![Page 1: Hybridization of Search Meta-Heuristics Bob Buehler](https://reader035.vdocument.in/reader035/viewer/2022062407/56649d385503460f94a12558/html5/thumbnails/1.jpg)
Hybridization of SearchMeta-Heuristics
Bob Buehler
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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
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EAnt
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The Power of Ants
The World The Ant The Pheromone The Dream
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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)
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Basic ACO Algorithm
Initialize pheromones and heuristics Iterate until termination condition
Generate Solutions Update pheromones
Decay all Increase those present in
high fitness solutions
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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
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Testing
EA
vs ACO
vs EAnt
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Euclidean TSP
5
4
2
13
0
1 4 3 5 20 0
0 X
Y
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EA Representation
1 4 3 5 20 01 4 3 5 2 00
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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
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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).
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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
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EAnt Reproduction
Parameterized Uniform Crossover Gaussian Mutation with σ = 1
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Results-Time Ranking
1. EA
2. ACO Step-wise cycle creation
3. EAnt Step-wise cycle creation O(n2) individual size and reproduction
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Results- EA and ACO Convergence
0
200
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6800
7400
8000
8600
9200
9800
Cycles Generated
Cyc
le L
eng
th EA Local
EA Global
ACO Local
ACO Global
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Results- EAnt Convergence
0
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5000
5600
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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)
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Hope
0
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5000
5600
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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
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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?
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Questions?