1/30
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Introduction
Anytime
optimization
Experimental
setup
Automatically Improving the Anytime Behaviour
of Multiobjective Evolutionary Algorithms
Andreea Radulescu1 Manuel López-Ibáñez2
Thomas Stützle2
1 LINA,
Results
Conclusion
UMR CNRS 6241, Université de Nantes, Nantes, France
[email protected]
2 IRIDIA,
CoDE, Université Libre de Bruxelles (ULB), Brussels, Belgium
[email protected],[email protected]
March 22nd, 2013
2/30
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Summary
1
Introduction
2
Anytime optimization
3
Experimental setup
4
Results
5
Conclusion
Introduction
Anytime
optimization
Experimental
setup
Results
Conclusion
3/30
Introduction
Evolutionary Algorithms
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Initialization
Parent selection
Parents
Recombination
Population
Introduction
Anytime
optimization
Experimental
setup
Termination
Survivor selection
Mutation
Offspring
Results
Conclusion
Figure: General framework of Evolutionary Algorithms
4/30
Introduction
Manual vs Automatic Tuning
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Finding an appropriate parameter configuration for a
specific algorithm is a difficult optimization problem;
Introduction
Many evolutionary algorithms are still manually tuned;
Anytime
optimization
Experimental
setup
Results
Conclusion
Parameter values are established by conventions, ad hoc
choices and experimental comparisons on a limited scale;
Automatic tuning methods are available that configure
evolutionary algorithms without much human effort.
Introduction
5/30
Automatic Tuning
Final quality
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Introduction
Anytime
optimization
Experimental
setup
Results
Conclusion
Figure: Quality of Pareto-front approximations through a run
Introduction
6/30
Automatic Tuning
Anytime behaviour
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Introduction
Anytime
optimization
Experimental
setup
Results
Conclusion
Figure: Anytime behaviour quality
7/30
Introduction
Purpose of the research
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Parameter values greatly determine the success of an EA
in reaching optimal solutions;
Introduction
Anytime
optimization
Experimental
setup
Results
Conclusion
Improve the anytime behaviour of multi-objective
evolutionary algorithms;
Find automatically the algorithm configurations that
produce the best anytime behaviour.
8/30
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Summary
1
Introduction
2
Anytime optimization
3
Experimental setup
Tested MOEAs
Benchmark problems
Monotonicity of hypervolume in MOEA
The irace package
4
Results
Tuning for anytime behaviour
Tuning for final quality
5
Conclusion
Introduction
Anytime
optimization
Experimental
setup
Results
Conclusion
9/30
Anytime optimization
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
An anytime algorithm returns as high-quality solutions as
possible at any moment of its execution;
Introduction
Anytime
optimization
Experimental
setup
Results
Conclusion
The evaluation of the anytime behaviour of an algorithm
can be seen as a bi-objective problem;
The non-dominated front so obtained reflects the quality
of the anytime behaviour of the algorithm.
10/30
Anytime optimization
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Introduction
Anytime
optimization
Experimental
setup
Results
Conclusion
Figure: Anytime behaviour quality
11/30
Anytime optimization
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Introduction
Anytime
optimization
Experimental
setup
Results
Conclusion
Figure: Anytime behaviour quality
12/30
Anytime optimization
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Introduction
Anytime
optimization
Experimental
setup
Results
Conclusion
Figure: Anytime behaviour quality
13/30
Anytime optimization
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Introduction
Anytime
optimization
Experimental
setup
Results
Conclusion
Figure: Anytime behaviour quality
14/30
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Summary
1
Introduction
2
Anytime optimization
3
Experimental setup
Tested MOEAs
Benchmark problems
Monotonicity of hypervolume in MOEA
The irace package
4
Results
Tuning for anytime behaviour
Tuning for final quality
5
Conclusion
Introduction
Anytime
optimization
Experimental
setup
Tested MOEAs
Benchmark problems
Monotonicity of
hypervolume in
MOEA
The irace package
Results
Conclusion
15/30
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Tested MOEAs
IBEA (Indicator-Based Evolutionary Algorithm)
it can be adapted to arbitrary preference information;
does not require additional techniques in order to preserve
the diversity of the population.
Introduction
Anytime
optimization
Experimental
setup
NSGAII (Nondominated Sorting Genetic Algorithm II)
Uses a fast nondominated sorting procedure;
Implements an elitist-preserving approach.
Tested MOEAs
Benchmark problems
Monotonicity of
hypervolume in
MOEA
The irace package
Results
Conclusion
SPEA2 (Strength Pareto Evolutionary Algorithm 2)
a fixed-sized archive method;
a nearest neighbor density estimation technique.
16/30
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Introduction
Anytime
optimization
Experimental
setup
Tested MOEAs
Parameters
Name
crossoverProbability
externalMutationProbability
internalMutationProbability
populationSize
crossoverDistrIndex
Tested MOEAs
Benchmark problems
Monotonicity of
hypervolume in
MOEA
The irace package
Results
Conclusion
mutationDistrIndex
scalingFactor (IBEA)
archiveSize (SPEA2)
k(SPEA2)
Role
probability of mating two
solutions
probability of mutating
a solution
probability of mutating
a variable in a solution
number of solutions
distance between the children
and their parents
distribution of the
mutated values
fitness scaling factor
size of the archive
k-th nearest neighbour
Table: Parameters of IBEA, NSGAII and SPEA2
Type
real
real
real
integer
integer
integer
real
integer
integer
17/30
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Benchmark problems
ZDT
Scalable to any number of decision variables;
Controlled difficulty in converging to the Pareto-optimal
front;
Pareto-optimal front easy to construct.
Introduction
Anytime
optimization
Experimental
setup
Tested MOEAs
Benchmark problems
Monotonicity of
hypervolume in
MOEA
The irace package
Results
Conclusion
ZDT1 convex
ZDT2 nonconvex
ZDT3 noncontiguous
18/30
Benchmark problems
DTLZ
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
+ scalable to any number of objectives.
Introduction
Anytime
optimization
Experimental
setup
Tested MOEAs
Benchmark problems
Monotonicity of
hypervolume in
MOEA
The irace package
Results
Conclusion
DTLZ2
DTLZ5
DTLZ7 disconnected set
19/30
Monotonicity of hypervolume in MOEA
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Introduction
Anytime
optimization
ZDT1 without an external
archive
ZDT1 with an external
unbounded archive
DTLZ1 without an external
archive
DTLZ1 with an external
unbounded archive
Experimental
setup
Tested MOEAs
Benchmark problems
Monotonicity of
hypervolume in
MOEA
The irace package
Results
Conclusion
20/30
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Introduction
Anytime
optimization
Experimental
setup
The irace package
The iterated racing algorithm
sampling: parameter configurations are sampled from a
probabilistic distribution (uniformly random at the start);
selecting: parameter configurations are run on a few
training problem instances, and statistically worse
configurations are discarded until a few remain or
computational budget exhausted;
Tested MOEAs
Benchmark problems
Monotonicity of
hypervolume in
MOEA
The irace package
Results
Conclusion
updating: the sampling distribution is modified according
to the selected configurations to bias sampling towards
best configurations found.
21/30
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Summary
1
Introduction
2
Anytime optimization
3
Experimental setup
Tested MOEAs
Benchmark problems
Monotonicity of hypervolume in MOEA
The irace package
4
Results
Tuning for anytime behaviour
Tuning for final quality
5
Conclusion
Introduction
Anytime
optimization
Experimental
setup
Results
Tuning for anytime
behaviour
Tuning for final
quality
Conclusion
22/30
Tuning for anytime behaviour
Anytime behaviour values
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
NSGAII DTLZ
IBEA DTLZ
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optimization
Default
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Introduction
SPEA2 DTLZ
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1.0
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Experimental
setup
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AnytimeTuned
1.1
●
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1.0
AnytimeTuned
Results
Tuning for anytime
behaviour
Tuning for final
quality
Conclusion
Figure: Anytime behaviour quality for the default configuration
versus configurations tuned for anytime behaviour
1.1
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23/30
Tuning for anytime behaviour
Quality variation
2000
Evaluations
3000
500 1000
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Evaluations
3000
1.20
Hypervolume
0
1.10
1.20
ParetoOptimal
SPEA2Default
SPEA2Anytime
SPEA2Final
ParetoOptimal
IBEADefault
IBEAAnytime
IBEAFinal
1.00
1.25
1.30
500 1000
1.15
Hypervolume
0
1.10
Hypervolume
1.20
ParetoOptimal
NSGAIIDefault
NSGAIIAnytime
NSGAIIFinal
1.05
Experimental
setup
1.10
Anytime
optimization
1.00
Introduction
1.30
A. Radulescu,
M. LópezIbáñez, T.
Stützle
1.30
Automatically
Improving the
Anytime
Behaviour of
MOEAs
0
500 1000
2000
Evaluations
Results
Tuning for anytime
behaviour
Tuning for final
quality
Conclusion
Figure: Variation of the quality of the Pareto front obtained for the
three different configurations
3000
24/30
Tuning for anytime behaviour
Final values
Automatically
Improving the
Anytime
Behaviour of
MOEAs
1.2
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Anytime
optimization
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setup
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Introduction
SPEA2 DTLZ
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NSGAII DTLZ
Default
A. Radulescu,
M. LópezIbáñez, T.
Stützle
●
1.2
AnytimeTuned
1.3
0.9
1.0
1.1
AnytimeTuned
1.2
1.3
●
0.8
0.9
1.0
1.1
1.2
1.3
AnytimeTuned
Results
Tuning for anytime
behaviour
Tuning for final
quality
Conclusion
Figure: Final Pareto front quality for the default configuration versus
configurations tuned for anytime behaviour
25/30
Tuning for final quality
Anytime behaviour values
Automatically
Improving the
Anytime
Behaviour of
MOEAs
NSGAII ZDT
SPEA2 ZDT
1.1
●● ●
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Tuning for final
quality
Conclusion
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0.8
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Tuning for anytime
behaviour
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setup
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0.9
FinalTuned
●
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0.8
Anytime
optimization
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Introduction
IBEA ZDT
● ●
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A. Radulescu,
M. LópezIbáñez, T.
Stützle
0.8
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AnytimeTuned
1.0
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1.1
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AnytimeTuned
Figure: Difference for anytime behaviour quality
1.1
●
26/30
Tuning for final quality
Final values
Automatically
Improving the
Anytime
Behaviour of
MOEAs
SPEA2 ZDT
● ● ● ●
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IBEA ZDT
1.2
NSGAII ZDT
1.2
A. Radulescu,
M. LópezIbáñez, T.
Stützle
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behaviour
Tuning for final
quality
Conclusion
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FinalTuned
1.10
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1.15
0.7
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Results
●
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Experimental
setup
●
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Anytime
optimization
FinalTuned
●
Introduction
1.20
0.6
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AnytimeTuned
1.1
1.2
0.7
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AnytimeTuned
Figure: Difference for the quality of the final Pareto front
1.1
1.2
27/30
Tuning for final quality
Quality variation
Automatically
Improving the
Anytime
Behaviour of
MOEAs
Results
Tuning for anytime
behaviour
Tuning for final
quality
Conclusion
2000
Evaluations
Default conf.
3000
ParetoOptimal
IBEA
NSGAII
SPEA2
0
500 1000
2000
Evaluations
Anytime conf.
3000
1.25
1.20
ParetoOptimal
IBEA
NSGAII
SPEA2
1.15
Hypervolume
1.30
1.30
500 1000
1.20
Hypervolume
0
1.10
Hypervolume
1.20
ParetoOptimal
IBEA
NSGAII
SPEA2
1.00
Experimental
setup
1.10
Anytime
optimization
1.00
Introduction
1.30
A. Radulescu,
M. LópezIbáñez, T.
Stützle
0
500 1000
2000
Evaluations
Final conf.
Figure: Variation of the quality of the Pareto front approximation
obtained by the three MOEAs
3000
28/30
Conclusion
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
1
The quality of the anytime behaviour is significantly
improved;
Introduction
2
The tuned configurations improve the search behaviour of
MOEAs;
3
The MOEAs are more robust to specific termination
criteria;
4
Substantial human effort is saved.
Anytime
optimization
Experimental
setup
Results
Conclusion
29/30
Future work
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
−→ The impact of the anytime behaviour tuning can be
extended:
Introduction
Anytime
optimization
Experimental
setup
Results
Conclusion
Different categorical parameters;
Analysis of others MOEAs;
Tests with different benchmark problems.
30/30
Automatically
Improving the
Anytime
Behaviour of
MOEAs
A. Radulescu,
M. LópezIbáñez, T.
Stützle
Introduction
Anytime
optimization
Experimental
setup
Automatically Improving the Anytime Behaviour
of Multiobjective Evolutionary Algorithms
Andreea Radulescu1 Manuel López-Ibáñez2
Thomas Stützle2
1 LINA,
Results
Conclusion
UMR CNRS 6241, Université de Nantes, Nantes, France
[email protected]
2 IRIDIA,
CoDE, Université Libre de Bruxelles (ULB), Brussels, Belgium
[email protected],[email protected]
March 22nd, 2013