1. 1 Learning Guided Multiobjective Optimization Aimin Zhou East China Normal University, Shanghai, China 7/9, 2015

2. 2 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 @ ECNU7/9,2015

3. 3 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 @ ECNU7/9,2015

4. 4 Multiobjective Optimization Problem o MOP where o real-world applications o scientific and engineering problems 7/9,2015LGMO - A.Zhou @ ECNU

5. 5 Optimum of an MOP o For a minimization problem o dominate = be better than o Examples: 7/9,2015LGMO - A.Zhou @ ECNU why MOPs are harder than single opt. problems domination is a partial ordering

6. 6 Optimum of an MOP o 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) 7/9,2015LGMO - A.Zhou @ ECNU Pareto front (PF) Pareto set (PS) The PF is the southwest boundary of F(D).

7. 7 Task of MOEA Very often, a decision maker wants 7/9,2015LGMO - A.Zhou @ ECNU Task of most Multiobjective Evolutionary Algorithms (MOEAs) Pareto front (PF) Pareto set (P) 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.

8. 8 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 @ ECNU7/9,2015

9. 9 Motivation o Regularity of continuous MOPs: o Problem-specific knowledge is useful for algorithm design. 7/9,2015LGMO - A.Zhou @ ECNU Under certain conditions, the PS (PF) is a (m-1)-dimensional piecewise continuous manifold in decision (objective) space. (m is the # of the objs.) Pareto front (PF) Pareto set (PS) 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.

10. 10 Motivation o Classical reproduction operators  scalar-objective optimization  multiobjective optimization 7/9,2015LGMO - A.Zhou @ ECNU x2x2 x1x1 x1x1 x1x1 x1x1 x*x* x*x* x*x* x*x* A A B B a a b b x2x2 x2x2 x2x2 (a) 当前种群 (b) 单点杂交 (c) 算术杂交 (d) 高斯模型采样 x2x2 x1x1 x1x1 x1x1 x1x1 PS A A B B a a b b x2x2 x2x2 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.

11. 11 Basic Idea o Algorithm framework 7/9,2015LGMO - A.Zhou @ ECNU Population New Solutions Reproduction operators Competition Replacement Selection (Replacement): quite a lot of works Reproduction: our focus

12. 12 Self-Organizing Maps 7/9,2015LGMO - A.Zhou @ ECNU [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

13. 13 SOM Assisted MOEA 7/9,2015LGMO - A.Zhou @ ECNU 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

14. 14 Other Issues o Reproduction operator:  Differential Evolution (DE)  Polynominal Mutation 7/9,2015LGMO - A.Zhou @ ECNU o Selection operator:  Nondominated sorting scheme

15. 15 Experimental Results o On irregular problems  GLT test suite  CellDE, MOEA/D-DE, RM-MEDA, NSGA-II, SMS-EMOA,SOM-NSGA-II  IGD,HV metrics 7/9,2015LGMO - A.Zhou @ ECNU

16. 16 Experimental Results o Run time performance  Converges faster in most cases. 7/9,2015LGMO - A.Zhou @ ECNU

17. 17 Experimental Results o Visual performance 7/9,2015LGMO - A.Zhou @ ECNU

18. 18 Experimental Results o Visual performance 7/9,2015LGMO - A.Zhou @ ECNU

19. 19 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 @ ECNU7/9,2015

20. 20 Basic Questions Learning + Evolutionary Optimization o What?  Learning Guided Evolution (LGE) is a kind of evolutionary algorithms that utilize statistical and machine learning techniques to guide the search. o Why?  Priori & learnt problem specific knowledge to guide the search, and thus to improve search performance. o How? 7/9,2015LGMO - A.Zhou @ ECNU  initialization  reproduction  selection  stop condition  data organization  pattern recognition  pattern usage

21. 21 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 populations model & sample populations replace evaluation LGMO - A.Zhou @ ECNU7/9,2015 Related Work

22. 22 Taxonomy o Angle of Machine Learning 7/9,2015LGMO - A.Zhou @ ECNU Learning Guided Evolution Learning Guided Evolution Supervised Evolution Supervised Evolution Unsupervised Evolution Unsupervised Evolution Semi- supervised Evolution Semi- supervised Evolution Regression based EAs Classification based EAs Manifold learning based EAs Clustering based EAs Density estimation based EAs

23. 23 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) LGMO - A.Zhou @ ECNU7/9,2015 A Short Survey of Our Recent Work PS estimation = PS manifold learning + center point prediction

24. 24 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 @ ECNU7/9,2015 A Short Survey of Our Recent Work selection = classification

25. 25 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. LGMO - A.Zhou @ ECNU7/9,2015 A Short Survey of Our Recent Work x2 x1 x population simplication & modeling sampling

26. 26 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 @ ECNU7/9,2015 A Short Survey of Our Recent Work

27. 27 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) LGMO - A.Zhou @ ECNU7/9,2015 A Short Survey of Our Recent Work fitness estimation by cheap models

28. 28 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) LGMO - A.Zhou @ ECNU7/9,2015 A Short Survey of Our Recent Work subproblem index cost resource control

29. 29 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 @ ECNU7/9,2015

30. 30 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? LGMO - A.Zhou @ ECNU7/9,2015 Conclusions & Future Remarks Cost Alg. Cost Problem Cost

31. 31 Thanks! Dr. Aimin Zhou, East China Normal University amzhou@cs.ecnu.edu.cn, http://www.cs.ecnu.edu.cn/~amzhou http://faculty.ecnu.edu.cn/s/1949/t/22630/main.jspy LGMO - A.Zhou @ ECNU7/9,2015