hybridization of search meta-heuristics bob buehler
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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
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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
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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?