1. Hybridization of Search Meta-Heuristics Bob Buehler

2. A Recombination of Strengths Genetic Algorithm  High correlation reproduction operators  Fast computation excluding fitness Ant Colony Optimization  Well suited in step- wise solution creation  Strong local search using probabilistic pheromone model EAnt

4. The Power of Ants The World The Ant The Pheromone The Dream

5. Combinatorial Optimizers Ant Colony Optimization Traveling Salesman Problem  S = The space of all possible solutions  Τ = Pheromone model  η = Heuristic values Step-wise solution creation  About to select the next component for a partial solution  c j = set of possible next components  w(c i j ) = [τ i j ] α [η(c i j )] β  p(c i j ) = w(c i j ) / Σ w(c j )

6. Basic ACO Algorithm Initialize pheromones and heuristics Iterate until termination condition  Generate Solutions  Update pheromones Decay all Increase those present in high fitness solutions

7. EAnt Evolving Pheromone Models  Create random pheromone models as arrays of real values  Let k ants walk the pheromone and create solutions  Assign a fitness to the model equal to the average of all solutions created  Use GA reproduction operators  Profit

8. Testing EA vs ACO vs EAnt

9. Euclidean TSP 5 4 2 1 3 0 1435200 0X Y

10. EA Representation 1435200 14352100

11. EA Reproduction 3421500 1432500 1435200 1432500

12. EAnt Representation Pheromone Model is a two dimensional array M[n,m] where n is the node an ant is currently at and m is a node connected to n. Every element is initialized with a random value in the range [0,5).

13. EAnt Representation Example 4 2 1 3 0 5 41 12 03 31 1 2 45 4 2 3 0 31 1 01234 0 1 2 3 4 EAnt Genotype 143200 Environment

14. EAnt Reproduction Parameterized Uniform Crossover Gaussian Mutation with σ = 1

15. Results -Time Ranking 1. EA 2. ACO  Step-wise cycle creation 3. EAnt  Step-wise cycle creation  O(n 2 ) individual size and reproduction

16. Results - EA and ACO Convergence

17. Results - EAnt Convergence (generations, individuals, fitness)

18. Hope

19. Final Thoughts Test for better final solution Different problem types EAnt pheromone model initialization 5 41 12 03 31 1 2 45 4 2 3 0 31 1 01234 0 1 2 3 4 5 50 15 05 20 2 1 25 2 2 1 0 10 1 01234 0 1 2 3 4 Improved?

20. Questions?