The Design and Analysis of Algorithms
Chapter 6:
Transform and Conquer
Genetic Algorithms
Genetic Algorithms
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What is a GA
Terms and Definitions
Basic Genetic Algorithm
Example
Selection Methods
Crossover Methods
Mutation
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What is a GA
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Searches for good solutions among possible
solutions.
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Uses evolutionary mechanisms including
natural selection, reproduction, mutation
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The best possible solution may be missed
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Useful in problems that are too big or too
difficult to solve with conventional techniques.
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Terms and Definitions (1)
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A solution is coded by a string , also called
chromosome. The words string and
chromosome are used interchangeably
A strings fitness is a measure of how good
a solution it codes. Fitness is calculated by
a fitness function.
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Terms and Definitions (2)
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Selection: The procedure to choose parents
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Roulette wheel selection is a way of picking out
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A wedge on a roulette wheel proportional to the
string's fitness.
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A 'fit' string is more likely to be chosen than an
'unfit' string.
a string from among a group of strings (a
population).
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Terms and Definitions (3)
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Crossover is the procedure by which two
chromosomes mate to create a new offspring
chromosome
parent 1 is copied of up to a randomly chosen
point, and parent 2 is copied from that point
onwards.
Parent 1
100|110
Parent 2
011|100
Offspring1
100 100
Offspring2
011 110
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Terms and Definitions (4)
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Mutation : with a certain probability flip a
bit in the offspring
Various ways to implement mutation,
optional.
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Basic Genetic Algorithm
1.
2.
3.
4.
Start: Generate random population of n
chromosomes (suitable solutions for the
problem)
Fitness: Evaluate the fitness f(x) of each
chromosome x in the population
New population: Create a new population
by repeating following steps until the new
population is complete
Test: If the end condition is satisfied, stop,
and return the best solution in current
population
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New Population
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Selection: Select two parent chromosomes from
a population according to their fitness (the
better fitness, the bigger chance to be selected)
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Crossover: With a crossover probability cross
over the parents to form a new offspring
(children). If no crossover was performed,
offspring is an exact copy of parents.
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Mutation: With a mutation probability mutate
new offspring at each locus (position in
chromosome).
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Termination Criteria
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After a pre-specified number of generations
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When an individual solution reaches a prespecified level of fitness
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When the variation of individuals from one
generation to the next reaches a prespecified level of stability, e.g. all become
equal
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Example: The Knapsack Problem
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A knapsack with capacity C,
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A set of items each with volume and value.
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Find a subset of the items that can fit in the
knapsack and has maximum value.
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This is an optimization NP problem. Given n
items, the number of all subsets to be
examined is 2n.
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Example (cont.)
O1
O2
O3
O4
Volume
4
3
1
5
Value
3
2
3
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Sample candidate solutions
O1
O2
O3
O4
Volume Value
1
2
3
0
1
1
1
0
0
0
0
1
1
1
0
8
9
5
4
0
1
1
1
9
5
0
1
1
0
4
7
8
6
10 <<<<<
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Issues
 How
to represent an individual
 How to choose
 the
fitness function
 the
selection method
 the
crossover method
 the
frequency of mutations
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More on Selection
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Roulette Wheel Selection: proportional to the
fitness
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Rank Selection: rank is assigned based on
fitness, then choose proportional to the rank
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Steady-State Selection: sort and always
choose the best
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Elitism: copy the best individuals in the next
generation
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Tournament selection
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Tournament Selection
Saves time used for sorting
 Fix a constant k < 1, e.g. k =0.75
 Randomly choose two individuals and a
random number r < 1
 if r < k, select the individual with the higher
fitness to be a parent, otherwise select the other
individual to be a parent
 Repeat steps 2 and 3 until the new generation is
created
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More on Crossover
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Random point of split
Fixed point of split
Single point: split in two
Two points: split in three
Uniform: bits are chosen randomly
Arithmetic crossover: the offspring is a result
of some arithmetic operation
Two parents
Three parents
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Applications
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Optimization problems
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Search in a pool of candidate solutions
Tutorial:
http://cs.felk.cvut.cz/~xobitko/ga/
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