ga for mam
TRANSCRIPT
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Genetic
Algorithm
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Genetic Algorithms
Bio-Inspired artificial intelligence class of
probabilistic optimization algorithms
Well-suited for nonlinear/hard problems with
a large search space
Developed by John Holland
Influenced by Darwins Origin of species
What are Genetic Algorithms?
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Evolution
Variety of species individuals within
the population
Competition for limited resources
Overproduction of offspring
generation
Survival of the fittestOrigin of Species, 1859
Darwins principles
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Evolution
Initial population
Variety of shapes, colors, behaviors
Each individual fits differently to the environment
How does it work?
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Evolution
Initial population
Reproduction
Offspring combines both parents properties
Siblings may differ
in properties
Mutations may occur
How does it work?
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Evolution
Initial population
Reproduction
Limited environmental resources
Only a portion of the
individuals survive
Survival chances
according to fitnessmeasure...
... usually.
How does it work?
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Evolution
Changes in the population content
good properties are kept, bad are distinct
evolutionary pressure
Observations
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Genetic Algorithms
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individualsselect fitter individuals for reproduction
recombine between individuals
mutate individuals
The computational model
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Genetic Algorithms
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individualsselect fitter individuals for reproduction
recombine between individuals
mutate individuals
The computational model
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Genetic Algorithms
The computational model
Gn
55
44
12
31
95
32
87
120
65
53
2
91
73
+
Gn+1
=
crossover
mutation
fitness
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GA in action
There are N items:
Each item i has a weight wi
Each item i has a value vi
The knapsack has a limited capacity of W
units.
The problem description:
Maximize
While
The Knapsack problem (NP)
i
iv
Ww
i
i
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GA in action
For example:
Knapsack capacity = 100
The Knapsack problem (NP)
JIHGFEDCBA
1230183425545192614
21411750231470182420
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GA in action
A. Define the genome encoding
B. Define the fitness function
Before we begin
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GA in action
Bit array:
0 = dont take the item1 = take the item
(items taken: A, B, E)
Genome Encoding
0000010011
-----E--BA
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GA in action
Bit array:
0 = dont take the item
1 = take the item
(items taken: A, B, C, D, E, F, G, I)
Genome Encoding
0101111111
-I-GFEDCBA
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GA in action
Fitness Function
otherwisewW
Wwv
Fitness
items
i
items
i
items
i
:
:
JIHGFEDCBA
1230183425545192614
21411750231470182420
58
10045
EBA
EBA
vvvFitness
www
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GA in action
Fitness Function
otherwisewW
Wwv
Fitness
items
i
items
i
items
i
:
:
JIHGFEDCBA
1230183425545192614
21411750231470182420
98
100198
IGFEDCBA
IGFEDCBA
wwwwwwwwWFitness
wwwwwwww
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Genetic Algorithms
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individuals
select fitter individuals for reproduction
recombine between individuals
mutate individuals
Fitness Evaluation
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Genetic Algorithms
For each individual, calculate the fitness value:
Fitness Evaluation
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Genetic Algorithms
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individualsselect fitter individuals for reproduction
recombine between individuals
mutate individuals
Selection
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Genetic Algorithms
Fitness-proportionate (roulette wheel)
Rank Selection (scaling)
Tournament Selection
Selection
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Genetic Algorithms
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individuals
select fitter individuals for reproduction
recombine between individuals
mutate individuals
Crossover
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Genetic Algorithms
Using a crossover probability PCper individual:
Single point crossover
Two/multi points crossover Uniform / weighted crossover
Crossover
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Genetic Algorithms
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individuals
select fitter individuals for reproduction
recombine between individuals
mutate individuals
Mutation
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Genetic Algorithms
Using a crossover probability PMper bit:
Bit flip mutation
Bit switch mutation
Mutation
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Genetic Algorithms
Crossover & Mutation examples
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Genetic Algorithms
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individualsselect fitter individuals for reproduction
recombine between individuals
mutate individuals
Initial Population
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Genetic Algorithms
Create a fixed size population using:
Random generated individuals
Individuals resulted from previous
evolutionary runs
Initial Population
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GA in action
Example of random population:
Initial Population
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Genetic Algorithms
When an optimal solution is found
When the results converge to constant value
After a predetermined number of generations
Termination Condition
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Genetic Algorithms
Population size: 100 individuals
Crossover: Single pt., PC=0.9
Mutation: Bit flip, PM=0.01
Selection: tournament, groups of 2
Termination condition: after 100
generations
Sample Evolutionary Run
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Genetic Algorithms
Sample Evolutionary Run
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Genetic Algorithms
GA is nondeterministictwo runs may end
with different results
Theres no indication whether bestindividual is optimal
Fitness tends to converge during time
Conclusions