# Immune Genetic Algorithms

AI and Robotics

Nov 30, 2013 (4 years and 5 months ago)

89 views

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

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??