Hybridization of SearchMeta-Heuristics

Bob Buehler

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

EAnt

The Power of Ants

The World The Ant The Pheromone The Dream

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 cj = set of possible next components w(ci

j) = [τij]α[η(ci

j)]β

p(cij) = w(ci

j) / Σ w(cj)

Basic ACO Algorithm

Initialize pheromones and heuristics Iterate until termination condition

Generate Solutions Update pheromones

Decay all Increase those present in

high fitness solutions

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

Testing

EA

vs ACO

vs EAnt

Euclidean TSP

5

4

2

13

0

1 4 3 5 20 0

0 X

Y

EA Representation

1 4 3 5 20 01 4 3 5 2 00

EA Reproduction

3 4 2 1 50 0

1 4 3 2 50 0

1 4 3 5 20 0

1 4 3 2 50 0

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).

EAnt Representation Example

4

2

13

0

54 11 2

033 1

12

4 5

4

23

03 1

10 1 2 3 4

01234

EAnt Genotype

1 4 3 2 00

Environment

EAnt Reproduction

Parameterized Uniform Crossover Gaussian Mutation with σ = 1

Results-Time Ranking

1. EA

2. ACO Step-wise cycle creation

3. EAnt Step-wise cycle creation O(n2) individual size and reproduction

Results- EA and ACO Convergence

0

200

400

600

800

1000

1200

1400

1600

1800

200

800

1400

2000

2600

3200

3800

4400

5000

5600

6200

6800

7400

8000

8600

9200

9800

Cycles Generated

Cyc

le L

eng

th EA Local

EA Global

ACO Local

ACO Global

Results- EAnt Convergence

0

200

400

600

800

1000

1200

1400

1600

200

800

1400

2000

2600

3200

3800

4400

5000

5600

6200

6800

7400

8000

8600

9200

9800

Cycles

Cyc

le L

eng

th

Eant(50,20,10)

Eant(50,40,5)

EAnt(100,10,5)

ACO

EA

(generations, individuals, fitness)

Hope

0

200

400

600

800

1000

1200

1400

1600

200

800

1400

2000

2600

3200

3800

4400

5000

5600

6200

6800

7400

8000

8600

9200

9800

Cycles

Cy

cle

Le

ng

th

Eant(50,20,10)

Eant(50,40,5)

EAnt(100,10,5)

EAnt(1000,10,1)

ACO

EA

Final Thoughts

Test for better final solution Different problem types EAnt pheromone model initialization

54 11 2

033 1

12

4 5

4

23

03 1

10 1 2 3 4

01234

55 01 5

052 0

21

2 5

2

21

01 0

10 1 2 3 4

01234

Improved?

Questions?