Presentation of the Evolving Distribution Objects Framework

General Idea
Overview
EDO framework
Conclusion

Evolving Distribution Objects Framework1

Caner Candan
caner@candan.fr

Thales Research & Technology
Palaiseau, France

September 5, 2011

1
Except as otherwise noted, content is licensed under the Free Art License.
Caner Candan caner@candan.fr MSc Thesis: Evolving Distribution Objects Framework

General Idea
Overview
EDO framework
Conclusion

Hard optimization problems heuristic optimizer

Aims to optimize hard optimization problems.


General Idea
Overview
EDO framework
Conclusion


Usually used in operations research and decision aids.


General Idea
Overview
EDO framework
Conclusion


More eﬃcient than classical heuristic search.


General Idea
Overview
EDO framework
Conclusion


Generally based on a stochastic process.


General Idea
Overview
EDO framework
Conclusion


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.


General Idea
Overview
EDO framework
Conclusion


Figure: Example of hard optimization problem. Source: J. Dr´o
e


General Idea
Overview
EDO framework
Conclusion


f(x) D
L

G
x
Figure: Hard optimization problem illustrating global optimum, local
optima and discountinuties. Source: J. Dr´o
e


General Idea
Overview
EDO framework
Conclusion


M

f(x) D
L

G
x
Figure: Hard optimization solved using metaheuristic algorithms. Source:
J. Dr´o
e


General Idea
Overview
EDO framework
Conclusion


P1 M1
M2
M3
P6 P2

P5 P3

P4

Figure: “No Free Lunch” theorem. Source: J. Dr´o
e


General Idea
Overview
EDO framework
Conclusion

An overview of my work


General Idea
Overview
EDO framework
Conclusion


Black-Box
EDO framework
EDA-SA
Parallelization of EDA-SA


General Idea
Overview
EDO framework
Conclusion

Black-Box
EDO framework
EDA-SA→ paper submitted in a national congressa
a ´
Roadef 2011, Saint-Etienne, France


General Idea
Overview
EDO framework
Conclusion


Temporal Planning
EO framework
Parallelization of EO
Scalability


General Idea
Overview
EDO framework
Conclusion


Temporal Planning
EO framework
Parallelization of EO→ paper submitted in an international
congressa
Scalability
a
GECCO ’11, Dublin, Ireland


General Idea
Overview
EDO framework
Conclusion


Experiments tool
Design of experiments


General Idea
Overview
EDO framework
Conclusion


Black-Box
EDO framework
EDA-SA

Temporal Planning
EO framework
Parallelization of EO
Scalability

Experiments tool
Design of experiments


General Idea
Overview Theoretical aspect
EDO framework Design
Conclusion

Theoretical aspect

E.

I.

D.

Figure: Explicit, Implicit and Direct classes. Source: J. Dr´o
e


General Idea
Conclusion

Theoretical aspect
Metaheuristics

Population

Naturally inspired Evolutionary
algorithm

Implicit
Genetic algorithm
Particle swarm
Genetic optimization
programming
Evolution Ant colony optimization
Evolutionary strategy algorithms
programming

Explicit

No memory
Differential Estimation of distribution
evolution algorithm

Scatter search

Direct
Simulated
annealing

Local search
Tabu search
Iterated local search
GRASP
Stochastic local search

Trajectory Variable neighborhood search Guided local search

Dynamic objective function

Figure: Different classifications of metaheuristics. Source: J. Dró
e


General Idea
Conclusion

Estimation of Distribution Algorithm
f(x)

U
0
O
x
i0

i1

P
PS
PDe i2
PDu

Figure: Estimation of distribution algorithm. Source: J. Dr´o
e


General Idea
Conclusion


i0

N
1

i1

P
PS
PDe i2
PDu

e


General Idea
Conclusion


i0

2

i1

P
PS
PDe i2
PDu

e


General Idea
Conclusion


i0

i1

3

P
PS
PDe i2
PDu

e


General Idea
Conclusion


i0

i1

P
PS
4
PDe i2
PDu

e


General Idea
Conclusion

f(x)

U
0
O
x
i0

N
1

2

i1

3

P
PS
4
PDe i2
PDu

e


General Idea
Conclusion

Simulated Annealing Algorithm

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

General Idea
Conclusion

Design of the EDO framework


General Idea
Conclusion

The EDA-SA algorithm
f(x)

U
0
O
x
i0

N
1

2

+
i1

3

P
PS
4
PDe i2
PDu

(a) EDA (c) SA

Figure: Hybridization of the estimation of distribution (a) and simulated
annealing (c) algorithms. Source: J. Dr´o, E. Triki and Y. Collette
e


General Idea
Conclusion

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 thanks
to EDO and MO.
Source available on SourceForge3 .

2
Evolving Objects
3
http://eodev.sf.net

General Idea
Conclusion

Pseudo-code Deﬁnition
S0 = Uxmin ,xmax Uniform sampling

Inheritance
eoF< T >

eoRndGenerator< T >

eoUniformGenerator< T >

C++ code
eoRndGenerator<double>*
gen = new
eoUniformGenerator<double>
(-5, 5);

General Idea
Conclusion


Inheritance
eoUF< EOT &, void >

eoInit< EOT >

eoInitFixedLength< EOT >

C++ code
eoInitFixedLength<EOT>*
init = new
eoInitFixedLength<EOT>
(dimension size, *gen);


General Idea
Conclusion


Inheritance
eoPrintable

std::vector< EOT > eoObject eoPersistent

eoPop< EOT >

C++ code
eoPop<EOT>& pop =
do make pop(*init);
apply(eval, pop);


General Idea
Conclusion

External iteration
for i = 0 to g do
Inheritance
edoAlgo< D >

edoEDASA< D >

C++ code
edoAlgo<Distrib>* algo =
new
edoEDASA<Distrib>(...);


General Idea
Conclusion

Selection of the best points in
for i = 0 to g do the population
Si = sel (Si , ρ)
Inheritance
eoBF< const eoPop< EOT > &, eoPop< EOT > &, void >

eoSelect< EOT >

eoDetSelect< EOT >

C++ code
eoSelect<EOT>* selector =
new eoDetSelect<EOT>
(selection rate);


General Idea
Conclusion

Modiﬁer of the distribution
for i = 0 to g do parameters

Si = Si − Si Inheritance
edoModifier< edoNormalMulti< EOT > >

edoModifierMass< edoNormalMulti< EOT > >

edoNormalMultiCenter< EOT >

C++ code
edoModifierMass<Distrib>*
modifier = new
edoNormalMultiCenter<EOT>
();

General Idea
Conclusion

Estimator of the distribution
for i = 0 to g do parameters: covariance matrix

Inheritance
T
Vi = Si · Si edoEstimator< edoNormalMulti< EOT > >

edoEstimatorNormalMulti< EOT >

C++ code
edoEstimator<Distrib>*
estimator = new
edoEstimatorNormalMulti
<EOT>();

General Idea
Conclusion

Estimator of the distribution
for i = 0 to g do parameters: mean

Inheritance
edoEstimator< edoNormalMulti< EOT > >
xo = arg min Si
edoEstimatorNormalMulti< EOT >

C++ code
edoEstimator<Distrib>*
estimator = new
edoEstimatorNormalMulti
<EOT>();

General Idea
Conclusion

Internal iteration
for i = 0 to g do
Inheritance
edoAlgo< D >

edoEDASA< D >
for j = 0 to p do
C++ code
new


General Idea
Conclusion

Drawing in a multi-normal
for i = 0 to g do neighborhood

Inheritance
edoSampler< edoNormalMulti< EOT > >

for j = 0 to p do edoSamplerNormalMulti< EOT >

xj = Nxj ,Vi
C++ code
edoSampler<Distrib>*
sampler = new
edoSamplerNormalMulti<
EOT >(...);

General Idea
Conclusion

Metropolis algorithm threshold
for i = 0 to g do acceptance

Inheritance
edoAlgo< D >

for j = 0 to p do edoEDASA< D >

if f (xi ) < f (xj ) and C++ code
|f (xj )−f (xj )|
−1. edoAlgo<Distrib>* algo =
U0,1 < e Ti
then
new


General Idea
Conclusion

Metropolis algorithm threshold
for i = 0 to g do acceptance

Inheritance
edoAlgo< D >

for j = 0 to p do edoEDASA< D >

if f (xi ) < f (xj ) and C++ code
|f (xj )−f (xj )|
−1. edoAlgo<Distrib>* algo =
U0,1 < e Ti
then
Si+1 ← xj new


General Idea
Conclusion

Keeping current solution
for i = 0 to g do
Inheritance
edoAlgo< D >

edoEDASA< D >
for j = 0 to p do
C++ code
new
xj+1 = xj


General Idea
Conclusion

Decrease of temperature
for i = 0 to g do
Inheritance
moCoolingSchedule< EOT >

moSimpleCoolingSchedule< EOT >

C++ code
moCoolingSchedule<EOT>*
cooling schedule = new
moSimpleCoolingSchedule
<EOT>(...);
Ti+1 = Ti .α

General Idea
Conclusion

Pseudo-code
S0 = Uxmin ,xmax
for i = 0 to g do
Si = sel (Si , ρ)
Si = Si − Si
T
Vi = Si · Si
xo = arg min Si
for j = 0 to p do
xj = Nxj ,Vi
if f (xi ) < f (xj ) and
|f (xj )−f (xj )|
−1.
U0,1 < e Ti
then
Si+1 ← xj
xj+1 = xj
Ti+1 = Ti .α

General Idea
Conclusion

C++ code: parameters declaration

Algorithm 1 Declaration of the needed parameters for EDA-SA
algorithm

double initial_temperature = ...;
double selection_rate = ...;
unsigned long max_eval = ...;
unsigned int dimension_size = ...;
unsigned int popSize = ...;
double threshold_temperature = ...;
double alpha = ...;


General Idea
Conclusion

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);


General Idea
Conclusion

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(...);


General Idea
Conclusion

C++ code: running of the algorithm

Algorithm 4 Running of the algorithm

do_run(algo, pop);


General Idea
Overview
EDO framework
Conclusion

Conclusion

Conclusion & Discussion


General Idea
Overview
EDO framework
Conclusion

Conclusion

Expected algorithm behaviour.


General Idea
Overview
EDO framework
Conclusion

Conclusion

Performance to improve.


General Idea
Overview
EDO framework
Conclusion

Conclusion

Easy-to-manipulate algorithm.


General Idea
Overview
EDO framework
Conclusion

Conclusion


Perspective


General Idea
Overview
EDO framework
Conclusion

Conclusion


Perspective
Integrate and test some other distributions (cf. Gaussian
mixture model)


General Idea
Overview
EDO framework
Conclusion

Conclusion


Perspective
mixture model)
Test some other selection operators.


General Idea
Overview
EDO framework
Conclusion

Conclusion


Perspective
mixture model)
Test some other selection operators.
Parallelization of the linear algebra operators.


General Idea
Overview
EDO framework
Conclusion

Any questions ?

Thank you.
caner@candan.fr


Presentation of the Evolving Distribution Objects Framework

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