Presentation of the Evolving Distribution Objects Framework

General IdeaOverview

EDO frameworkConclusion

Evolving Distribution Objects Framework1

Caner [email protected]

Thales Research & TechnologyPalaiseau, France

September 5, 2011

1Except as otherwise noted, content is licensed under the Free Art License.Caner Candan [email protected] MSc Thesis: Evolving Distribution Objects Framework

http://artlibre.org/licence/lal/en



Hard optimization problems heuristic optimizer

Aims to optimize hard optimization problems.

Usually used in operations research and decision aids.

More efficient than classical heuristic search.

Generally based on a stochastic process.

Caner Candan [email protected] MSc Thesis: Evolving Distribution Objects Framework




































Figure: Example of hard optimization problem. Source: J. Dreo





L

G

f(x)

x

D

Figure: Hard optimization problem illustrating global optimum, localoptima and discountinuties. Source: J. Dreo





L

G

f(x)

x

D

M

Figure: Hard optimization solved using metaheuristic algorithms. Source:J. Dreo





P1

P2

P3

P4

P5

P6M3M2M1

Figure: “No Free Lunch” theorem. Source: J. Dreo




An overview of my work

Black-Box

EDO framework

EDA-SA

Parallelization of EDA-SA

Temporal Planning

EO framework

Parallelization of EO

Scalability

Experiments tool

Design of experiments





Black-Box

EDO framework

EDA-SA


Temporal Planning

EO framework


Scalability

Experiments tool






Black-Box

EDO framework

EDA-SA→ paper submitted in a national congressa


aRoadef 2011, Saint-Etienne, France

Temporal Planning

EO framework


Scalability

Experiments tool






Black-Box

EDO framework

EDA-SA


Temporal Planning

EO framework


Scalability

Experiments tool






Black-Box

EDO framework

EDA-SA


Temporal Planning

EO framework

Parallelization of EO→ paper submitted in an internationalcongressa

Scalability

aGECCO ’11, Dublin, Ireland

Experiments tool






Black-Box

EDO framework

EDA-SA


Temporal Planning

EO framework


Scalability

Experiments tool






Black-Box

EDO framework

EDA-SA


Temporal Planning

EO framework


Scalability

Experiments tool






Black-Box

EDO framework

EDA-SA


Temporal Planning

EO framework


Scalability

Experiments tool





Theoretical aspectDesign

Theoretical aspect

E.

I.

D.

Figure: Explicit, Implicit and Direct classes. Source: J. Dreo





Theoretical aspect

Metaheuristics

Local s

earc

h

Population

Trajectory

Natu

rally in

sp

ired

Dynamic objective function

Evolutionaryalgorithm

No m

em

ory

Dire

ct

Exp

licit

Imp

licit

Tabu search

Particle swarmoptimization

Simulatedannealing

Ant colony optimizationalgorithms

Evolutionstrategy

Genetic algorithm

Estimation of distributionalgorithm

Geneticprogramming

Differentialevolution

GRASP

Variable neighborhood search

Stochastic local search

Iterated local search

Guided local search

Scatter search

Evolutionaryprogramming

Figure: Different classifications of metaheuristics. Source: J. Dreo





Theoretical aspect

Metaheuristics

Local s

earc

h

Population

Trajectory

Natu

rally in

sp

ired



No m

em

ory

Dire

ct

Exp

licit

Imp

licit

Tabu search


Simulatedannealing


Evolutionstrategy

Genetic algorithm


Geneticprogramming


GRASP




Guided local search

Scatter search







Theoretical aspect

Metaheuristics

Local s

earc

h

Population

Trajectory

Natu

rally in

sp

ired



No m

em

ory

Dire

ct

Exp

licit

Imp

licit

Tabu search


Simulatedannealing


Evolutionstrategy

Genetic algorithm


Geneticprogramming


GRASP




Guided local search

Scatter search







Estimation of Distribution Algorithm

i1

i2

i0x

f(x)

U

O0

PS

P

PDu

PDe

Figure: Estimation of distribution algorithm. Source: J. Dreo






i1

i2

i0

N

1

PS

P

PDu

PDe







i1

i2

i0

2

PS

P

PDu

PDe







i1

i2

i0

3

PS

P

PDu

PDe







i1

i2

i0

4PS

P

PDu

PDe







i1

i2

i0x

f(x)

U

O0

N

1

2

3

4PS

P

PDu

PDe






Simulated Annealing Algorithm

Figure: The temperature variation of the simulated annealing algorithm.Source: E. Triki and Y. Collette





Design of the EDO framework





The EDA-SA algorithm

i1

i2

i0x

f(x)

U

O0

N

1

2

3

4PS

P

PDu

PDe

(a) EDA

+(c) SA

Figure: Hybridization of the estimation of distribution (a) and simulatedannealing (c) algorithms. Source: J. Dreo, E. Triki and Y. Collette





Implementation of the EDA-SA algorithm

EDO is based on the C++ template-based EO framework2.

EO provides a functor-based design.

The implementation of the EDA-SA algorithm done thanksto EDO and MO.

Source available on SourceForge3.

2Evolving Objects3http://eodev.sf.net


http://eodev.sf.net





Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do

S ′i = sel (Si , ρ)

Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)for j = 0 to p do

xj = Nxj ,Vi

if f (xi ) < f (xj) and

U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xj

xj+1 = xj

Ti+1 = Ti .α

Definition

Uniform sampling

Inheritance

eoRndGenerator< T >

eoF< T >

eoUniformGenerator< T >

C++ code

eoRndGenerator<double>*

gen = new

eoUniformGenerator<double>

(-5, 5);






Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do


Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)for j = 0 to p do

xj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xj

xj+1 = xj

Ti+1 = Ti .α

Definition

Uniform sampling

Inheritance

eoInit< EOT >

eoUF< EOT &, void >

eoInitFixedLength< EOT >

C++ code

eoInitFixedLength<EOT>*

init = new

eoInitFixedLength<EOT>

(dimension size, *gen);






Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do


Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)for j = 0 to p do

xj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xj

xj+1 = xj

Ti+1 = Ti .α

Definition

Uniform sampling

Inheritance

std::vector< EOT > eoObject eoPersistent

eoPrintable

eoPop< EOT >

C++ code

eoPop<EOT>& pop =

do make pop(*init);

apply(eval, pop);






Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do


Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)for j = 0 to p do

xj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xj

xj+1 = xj

Ti+1 = Ti .α

Definition

External iteration

Inheritance

edoAlgo< D >

edoEDASA< D >

C++ code

edoAlgo<Distrib>* algo =

new

edoEDASA<Distrib>(...);






Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g doS ′i = sel (Si , ρ)

Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)for j = 0 to p do

xj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xj

xj+1 = xj

Ti+1 = Ti .α

Definition

Selection of the best points inthe population

Inheritance

eoSelect< EOT >

eoBF< const eoPop< EOT > &, eoPop< EOT > &, void >

eoDetSelect< EOT >

C++ code

eoSelect<EOT>* selector =

new eoDetSelect<EOT>

(selection rate);






Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do


Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)for j = 0 to p do

xj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xj

xj+1 = xj

Ti+1 = Ti .α

Definition

Modifier of the distributionparameters

Inheritance

edoModifierMass< edoNormalMulti< EOT > >

edoModifier< edoNormalMulti< EOT > >

edoNormalMultiCenter< EOT >

C++ code

edoModifierMass<Distrib>*

modifier = new

edoNormalMultiCenter<EOT>

();Caner Candan [email protected] MSc Thesis: Evolving Distribution Objects Framework





Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do


Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)for j = 0 to p do

xj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xj

xj+1 = xj

Ti+1 = Ti .α

Definition

Estimator of the distributionparameters: covariance matrix

Inheritance

edoEstimator< edoNormalMulti< EOT > >

edoEstimatorNormalMulti< EOT >

C++ code

edoEstimator<Distrib>*

estimator = new

edoEstimatorNormalMulti

<EOT>();






Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do


Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)

for j = 0 to p do

xj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xj

xj+1 = xj

Ti+1 = Ti .α

Definition

Estimator of the distributionparameters: mean

Inheritance

edoEstimator< edoNormalMulti< EOT > >

edoEstimatorNormalMulti< EOT >

C++ code

edoEstimator<Distrib>*

estimator = new

edoEstimatorNormalMulti

<EOT>();






Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do


Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)

for j = 0 to p do

xj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xj

xj+1 = xjTi+1 = Ti .α

Definition

Internal iteration

Inheritance

edoAlgo< D >

edoEDASA< D >

C++ code


new







Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do


Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)

for j = 0 to p doxj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xj


Definition

Drawing in a multi-normalneighborhood

Inheritance

edoSampler< edoNormalMulti< EOT > >

edoSamplerNormalMulti< EOT >

C++ code

edoSampler<Distrib>*

sampler = new

edoSamplerNormalMulti<

EOT >(...);






Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do


Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)

for j = 0 to p do

xj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xjxj+1 = xj

Ti+1 = Ti .α

Definition

Metropolis algorithm thresholdacceptance

Inheritance

edoAlgo< D >

edoEDASA< D >

C++ code


new







Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do


Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)

for j = 0 to p do

xj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti thenSi+1 ← xj


Definition

Metropolis algorithm thresholdacceptance

Inheritance

edoAlgo< D >

edoEDASA< D >

C++ code


new







Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do


Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)

for j = 0 to p do

xj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xj

xj+1 = xj

Ti+1 = Ti .α

Definition

Keeping current solution

Inheritance

edoAlgo< D >

edoEDASA< D >

C++ code


new







Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g do


Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)for j = 0 to p do

xj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti then

Si+1 ← xj

xj+1 = xj

Ti+1 = Ti .α

Definition

Decrease of temperature

Inheritance

moCoolingSchedule< EOT >

moSimpleCoolingSchedule< EOT >

C++ code

moCoolingSchedule<EOT>*

cooling schedule = new

moSimpleCoolingSchedule

<EOT>(...);






Pseudo-code

S0 = Uxmin,xmax

for i = 0 to g doS ′i = sel (Si , ρ)

Si = S ′i − S ′i

Vi = SiT· Si

xo = arg min(Si

)for j = 0 to p doxj = Nxj ,Vi


U0,1 < e−1.|f (xj )−f (x′j )|

Ti thenSi+1 ← xj






C++ code: parameters declaration

Algorithm 1 Declaration of the needed parameters for EDA-SAalgorithm

double initial_temperature = ...;

double selection_rate = ...;

unsigned long max_eval = ...;

unsigned int dimension_size = ...;

unsigned int popSize = ...;

double threshold_temperature = ...;

double alpha = ...;





C++ code: common operators instantiations

Algorithm 2 Instantiations of the common operators

eoDetSelect<EOT> selector(selection_rate);

edoEstimatorNormalMulti<EOT> estimator();

eoDetTournamentSelect<EOT> selectone(2);

edoNormalMultiCenter<EOT> modifier();

Rosenbrock<EOT> plainEval();

eoEvalFuncCounterBounder<EOT> eval(plainEval, max_eval);

eoUniformGenerator<double> gen(-5, 5);

eoInitFixedLength<EOT> init(dimension_size, gen);





C++ code: EDA-SA operators instantiations

Algorithm 3 Instantiations of the EDA and SA operators

eoPop<EOT>& pop = do_make_pop(init);

apply(eval, pop);

edoBounderRng< EOT > bounder(EOT(popSize, -5),

EOT(popSize, 5), gen);

edoSamplerNormalMulti< EOT > sampler(bounder);

moSimpleCoolingSchedule<EOT> cooling_schedule(...);

eoEPReplacement<EOT> replacor(pop.size());

edoEDASA<Distrib> algo(...);





C++ code: running of the algorithm

Algorithm 4 Running of the algorithm

do_run(algo, pop);




Conclusion

Conclusion & Discussion

Expected algorithm behaviour.

Performance to improve.

Easy-to-manipulate algorithm.

Perspective

Integrate and test some other distributions (cf. Gaussianmixture model)

Test some other selection operators.

Parallelization of the linear algebra operators.




Conclusion





Perspective







Conclusion





Perspective







Conclusion





Perspective







Conclusion





Perspective







Conclusion





Perspective







Conclusion





Perspective







Conclusion





Perspective







Any questions ?

Thank [email protected]


Presentation of the Evolving Distribution Objects Framework

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