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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.
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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 LGMO - A.Zhou @ ECNU
Outline • Evolutionary Multiobjective Optimization • A Self-Organizing Map based Approach • Learning Guided Evolution – A Short Survey • Conclusions & Future Remarks LGMO - A.Zhou @ ECNU
Multiobjective Optimization Problem • MOP where • real-world applications • scientific and engineering problems LGMO - A.Zhou @ ECNU
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
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
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
Outline • Evolutionary Multiobjective Optimization • A Self-Organizing Map based Approach • Learning Guided Evolution – A Short Survey • Conclusions & Future Remarks LGMO - A.Zhou @ ECNU
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
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
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
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
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
Other Issues • Reproduction operator: • Differential Evolution (DE) • Polynominal Mutation • Selection operator: • Nondominated sorting scheme LGMO - A.Zhou @ ECNU
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
Experimental Results • Run time performance • Converges faster in most cases. LGMO - A.Zhou @ ECNU
Experimental Results • Visual performance LGMO - A.Zhou @ ECNU
Experimental Results • Visual performance LGMO - A.Zhou @ ECNU
Outline • Evolutionary Multiobjective Optimization • A Self-Organizing Map based Approach • Learning Guided Evolution – A Short Survey • Conclusions & Future Remarks LGMO - A.Zhou @ ECNU
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
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
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
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
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
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
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
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
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
Outline • Evolutionary Multiobjective Optimization • A Self-Organizing Map based Approach • Learning Guided Evolution – A Short Survey • Conclusions & Future Remarks LGMO - A.Zhou @ ECNU
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
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