1 learning guided multiobjective optimization aimin zhou east china normal university, shanghai,...

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Learning Guided Multiobjective Optimization

Aimin Zhou

East China Normal University, Shanghai, China

7/9, 2015

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Outline

o Evolutionary Multiobjective Optimization

o A Self-Organizing Map based Approach

o Learning Guided Evolution – A Short Survey

o Conclusions & Future Remarks

LGMO - A.Zhou @ ECNU 7/9,2015

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Outline






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Multiobjective Optimization Problem

o MOP

where

o real-world applications

o scientific and engineering problems

7/9,2015LGMO - A.Zhou @ ECNU

D

2f

1f

)(DF

x

F

z

)()(

)()(

2211

21

xf, zxfz

xF,zzz

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Optimum of an MOPo For a minimization problem

o dominate = be better than

o Examples:


D

2f

1f

)(DF

1x

F

2z

2x3x

1z3z

why MOPs are harder than single opt. problems

domination is a partial ordering

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Optimum of an MOPo Pareto optimal solution

a solution cannot be dominated by any other solutions.

o Pareto set (PS) the set of all the Pareto optimal solutions in decision variable space.

o Pareto front (PF)PF=F(PS) (in objective space)


2f

1f

)(DF

Pareto front (PF)

Pareto set (PS)

F

The PF is the southwest boundary of F(D).

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Task of MOEA

Very often, a decision maker wants


Task of mostMultiobjective Evolutionary Algorithms

(MOEAs)

2f

1f

)(DF

Pareto front (PF)

Pareto set (P)

F

A representative set of Pareto optimal solutions

(uniformly distributed along the PF or PS)

[1] A. Zhou, B. Qu, H. Li, S. Zhao, P. Suganthan, and Q. Zhang, Multiobjective evolutionary algorithms: A survey of the state of the art, Swarm and Evolutionary Computation, 1(1): 32–49, 2011.

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Outline






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Motivationo Regularity of continuous MOPs:

o Problem-specific knowledge is useful for algorithm design.


Under certain conditions, the PS (PF) is a (m-1)-dimensional piecewise continuous manifold in decision (objective) space.

(m is the # of the objs.)

2f

1f

)(DF

Pareto front (PF)

Pareto set (PS)

F

How can we deal with a continuous MOP if its PS is (m-1)-D piecewise continuous manifold?

[1] Q. Zhang, A. Zhou, and Y. Jin, RM-MEDA: a regularity model-based multiobjective estimation of distribution algorithm, IEEE Transactions on Evolutionary Computation, 12(1):797-799, 2008.

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Motivationo Classical reproduction operators

scalar-objective optimization

multiobjective optimization


x2

x1 x1 x1 x1

x* x* x* x*

A A

B Baa

b

b

x2 x2 x2

(a) 当前种群 (b) 单点杂交 (c) 算术杂交 (d) 高斯模型采样

x2

x1 x1 x1 x1

PS PS PS PS

AA

B Baa

b

b

x2 x2x2

(a) 当前种群 (b) 单点杂交 (c) 算术杂交 (d) 高斯模型采样

[1] A. Zhou, Q. Zhang, and G. Zhang, Multiobjective evolutionary algorithm based on mixture Gaussian models, Journal of Software, 25(5):913-928, 2014.

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Basic Ideao Algorithm framework


Population

New Solutions

Reproductionoperators

CompetitionReplacement Selection (Replacement): quite

a lot of works

Reproduction: our focus

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Self-Organizing Maps


[1] H. Zhang, A. Zhou, S. Song, Q. Zhang, X. Gao, and J. Zhang, A self-organizing multiobjective evolutionary algorithm, 2015 (submit).

o SOM latent model

similarity detection

o MOP regularity property

mating registration

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SOM Assisted MOEA


o Characteristics: Call SOM and MOEA main steps iteratively

detect the population structure in an incremental manner save computational cost

Generate offspring by neighboring parents

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Other Issueso Reproduction operator:

Differential Evolution (DE)

Polynominal Mutation


o Selection operator: Nondominated sorting

scheme

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Experimental Resultso On irregular problems

GLT test suite

CellDE, MOEA/D-DE, RM-MEDA, NSGA-II, SMS-EMOA,SOM-NSGA-II

IGD,HV metrics


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Experimental Resultso Run time performance

Converges faster in most cases.


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Experimental Resultso Visual performance


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Experimental Resultso Visual performance


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Outline






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Basic Questions

Learning + Evolutionary Optimization

oWhat? Learning Guided Evolution (LGE) is a kind of evolutionary algorithms that

utilize statistical and machine learning techniques to guide the search.

oWhy? Priori & learnt problem specific knowledge to guide the search, and

thus to improve search performance.

oHow?


initialization reproduction selection stop condition

data organization pattern recognition pattern usage

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o Adaptive Evolution

Parameter tuning

Operator selection

Stopping condition

o Estimation of Distribution Algorithm (EDA)

Ant Colony Optimization (ACO)

Cross-entropy method (CE)

Covariance Matrix Adaptation Evolution Strategy (CMA-ES)

o Surrogate Assist Evolutionary Algorithm (SAEA)

mine populationsmine populations

model & sample populations

model & sample populations

replace evaluationreplace evaluation


Related Work

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Taxonomyo Angle of Machine Learning


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o Regression based approaches Surrogate assisted minimax optimization

Time series prediction for dynamic

multiobjective optimization

Cheap surrogate model

[1] A. Zhou, and Q. Zhang, A surrogate-assisted evolutionary algorithm for minimax optimization, in IEEE Congress on Evolutionary Computation (CEC 2010), Barcelona: IEEE Press, 2010, pp.1-7.

[2] A. Zhou, Y. Jin, and Q. Zhang, A population prediction strategy for evolutionary dynamic multiobjective optimization, IEEE Transactions on Cybernetics, 44(1):40-53,2014.

[3] A. Zhou, J. Sun, and Q. Zhang, An estimation of distribution algorithm with cheap and expensive local search, IEEE Transactions on Evolutionary Computation, 2015. (accepted)


A Short Survey of Our Recent Work

PS estimation=

PS manifold learning +

center point prediction

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o Classification based approaches Classification based preselection

Classification based selection

[1] J. Zhang, A. Zhou, and G. Zhang, A Classification and Pareto domination based multiobjective evolutionary algorithm, in Proceedings of IEEE Congress on Evolutionary Computation (CEC 2015), 2015, pp.1-8.

[2] J. Zhang, A. Zhou, and G. Zhang, A classification based preselection for evolutionary algorithms, 2015 (submit). LGMO - A.Zhou @ ECNU 7/9,2015


selection = classification

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o Manifold learning based approaches Regularity model based multiobjective estimation of distribution

algorithm (RM-MEDA)

[1] Q. Zhang, A. Zhou, and Y. Jin, RM-MEDA: a regularity model-based multiobjective estimation of distribution algorithm, IEEE Transactions on Evolutionary Computation, 12(1):797-799, 2008.

[2] A. Zhou, Q. Zhang, and Y. Jin, Approximating the set of Pareto-optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm, IEEE Transactions on Evolutionary Computation, 13(5):1167-1189, 2009.



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31C

3C2Cx2

x1

x

population

simplicatio

n &

modeling

sampling

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o Clustering based approaches Clustering based mating selection

Self-organizing multiobjective evolutionary algorithm

[1] H. Zhang, S. Song, and A. Zhou, A clustering based multiobjective evolutionary algorithm, in IEEE Congress on Evolutionary Computation (CEC 2014), 2014.

[2] H. Zhang, A. Zhou, S. Song, X. Gao, and J. Zhang, A self-organising multiobjective evolutionary algorithm, 2015. (submit)LGMO - A.Zhou @ ECNU 7/9,2015


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o Density estimation based approaches Mixture Gaussian model

model base reproduction model re-use

Non-parametric density estimation model based pre-selection multi-operator search locally weighted model

[1] L. Zhou, A. Zhou, G. Zhang, C. Shi, An estimation of distribution algorithm based on nonparametric density estimation, in IEEE Congress on Evolutionary Computation (CEC 2011), New Orleans: IEEE Press, 2011, pp.1597-1604.

[2] A. Zhou, Q. Zhang, and G. Zhang, A multiobjective evolutionary algorithm based on decomposition and probability model, in IEEE Congress of Evolutionary Computation (CEC 2012), Brisbane: IEEE Press, 2012, pp.1-8.

[3] A. Zhou, Q. Zhang, and G. Zhang, A multiobjective evolutionary algorithm based on mixture Gaussian models, Journal of Software, 25(5):913−928, 2014.

[4] Q. Liao, A. Zhou, and G. Zhang, A locally weighted metamodel for pre-selection in evolutionary optimization, in The IEEE Congress on Evolutionary Computation (CEC 2014), 2014.

[5] A. Zhou, Y. Zhang, G. Zhang, and W. Gong, On neighborhood exploration and subproblem exploitation in decomposition based multiobjective evolutionary algorithms, in Proceedings of IEEE Congress on Evolutionary Computation (CEC 2015), 2015, pp.1-8.

[6] W. Gong, A. Zhou, and Z. Cai, A multi-operator search strategy based on cheap surrogate models for evolutionary optimization, IEEE Transactions on Evolutionary Computation, 2015. (accepted)



fitness estimation by cheap models

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o Adaptive approaches Adaptive replacement strategy in MOEA/D

Adaptive resource allocation in MOEA/D

[1] Z. Wang, Q. Zhang, A. Zhou, M. Gong, and L. Jiao, Adaptive replacement strategies for MOEA/D, IEEE Transactions on Cybernetics, 2015. (accepted)

[2] A. Zhou, and Q. Zhang, Are all the subproblems equally important? Resource allocation in decomposition based multiobjective evolutionary algorithms, IEEE Transactions on Evolutionary Computation, 2015. (accepted)



subproblem index

cost

resource control

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Outline






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o Random Search: Alg. Cost is LOW, Problem Cost is HIGH.

o Mathematical Programming: Alg. Cost is HIGH, Problem Cost is LOW.

o Evolutionary Optimization: BETWEEN the above two approaches.

o Learning Guided Evolutionary Optimization

o It Is promising to balance the two costs.

o There is no systematic study yet.

o Which knowledge to detect?

o Which learning method to use?

o How to combine learning methods and evolutionary algorithms?


Conclusions & Future Remarks

CostCost Alg. CostAlg. Cost Problem CostProblem Cost

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Thanks!

Dr. Aimin Zhou, East China Normal [email protected], http://www.cs.ecnu.edu.cn/~amzhouhttp://faculty.ecnu.edu.cn/s/1949/t/22630/main.jspy


1 learning guided multiobjective optimization aimin zhou east china normal university, shanghai,...

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