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Basic genetic algorithms^ Step 1
:^ Represent the problem variable domain as
a chromosome of a fixed length, choose the sizeof a chromosome population
N , the crossover
probability
p and the mutation probability c^
p. m
Step 2
:^ Define a fitness function to measure the
performance, or fitness, of an individualchromosome in the problem domain. The fitnessfunction establishes the basis for selectingchromosomes that will be mated duringreproduction.
Step 3
:^ Randomly generate an initial population of
chromosomes of size
N :
x ,^ x^1
xN
Step 4
:^ Calculate the fitness of each individualchromosome: f ( x ),^ f^ 1
( x ),... ,^2
f^ ( x
) N
Step 5
:^ Select a pair of chromosomes for matingfrom the current population. Parentchromosomes are selected with a probabilityrelated to their fitness.
Genetic algorithmsGenetic algorithms ^ GA represents an iterative process. Each iteration is GA represents an iterative process. Each iteration iscalled a^ called a
generationgeneration
. A typical number of generations. A typical number of generations
for a simple GA can range from 50 to over 500. The^ for a simple GA can range from 50 to over 500. Theentire set of generations is called a^ entire set of generations is called a
runrun
^ Because^ Because ^ A common practice is to terminate a GA after a specified^ A common practice is to terminate a GA after a specifiednumber of generations and then examine the best^ number of generations and then examine the bestchromosomes in the population. If no satisfactory solution is^ chromosomes in the population. If no satisfactory solution isfound, the GA is restarted.^ found, the GA is restarted.
GAsGAs
use a stochastic search method, the fitness of ause a stochastic search method, the fitness of a
population may remain stable for a number of generations^ population may remain stable for a number of generationsbefore a superior chromosome appears.^ before a superior chromosome appears.
Now: •^ Consider operating on and maintaining an entire“population” of points simultaneously.^ •
So what?
It would be easier to just run my single point algorithm many times or maybe on multipleprocessors to save wall clock time.
Evolutionary Algorithms •^ Date back to the 1950’s. •^ Many researchers independently developeddifferent versions.^ •
Examples are:^ •^
Genetic Algorithms, • Evolution Strategies, • Evolutionary Programming.
Basic Terminology Most of the terminology is borrowed from Biology •^ Phenotype:
the "outward, physical manifestation" of an
organism. The physical parts, the sum of the atoms,molecules, macromolecules, cells, structures,metabolism, energy utilization, tissues, organs, reflexesand behaviors; anything that is part of the observablestructure, function or behavior of a living organism. • Genotype:
This is the "internally coded, heritable
information" carried by all living organisms. This storedinformation is used as a "blueprint" or set of instructionsfor building and maintaining a living creature.
Basic Terminology •^ Alleles:
Alternative forms of a genetic locus.
-^ Crossing Over:
The breaking during meiosis of one
maternal and one paternal chromosome, the exchangeof corresponding sections of DNA, and the rejoining ofthe chromosomes.^ •^ This process can result in an exchange of alleles betweenchromosomes. • Mutation:
A heritable change in the genetic makeup of
an organism.
Important Note We are not constrained by any of the rules ofbiological systems. •^ For example, we can have as many parents as we wishcontribute to the makeup of our offspring; •^ we can have members that live forever (don’t age). What is important to note here is that we are using natureas a model for our
mathematical
algorithms.
General Approach •^ General equation describing most evolutionaryalgorithms is:
]))[
] 1
[^
tx
vs
tx
Where:x[t] is the population at time
t ;
v() is/are the variation operator(s);s() is the selection operator
x[t+1] is the population at next time step
t+1.
Representation of Candidate Solutions^ •^ GAs can have the following types of representations:
-^ Binary-Coded; •^ Encoding as Vectors of integers; •^ Vectors of real numbers; •^ Vectors of binary bits; •^ Combination of the previous types; • Binary-Coded GAs must decode a chromosome into acandidate solution (CS), evaluate the CS and return theresulting fitness back to the binary-coded chromosomerepresenting the evaluated CS.
Encoding
Individual Chromosome:
^00101 Fitness =
????? d(2,1,5,
00101
) = 1.
Individual Chromosome: f(1.16) = 1.
^00101 Fitness =
The Fitness Assignment Process for Binary Coded
Chromosomes (
ub=2, lb=1, l=
)
Binary Coded Representations:
Encoding •^ Encoding as Vectors of integers.^ •
Useful for Traveling Salesman Problem, Integerproblems. 1 3 4 5
2 6 8 7 Traveling SalesmanProblem:
Possible Trips:
[ 1 8 6 5 2 3 4 7 ] [ 8 2 5 6 3 1 7 4 ] [ 2 4 6 3 7 5 1 8 ]
(where return home is implied).
Encoding Vectors of real numbers •^ Real-Coded GAs can be regarded as GAs thatoperate on the actual phenotype. •^ For Real-Coded GAs, no genotype-to-phenotype mapping is needed.
Real-Coded Representations
Individual Chromosome:
1. Fitness =
?????
Individual Chromosome: f( 1.16 ) = 1.
1. Fitness =
The Fitness Assignment Process for Real Coded Chromosomes
