Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Sporadic Model Building for Efficiency
Enhancement of Hierarchical BOA
Martin Pelikan1 , Kumara Sastry2 , and David E. Goldberg2
1
Missouri Estimation of Distribution Algorithms Laboratory (MEDAL)
University of Missouri, St. Louis, MO
http://medal.cs.umsl.edu/
pelikan@cs.umsl.edu
2
Illinois Genetic Algorithms Laboratory (IlliGAL)
University of Illinois at Urbana-Champaign, Urbana, IL
{ksastry,deg}@uiuc.edu
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Motivation
Background
Estimation of distribution algorithms (EDAs)
Scalable solution for many problems, often O(n2 ).
Often outperform standard optimization algorithms, making
intractable problems tractable.
Efficiency enhancement (EE)
O(n2 ) is sometimes not enough, we need further EE.
Reasons: Large n, expensive evaluation, online optimization.
Parallelization, fitness evaluation relaxation, hybridization, ...
Purpose
Address model building in hierarchical BOA (hBOA).
Use sporadic model building to speed up model building.
Model-building speedup shown to increase with problem size.
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Outline
Introduction
1
Sporadic model building
2
Experiments
3
Summary and conclusions
4
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Hierarchical BOA (hBOA)
Difference from standard genetic algorithms
Instead of applying crossover and mutation, hBOA builds and
samples a probabilistic model (Bayesian network).
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
What to Speed Up in EDAs?
Computational bottlenecks in hBOA and other EDAs
Potential bottlenecks
Fitness evaluation.
Model building.
Fitness evaluation
Finite element analysis, simulations, interactive evaluation.
Model building
High dimensionality, large subproblems in problem
decomposition, many interactions, complex representations.
Efficiency enhancement
Address the bottlenecks to further improve efficiency.
Our focus: Speed up model building.
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Efficiency Enhancement (EE) in EDAs
Classification of EEs for EDAs
1 Parallelization.
Hybridization.
2
Time continuation.
3
Fitness evaluation relaxation.
4
Prior knowledge utilization.
5
Incremental and sporadic model building.
6
Learning from experience.
7
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Bayesian Networks
Bayesian network has two parts
Structure
Structure determines edges in the network.
Parameters.
Parameters specify conditional probabilities of each variable
given its parents (variables that this variable depends on).
Example: p(X3 |X1 , X2 ).
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Sporadic Model Building (SMB)
Complexity of model building in hBOA
Two components of model building
Learn structure: complexity O(kn2 N ).
N =population size
k=order of subproblems
n=number of bits.
Learn parameters: complexity O(knN ).
Sporadic model building: Basic idea
Learn structure only in some generations.
Remaining generations use structure from the previous
iteration.
Parameters are always updated.
Goal: Save time in the most expensive part of model building.
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
SMB Schedule: When to Rebuild the Structure?
Question
How often to rebuild the network structure?
Simple schedule for SMB
Use constant structure-building period tsb .
Learn structure in the first iteration.
Then, learn structure in each tsb th iteration.
Examples
tsb = 1: Learn in every generation.
tsb = 3: Learn in every 3rd generation.
Tradeoff
Learn too frequently → Small speedup.
Learn too rarely → Models too bad to do well.
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Effects of Sporadic Model Building
Effects of sporadic model building
Speedup of structure building.
Due to building the structure only now and then.
Upper bounded by tsb .
But a bit lower because of population sizing and convergence
effects.
Slowdown of evaluation.
Due to building imperfect models.
May lead to higher population sizes.
May lead to more generations.
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Description of Experiments
Test problems
Concatenated deceptive function of order 3.
Concatenated trap function of order 5.
Hierarchical trap.
2D spin glass (Ising, ±J couplings, periodic boundary cond.).
Two types of experiments
Vary tsb to analyze its effects on hBOA performance.
1
Set tsb automatically
2
Try a very small problem to find reasonable value of tsb .
√
Ensure that tsb ∝ n.
Done only for spin glass.
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Description of Experiments (cont’d)
Experiments
Vary problem size to study scalability.
For each problem size use bisection to find sufficient
population size to ensure 100% convergence in 10
independent runs.
Repeat experiments for each problem size 10 times.
Observed statistics
Speedup of structure building vs. tsb and problem size.
Slowdown of evaluation vs. tsb and problem size.
Optimal speedup vs. problem size.
Slowdown corresponding to optimal speedup vs. problem size.
Overall CPU speedup vs. problem size.
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Speedup of Structure Building vs. tsb on dec-3
8
Speedup on dec−3, n=210
Speedup on dec−3, n=150
7
Structure−building speedup
Speedup on dec−3, n=90
Speedup on dec−3, n=30
6
5
4
3
2
1
0 5 10 15 20
Structure−building period
Speedup first increases with tsb , then drops down.
Bigger problems yield bigger maximum speedups.
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Slowdown of Evaluation vs. tsb on dec-3
10
Slowdown on dec−3, n=30
9 Slowdown on dec−3, n=90
Slowdown on dec−3, n=150
8
Evaluation slowdown Slowdown on dec−3, n=210
7
6
5
4
3
2
1
0 5 10 15 20
Structure−building period
Slowdown increases with tsb .
Bigger problems yield smaller evaluation slowdown!
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Optimal Speedup and Corresponding Slowdown on dec-3
Opt. speedup of structure building
O(n 0.65)
7
Corresponding slowdown of evaluation
Speedup or slowdown
6
5
4
3
2
60 75 90 105 120 135 150 165 180 195 210
Problem size
Opt. structure-building speedup increases with problem size.
Evaluation slowdown decreases with problem size!
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Optimal Speedup and Corresponding Slowdown on trap-5
Opt. speedup of structure building
7 O(n 0.28)
Corresponding slowdown of evaluation
Speedup or slowdown 6
5
4
3
2
60 75 90 105 120 135 150 165 180 195 210
Problem size
Opt. structure-building speedup increases with problem size.
Evaluation slowdown decreases with problem size!
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Optimal Speedup and Corresponding Slowdown on htrap
Optimal speedup of structure building
O(n 0.26)
3.5
Corresponding slowdown of evaluation
Speedup or slowdown
3
2.5
2
1.5
0 50 100 150 200 250
Problem size
Opt. structure-building speedup increases with problem size.
Evaluation slowdown increases slightly with problem size...
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Real-World Test: Struct. Building Speedup on Spin Glass
7
Speedup of structure−building
Slowdown of evaluation
6
Speedup or Slowdown
5
4
3
2
1
100 200 300 400 500 600
Problem size
Structure-building speedup increases with problem size.
Evaluation slowdown increases slightly with problem size...
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Real-World Test: Overall CPU Speedup on Spin Glass
CPU speedup with SMB
4.5
Speedup of CPU time per run 4
3.5
3
2.5
100 200 400 800
Problem size
Overall CPU speedup increases with problem size!
Without the need for determining optimal value of tsb .
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Summary and Conclusions
Sporadic model building (SMB)
Build model structure only in some iterations.
Remaining iterations use old structure.
SMB speeds up model building in hBOA on a single processor.
SMB can be used in other EDAs (e.g. ECGA).
Effects of SMB
Speedup of model building.
Slowdown of evaluation.
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA

Motivation Outline Introduction Sporadic model building Experiments Summary and conclusions
Summary and Conclusions (cont’d)
How well does it work?
Significant speedup of model building (without
parallelization).
Speedup grows with problem size and decreases asymptotic
complexity of model building.
Slowdown of evaluation exists but is much less significant.
If model building is the bottleneck, SMB yields great benefits.
Future work
Adaptive schedule for SMB.
Automatic setting of tsb .
Tradeoffs for specific problems (based on empirical evidence).
More testing.
Martin Pelikan, Kumara Sastry, and David E. Goldberg Sporadic Model Building for Efficiency Enhancement of hBOA