Immune Genetic Algorithms

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Nov 30, 2013 (3 years and 10 months ago)

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Immune Genetic Algorithms

By Jeremy Moreau

References


Licheng Jiao
, Senior Member, IEEE,
and
Lei Wang, “A Novel Genetic Algorithm
Based on Immunity,” IEEE Transactions
on Systems, Man, AND Cybernetics

Part
A: Systems and Humans, Vol. 30, No. 5,
September 2000




Outline


Introduction


Immune genetic algorithm (IGA)


Vaccination


Immune Selection


The immune operator


Simulations


Conclusions

Introduction


All genetic algorithms use the mutation
and crossover operators


This gives individuals the chance to evolve
into a more fit individual


If target is difficult to reach, crossover and
mutation may introduce degeneracy into
generations of individuals


Immunity can be introduced to help
prevent degeneration

The Immune Genetic Algorithm
(IGA)


Uses local information to intervene in the
global process of mutation and crossover


Curtails the degenerative phenomena from
arising during the evolution process


Consists of two basic steps:


The vaccination


The immune selection

The Vaccination


Given an individual, vaccination means
modifying the bits of some genes using
prior knowledge


Satisfies two conditions:


If each gene bit of an individual y is wrong,
the probability of transforming to y is 0


If each gene bit of an individual y is optimal,
the probability of transforming to y is 1

The Immune Selection


Consists of two steps:


Perform an immunity test: If the fitness of an
individual is less than that of its parent,
degeneration occurred during crossover and
mutation. Use the parent instead of the child


Annealing selection: an individual is selected
from the present offspring to join with the new
parents

The Algorithm


The immune genetic algorithm


1. Create initial random population A
1
.


2. Abstract vaccines according to the prior
knowledge.


3. If the current population contains the optimal
individual, then the algorithm halts.


4. Perform crossover on the kth parent and obtain the
results B
k
.


5. Perform mutation on B
k

to obtain C
k
.


6. Perform vaccination on C
k

to obtain D
k
.


7. Perform immune selection on D
k

and obtain the
next parent A
k+1
, and then go to step 3).


Algorithm Flow

Convergence


General GA algorithms are not guaranteed
to converge


The IGA is convergent with a probability


of 1


The Immune Operator


Uses the vaccination and immune selection
operators


During these operations, the basic problem
characteristics are abstracted into a schema


Theorem 2: Under the immune selection, if the
vaccination makes the fitness of an individual
higher than the average fitness of the current
population, then the schema of the
corresponding vaccine will be diffused at an
index level within the population. If not, it will be
restrained or attenuated by an index level

Simulations


Simulations were performed on the
Traveling Salesman Problem (TSP)


The following results were for the 75 city
TSP


Were L is the side of the smallest square
containing all cities, N is the number of
cities (75), and D is the path length of the
current permutation, the fitness function
used was:


Results for GA and IGA

Fitness of GA and IGA

(Bad Vaccine)

Conclusions


Introducing the immunity operator
guarantees convergence of the genetic
algorithm


Proper vaccine selection causes the
algorithm to converge quickly. However,
even poor vaccine selection causes the
algorithm to converge, just more slowly


For most large and/or complex problems,
the IGA speeds up performance drastically


Questions??