1. Immune Genetic Algorithms By Jeremy Moreau

2. 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

3. Outline Introduction Immune genetic algorithm (IGA) –Vaccination –Immune Selection The immune operator Simulations Conclusions

4. 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

5. 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

6. 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

7. 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

8. 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).

9. Algorithm Flow

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

11. 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

12. 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:

13. Results for GA and IGA

14. Fitness of GA and IGA (Bad Vaccine)

15. 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

16. Questions??