1 / 31

Learning Guided Multiobjective Optimization

Learning Guided Multiobjective Optimization. Aimin Zhou East China Normal University, Shanghai, China 7/9, 2015. Outline. Evolutionary Multiobjective Optimization A Self-Organizing Map based Approach Learning Guided Evolution – A Short Survey Conclusions & Future Remarks. Outline.

carolinegonzalez
Download Presentation

Learning Guided Multiobjective Optimization

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. Outline • Evolutionary Multiobjective Optimization • A Self-Organizing Map based Approach • Learning Guided Evolution – A Short Survey • Conclusions & Future Remarks LGMO - A.Zhou @ ECNU

  3. Outline • Evolutionary Multiobjective Optimization • A Self-Organizing Map based Approach • Learning Guided Evolution – A Short Survey • Conclusions & Future Remarks LGMO - A.Zhou @ ECNU

  4. Multiobjective Optimization Problem • MOP where • real-world applications • scientific and engineering problems LGMO - A.Zhou @ ECNU

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

  6. Optimum of an MOP Pareto set (PS) Pareto front (PF) • Pareto optimal solution a solution cannot be dominated by any other solutions. • Pareto set (PS) the set of all the Pareto optimal solutions in decision variable space. • Pareto front (PF) PF=F(PS) (in objective space) The PF is the southwest boundary of F(D). LGMO - A.Zhou @ ECNU

  7. Task of MOEA Pareto set (P) Pareto front (PF) Very often, a decision maker wants A representative set of Pareto optimal solutions (uniformly distributed along the PF or PS) Task of most Multiobjective Evolutionary Algorithms (MOEAs) [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. LGMO - A.Zhou @ ECNU

  8. Outline • Evolutionary Multiobjective Optimization • A Self-Organizing Map based Approach • Learning Guided Evolution – A Short Survey • Conclusions & Future Remarks LGMO - A.Zhou @ ECNU

  9. Motivation Pareto set (PS) Pareto front (PF) • Regularity of continuous MOPs: • 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.) 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. LGMO - A.Zhou @ ECNU

  10. Motivation x2 x2 x2 x2 x* x* x* x* b A A a b B B a x1 x1 x1 x1 (a) 当前种群 (b) 单点杂交 (c) 算术杂交 (d) 高斯模型采样 x2 x2 x2 x2 PS PS PS PS B b a B a A b A x1 x1 x1 x1 (a) 当前种群 (b) 单点杂交 (c) 算术杂交 (d) 高斯模型采样 • Classical reproduction operators • scalar-objective optimization • multiobjective optimization [1] A. Zhou, Q. Zhang, and G. Zhang, Multiobjective evolutionary algorithm based on mixture Gaussian models, Journal of Software, 25(5):913-928, 2014. LGMO - A.Zhou @ ECNU

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

  12. Self-Organizing Maps • SOM • latent model • similarity detection • MOP • regularity property • mating registration [1] H. Zhang, A. Zhou, S. Song, Q. Zhang, X. Gao, and J. Zhang, A self-organizing multiobjective evolutionary algorithm, 2015 (submit). LGMO - A.Zhou @ ECNU

  13. SOM Assisted MOEA • Characteristics: • Call SOM and MOEA main steps iteratively • detect the population structure in an incremental manner • save computational cost • Generate offspring by neighboring parents LGMO - A.Zhou @ ECNU

  14. Other Issues • Reproduction operator: • Differential Evolution (DE) • Polynominal Mutation • Selection operator: • Nondominated sorting scheme LGMO - A.Zhou @ ECNU

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

  16. Experimental Results • Run time performance • Converges faster in most cases. LGMO - A.Zhou @ ECNU

  17. Experimental Results • Visual performance LGMO - A.Zhou @ ECNU

  18. Experimental Results • Visual performance LGMO - A.Zhou @ ECNU

  19. Outline • Evolutionary Multiobjective Optimization • A Self-Organizing Map based Approach • Learning Guided Evolution – A Short Survey • Conclusions & Future Remarks LGMO - A.Zhou @ ECNU

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

  21. Related Work • Adaptive Evolution • Parameter tuning • Operator selection • Stopping condition • Estimation of Distribution Algorithm (EDA) • Ant Colony Optimization (ACO) • Cross-entropy method (CE) • Covariance Matrix Adaptation Evolution Strategy (CMA-ES) • Surrogate Assist Evolutionary Algorithm (SAEA) mine populations model & sample populations replace evaluation LGMO - A.Zhou @ ECNU

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

  23. A Short Survey of Our Recent Work • 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) PS estimation = PS manifold learning + center point prediction LGMO - A.Zhou @ ECNU

  24. A Short Survey of Our Recent Work • 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). selection = classification LGMO - A.Zhou @ ECNU

  25. A Short Survey of Our Recent Work x1 x2 x • 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. simplication & modeling sampling population LGMO - A.Zhou @ ECNU

  26. A Short Survey of Our Recent Work • 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-organisingmultiobjective evolutionary algorithm, 2015. (submit) LGMO - A.Zhou @ ECNU

  27. A Short Survey of Our Recent Work • 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 LGMO - A.Zhou @ ECNU

  28. A Short Survey of Our Recent Work • 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) cost subproblem index resource control LGMO - A.Zhou @ ECNU

  29. Outline • Evolutionary Multiobjective Optimization • A Self-Organizing Map based Approach • Learning Guided Evolution – A Short Survey • Conclusions & Future Remarks LGMO - A.Zhou @ ECNU

  30. Conclusions & Future Remarks • Random Search: Alg. Cost is LOW, Problem Cost is HIGH. • Mathematical Programming: Alg. Cost is HIGH, Problem Cost is LOW. • Evolutionary Optimization: BETWEEN the above two approaches. • Learning Guided Evolutionary Optimization • It Is promising to balance the two costs. • There is no systematic study yet. • Which knowledge to detect? • Which learning method to use? • How to combine learning methods and evolutionary algorithms? Cost Alg. Cost Problem Cost LGMO - A.Zhou @ ECNU

  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 @ ECNU

More Related