Immune Genetic Algorithms

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Immune Genetic Algorithms

• By Jeremy Moreau

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References

• Licheng Jiao, Senior Member, IEEE, and Lei Wang,
  A Novel Genetic Algorithm Based on Immunity,
  IEEE Transactions on Systems, Man, AND
  CyberneticsPart A Systems and Humans, Vol. 30,
  No. 5, September 2000

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Outline

• Introduction
• Immune genetic algorithm (IGA)
• Vaccination
• Immune Selection
• The immune operator
• Simulations
• Conclusions

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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

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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

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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

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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

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The Algorithm

• The immune genetic algorithm
• 1. Create initial random population A1.
• 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 Bk.
• 5. Perform mutation on Bk to obtain Ck.
• 6. Perform vaccination on Ck to obtain Dk.
• 7. Perform immune selection on Dk and obtain the
  next parent Ak1, and then go to step 3).

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Algorithm Flow
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Convergence

• General GA algorithms are not guaranteed to
  converge
• The IGA is convergent with a probability
• of 1

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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

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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

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Results for GA and IGA
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Fitness of GA and IGA (Bad Vaccine)
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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

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Questions??