1. Genetic Algorithms
CPSC 212
Spring 2004

2. Heuristic Stochastic optimization algorithm
Used to search for good/excellent solutions to large NP-complete problems
Does not guarantee optimal solution
Provides good solution very quickly

3. Basic Algorithm Create population of solutions Evaluate each solution
Sort in increasing order of quality of solution (i.e., best solution is #1)
Repeat:
Select and mate parents
Produce and evaluate offspring
Insert offspring into population

4. GAs Applied to Traveling Salesperson Problem
Given n cities: 0, 1, …, (n-1)
A solution is a permutation of the values 0 through (n-1)
Randomly create an initial population of solutions (permutations)
Evaluate (determine cost of each tour)
Sort by increasing cost

5. Traveling Salesperson Problem
Example: 6 cities
Initial population:
Adjacency Matrix:
=47

6. Traveling Salesperson Problem
Sort the population
Adjacency Matrix:

7. Traveling Salesperson Problem
Randomly select parents (2 and 5)  

8. Traveling Salesperson Problem
Mate parents (1-point crossover)
randomly select crossover point
cross-selection of genes
____
____

9. Traveling Salesperson Problem
Produce offspring
____
____

10. Traveling Salesperson Problem
Evaluate offspring
Adjacency Matrix:

11. Traveling Salesperson Problem
Insert offspring into population

12. Traveling Salesperson Problem
Repeat mating

13. Traveling Salesperson Problem
Mutation:
Randomly select 1 parent 

14. Traveling Salesperson Problem
Mutation:
Randomly select 2 genes
^ ^

15. Traveling Salesperson Problem
Mutation:
Swap 2 genes
Adjacency Matrix:
=>

16. Traveling Salesperson Problem
Mutation:
Insert mutant solution into population if it is better than worst member

17. Traveling Salesperson Problem
Perform mating 90% of time
Perform mutation 10% of time
Stop when time has expired