
• a sample chromosome would be
• 001 001 111 010
• How would you interpret this?
• subject 1 is scheduled in time slot 2 (001)
• subject 2 is scheduled in time slot 2 (001)
• subject 3 is scheduled in time slot 8 (111)
• subject 4 is scheduled in time slot 3 (010)
• Note that there only 4096 (212) possible
  timetables

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Genetic Algorithms

• Example (1)
• An alternative formulation?
• Which of the two representations is better?
• Can you see that the second formulation implies
  that a subject can only be scheduled once whereas
  the first formulation implies that no two
  subjects can be scheduled at the same time?

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Genetic Algorithms

• Example (2)
• file storage optimisation
• there are four locations on disc and five files
  to be stored
• the storage space for each location varies, the
  file sizes vary.
• two variables
• the location four values
• the file five values
• use gene position to indicate the file
• use gene value to indicate location
• the chromosome will therefore consist of five
  two bit genes (10 bits)

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Genetic Algorithms

• Example (2)
• gene value (location)
• binary decimal meaning
• 00 0 location 1
• 01 1 location 2
• 10 2 location 3
• 11 3 location 4

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Genetic Algorithms

• Example (2)

A sample chromosome could be
01
00
00
10
11
file A
file B
file C
file D
file E
Interpretation File A is stored in location
2 File B is stored in location 1 File C is stored
in location 1 File D is stored in location 3 File
E is stored in location 4 Note that more than
one file can be stored in a given location there
are 1024 (210) possible configurations
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Genetic Algorithms

• Example (2)
• Are there alternative representations?
• we could use the gene position to represent the
  location and the gene value to represent the file
• Only need a four gene chromosome there are only
  four locations
• but we need a gene that can have at least five
  values
• 3 bit gene max of eight values
• 000 0 file A
• 001 1 file B
• 010 2 file C
• 011 3 file D
• 100 4 file E
• 101 5 invalid file
• 110 6 invalid file
• 111 7 invalid file
• We now have a 12 bit chromosome (i.e four, three
  bit genes)

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Genetic Algorithms

• Example (2)
• Are there alternative representations?
• for example

001
100
100
111
location 1
location 2
location 3
location 4
i.e 001100100111 or 1 4 4 4 7
this means File B is in location 1 File E is in
location 2 File E is in location 3 ! An invalid
file is in location 4
Clearly this is a very poor problem
formulation. A file could be in different places
at the same time A location can only have one
file in it Some of the files may be invalid
The above chromosome is not a valid solution