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Presentation by Pier Luca Lanzi at the Optimization by Building and Using Probabilistic Models (OBUPM 2008) workshop at the Genetic and Evolutionary Computation Conference (GECCO-2008)
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Pier Luca Lanzi
Real-Coded Extended Compact Genetic Algorithm based on Mixtures of ModelsPier Luca Lanzi, Luigi Nichetti, Kumara Sastry,Davide Voltini, and David E. Goldberg
OBUPM-2008, July 12, 2008, Atlanta, GA
Estimation of Distribution Algorithms
Population
Probabilistic
ModelSelectionNew
Population
Extended Compact Genetic Algorithm
Motivations
OBUPM-2008, July 12, 2008, Atlanta, GA
What are the Motivations? 6
Real-Coded ECGA
Adaptive Discretization
Ying Ping Chen & c.
Real-Coded BOA
Chang Wook Ahn
Real-Coded ECGA
Basic Discretization
Fossati & al.
Is there something simpler?What if we downgrade RBOA to ECGA models?
This Talk:
From RBOA to RECGA
Real-Coded ECGA
OBUPM-2008, July 12, 2008, Atlanta, GA
8What is the Approach (This Time)
No discretization
Model Building
Model Scoring
Model Fitting
Model Sampling
What are the differences?
The model is simpler than the one used in RBOA
Therefore it should be faster
The analysis should be easier
More complex than the other two RECGAs
Real Domain
OBUPM-2008, July 12, 2008, Atlanta, GA
Model Building 10
A
Selected Population
Clustering Distributions for structure A B C D
A B C D
A B C D
A B C D
A B C D
B C D
A B C D
OBUPM-2008, July 12, 2008, Atlanta, GA
Model Building 11
[A B] C DA B C D
Accuracy + Complexity Accuracy + Complexityvs
OBUPM-2008, July 12, 2008, Atlanta, GA
12
A B C D
A C [B D]
[A C] B D
[A B] C D
A [B C] D
A B [C D]
[A D] B C
[A B] [C D]
[A B C] D
[A B D] C
[A B C D]
Searching for the Model Structure
Candidate Structures from A B C D
Candidate Structures from [A B] C D
Candidate Structures from [A B] [C D]
Final Structure:
[A B] [C D]
OBUPM-2008, July 12, 2008, Atlanta, GA
14
Selected population partitioned according to the model structure
Clustering(again)
A B C D
C D
A B
A B A B
A B
Model Building: Parameters Fitting
A B
Compute model parameters
Structure [A B] [C D]
OBUPM-2008, July 12, 2008, Atlanta, GA
15
Selected population partitioned according to the model structure
Clustering(again)
A B C D
C D
A B
Model Building: Parameters Fitting
A B
Compute model parameters
Structure [A B] [C D]
OBUPM-2008, July 12, 2008, Atlanta, GA
16
Selected population partitioned according to the model structure
Clustering(again)
A B C D
C D
A B
Model Building: Parameters Fitting
A B
Compute model parameters
Structure [A B] [C D]
OBUPM-2008, July 12, 2008, Atlanta, GA
17
Selected population partitioned according to the model structure
Clustering(again)
A B C D
C D
A B
Model Building: Parameters Fitting
A B
Compute model parameters
Structure [A B] [C D]
OBUPM-2008, July 12, 2008, Atlanta, GA
18
New Individual
Probabilistic model from the previous step
Random selection of the model components
Model Sampling
B C DA B C DA
[A B]
[C D]
OBUPM-2008, July 12, 2008, Atlanta, GA
19
New Individual
Probabilistic model from the previous step
Random selection of the model components
Model Sampling
B C DA B C DA
[A B]
[C D]
OBUPM-2008, July 12, 2008, Atlanta, GA
20
New Individual
Probabilistic model from the previous step
Random selection of the model components
Model Sampling
B C DA B C DA
[A B]
[C D]B C DA
OBUPM-2008, July 12, 2008, Atlanta, GA
What Experiments?
Scalability Analysis
Number of evaluations vs number of variables
Population size vs number of variables
Influence of the clustering algorithm
Model Selection (typically, k-means)
Model Sampling (typically, adaptive, randomized leader algorithm)
Requirement for convergence during bisection
In the 97% of the runs,
the 99.9% of the population is an optimum
22
OBUPM-2008, July 12, 2008, Atlanta, GA
First a Simple Function 23
Sphere Function
Analyze scalability when an univariate model is enough
OBUPM-2008, July 12, 2008, Atlanta, GA
First a Simple Function 24
Model Selection
O(n1.75)-O(0.5)
Model Fitting
OBUPM-2008, July 12, 2008, Atlanta, GA
Adapting Everything...
RLA+RLA scales as O(n1.1)
25
OBUPM-2008, July 12, 2008, Atlanta, GA
RDP
26Then a Deceptive One...
Analyze scalability when competent recombination is needed
+ + +….
+ +….
OBUPM-2008, July 12, 2008, Atlanta, GA
27Then a Deceptive One...
RECGA scales
subquadratically
OBUPM-2008, July 12, 2008, Atlanta, GA
More Results ... 29
Model Selection
(subquadratic)
Model Fitting
(subquadratic)
OBUPM-2008, July 12, 2008, Atlanta, GA
Adapting Everything... 30
Conclusions
OBUPM-2008, July 12, 2008, Atlanta, GA
Conclusions
Yet, another, real-coded ECGA
Behaves similarly to the simpler real-coded ECGA
Rules of thumb?
Sphere function
Scalability similar to univariate methods
The number of clusters using for selection, matters.
Real Deceptive function
Number of generations scale subquadratically
Increasing the number of clusters in sampling matters
Overall, the full adaptive version provides a good trade-off
34
OBUPM-2008, July 12, 2008, Atlanta, GA
What Next?
Please, not another real-coded ECGA ...
How do we go from simple discretization (Fossati et al.),Adaptive Discretization (Chen et al.), to this model?
Virtual alphabets (Goldberg 1991)
Theory of convergence for real-coded GAs
Selection restricts subsequent search to intervals with above average fitness, dimension by dimension
Intervals form the characters of a virtual alphabet, searched during recombination
35
Virtual alphabets, discretizations, models?
OBUPM-2008, July 12, 2008, Atlanta, GA
Thank You!
Any Question?
