MOEAs AutomaticallyImprovingtheAnytimeBehaviour A .../file/REF_39.pdf ·...

AutomaticallyImproving the

AnytimeBehaviour of

MOEAs

A. Radulescu,M. López-Ibáñez, T.Stützle

Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion

1/30

Automatically Improving the Anytime Behaviourof Multiobjective Evolutionary Algorithms

Andreea Radulescu1 Manuel López-Ibáñez2Thomas Stützle2

1LINA, UMR CNRS 6241, Université de Nantes, Nantes, [email protected]

2IRIDIA, CoDE, Université Libre de Bruxelles (ULB), Brussels, [email protected],[email protected]

March 22nd, 2013

[email protected]

[email protected],[email protected]


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion

2/30 Summary

1 Introduction

2 Anytime optimization

3 Experimental setup

4 Results

5 Conclusion


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion

3/30 IntroductionEvolutionary Algorithms

Population

Parents

Offspring

Initialization

TerminationSurvivor selection

Parent selection

Recombination

Mutation

Figure: General framework of Evolutionary Algorithms


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion

4/30 IntroductionManual vs Automatic Tuning

Finding an appropriate parameter configuration for aspecific algorithm is a difficult optimization problem;

Many evolutionary algorithms are still manually tuned;

Parameter values are established by conventions, ad hocchoices and experimental comparisons on a limited scale;

Automatic tuning methods are available that configureevolutionary algorithms without much human effort.


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion

5/30IntroductionAutomatic TuningFinal quality

Figure: Quality of Pareto-front approximations through a run


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion

6/30IntroductionAutomatic TuningAnytime behaviour

Figure: Anytime behaviour quality


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion

7/30 IntroductionPurpose of the research

Parameter values greatly determine the success of an EAin reaching optimal solutions;

Improve the anytime behaviour of multi-objectiveevolutionary algorithms;

Find automatically the algorithm configurations thatproduce the best anytime behaviour.


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion

8/30 Summary

1 Introduction


3 Experimental setupTested MOEAsBenchmark problemsMonotonicity of hypervolume in MOEAThe irace package

4 ResultsTuning for anytime behaviourTuning for final quality

5 Conclusion


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion

9/30 Anytime optimization

An anytime algorithm returns as high-quality solutions aspossible at any moment of its execution;

The evaluation of the anytime behaviour of an algorithmcan be seen as a bi-objective problem;

The non-dominated front so obtained reflects the qualityof the anytime behaviour of the algorithm.


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion




AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

ExperimentalsetupTested MOEAs

Benchmark problems

Monotonicity ofhypervolume inMOEA

The irace package

Results

Conclusion

14/30 Summary

1 Introduction




5 Conclusion


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization


Benchmark problems


The irace package

Results

Conclusion

15/30 Tested MOEAs

IBEA (Indicator-Based Evolutionary Algorithm)it can be adapted to arbitrary preference information;does not require additional techniques in order to preservethe diversity of the population.

NSGAII (Nondominated Sorting Genetic Algorithm II)Uses a fast nondominated sorting procedure;Implements an elitist-preserving approach.

SPEA2 (Strength Pareto Evolutionary Algorithm 2)a fixed-sized archive method;a nearest neighbor density estimation technique.


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization


Benchmark problems


The irace package

Results

Conclusion

16/30 Tested MOEAsParameters

Name Role TypecrossoverProbability probability of mating two real

solutionsexternalMutationProbability probability of mutating real

a solutioninternalMutationProbability probability of mutating real

a variable in a solutionpopulationSize number of solutions integer

crossoverDistrIndex distance between the children integerand their parents

mutationDistrIndex distribution of the integermutated values

scalingFactor (IBEA) fitness scaling factor realarchiveSize (SPEA2) size of the archive integer

k(SPEA2) k-th nearest neighbour integer

Table: Parameters of IBEA, NSGAII and SPEA2


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization


Benchmark problems


The irace package

Results

Conclusion

17/30 Benchmark problemsZDT

Scalable to any number of decision variables;Controlled difficulty in converging to the Pareto-optimalfront;Pareto-optimal front easy to construct.

ZDT1 convex ZDT2 nonconvex ZDT3 noncontiguous


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization


Benchmark problems


The irace package

Results

Conclusion

18/30 Benchmark problemsDTLZ

+ scalable to any number of objectives.

DTLZ2 DTLZ5 DTLZ7 disconnected set


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization


Benchmark problems


The irace package

Results

Conclusion

19/30 Monotonicity of hypervolume in MOEA

ZDT1 without an externalarchive

ZDT1 with an externalunbounded archive

DTLZ1 without an externalarchive

DTLZ1 with an externalunbounded archive

Figure: Monotonicity preservation of the hypervolume


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization


Benchmark problems


The irace package

Results

Conclusion

20/30 The irace packageThe iterated racing algorithm

sampling: parameter configurations are sampled from aprobabilistic distribution (uniformly random at the start);

selecting: parameter configurations are run on a fewtraining problem instances, and statistically worseconfigurations are discarded until a few remain orcomputational budget exhausted;

updating: the sampling distribution is modified accordingto the selected configurations to bias sampling towardsbest configurations found.


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

ResultsTuning for anytimebehaviour

Tuning for finalquality

Conclusion

21/30 Summary

1 Introduction




5 Conclusion


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup



Conclusion

22/30 Tuning for anytime behaviourAnytime behaviour values

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0.6 0.7 0.8 0.9 1.0 1.1

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Figure: Anytime behaviour quality for the default configurationversus configurations tuned for anytime behaviour


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup



Conclusion

23/30 Tuning for anytime behaviourQuality variation

0 500 1000 2000 30001.00

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1.30

Evaluations

Hyp

ervo

lum

e

ParetoOptimalNSGAIIDefaultNSGAIIAnytimeNSGAIIFinal

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Evaluations

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lum

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ParetoOptimalIBEADefaultIBEAAnytimeIBEAFinal

Figure: Variation of the quality of the Pareto front obtained for thethree different configurations


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup



Conclusion

24/30 Tuning for anytime behaviourFinal values

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0.9 1.0 1.1 1.2 1.30.

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Def

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Figure: Final Pareto front quality for the default configuration versusconfigurations tuned for anytime behaviour


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup



Conclusion

25/30 Tuning for final qualityAnytime behaviour values

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Figure: Difference for anytime behaviour quality


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup



Conclusion

26/30 Tuning for final qualityFinal values

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ned

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Figure: Difference for the quality of the final Pareto front


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup



Conclusion

27/30 Tuning for final qualityQuality variation

0 500 1000 2000 3000

1.00

1.10

1.20

1.30

Evaluations

Hyp

ervo

lum

e

ParetoOptimalIBEANSGAIISPEA2

Default conf.

0 500 1000 2000 30001.00

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1.30

Evaluations

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ervo

lum

e


Anytime conf.

0 500 1000 2000 3000

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1.30

Evaluations

Hyp

ervo

lum

e


Final conf.

Figure: Variation of the quality of the Pareto front approximationobtained by the three MOEAs


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion

28/30 Conclusion

1 The quality of the anytime behaviour is significantlyimproved;

2 The tuned configurations improve the search behaviour ofMOEAs;

3 The MOEAs are more robust to specific terminationcriteria;

4 Substantial human effort is saved.


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion

29/30 Future work

−→ The impact of the anytime behaviour tuning can beextended:

Different categorical parameters;Analysis of others MOEAs;Tests with different benchmark problems.


AnytimeBehaviour of

MOEAs


Introduction

Anytimeoptimization

Experimentalsetup

Results

Conclusion

30/30

Automatically Improving the Anytime Behaviourof Multiobjective Evolutionary Algorithms

Andreea Radulescu1 Manuel López-Ibáñez2Thomas Stützle2

1LINA, UMR CNRS 6241, Université de Nantes, Nantes, [email protected]

2IRIDIA, CoDE, Université Libre de Bruxelles (ULB), Brussels, [email protected],[email protected]

March 22nd, 2013

[email protected]

[email protected],[email protected]

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