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??

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