TEMASEK LABORATORIES Multidisciplinary Design Optimization Group UNSWADFA Surrogate

TEMASEK LABORATORIES Multidisciplinary Design Optimization Group, UNSW@ADFA Surrogate Assisted Optimization Methods: Recent Developments and Challenges Tapabrata Ray School of Engineering and Information Technology, University of New South Wales, Australian Defence Force Academy, Australia. Tel: +61 2 62688248; Fax: +61 2 62688276 Email: t. ray@adfa. edu. au Acknowledgements: Postgraduate Students (Amitay Isaacs and Hemant Kumar Singh), Sponsors and Collaborators. July 03 -2009, Marseille

Multidisciplinary Design Optimization Group, UNSW@ADFA Presentation Plan 2 o Multidisciplinary Design Optimization Group. o Background of Surrogate Assisted Optimization. o Fundamental Questions. o Recent Developments o Improvements to the Underlying Optimization Algorithm. o Improvements to Surrogate Model Management. o Next Generation Surrogate Assisted Optimization Framework: A Population Based Stochastic Optimization Model Powered by Infeasibility, Multiple Spatially Distributed Surrogates of Multiple Types, Memetic Recombination and Surrogate and Neighborhood Validity Checks. o Further Challenges and Ongoing Developments.

Multidisciplinary Design Optimization Group, UNSW@ADFA Areas of Our Interest Areas l l l l 3 Multiobjective Optimization Constrained Optimization Robust Design and Constrained Robust Design Shape and Topology Representation Evolutionary Algorithms, Memetic Algorithms, Simulated Annealing, Particle Swarms, Cultural Algorithms and Fast Evolutionary Programming. Surrogate Assisted Optimization Models Preserving Infeasible Solutions for. Tradeoff and Convergence Dynamic Multiobjective Optimization Many Objective Optimization Trans-dimensional Optimization Spatial Prediction Models Realistic Transportation Models Flexible Manufacturing System Models Co-evolution and Ensembles Applications l l l l Antenna Design, Dielectric Filter Design Aircraft Concept Design Optimal Identification of Parameters for Metal Forming Optimal Parameter Identification for Biochemical Kinetics. Topology Optimization of Compliant Mechanisms Optimal Design of Launch Vehicle Nose Cone Design Online Controller Design for UAV Models. Optimal Gas Injection Volumes for Oil Extraction UAV Path Planning Ship Hull Form Design Formula SAE Car Chassis Design Inlets for Hypersonic Flow Optimal Parameters for Flapping Wings

Multidisciplinary Design Optimization Group, UNSW@ADFA Why Surrogates and Our Focus Problem Nature Computationally Expensive Black Box Functions. Single and/or Multiobjective Problems with Large Number of Constraints. Mixed Variables (Real, Integers, Discrete) Approaches Use Multiple Processors Use Approximations in lieu of Actual Analysis (Surrogates). 4

Multidisciplinary Design Optimization Group, UNSW@ADFA Terminologies Initial Guess / Starting Point Local and Global Optimum F(X) Global Optimum Local Optimum X Unimodal Function 5 X Multimodal Function Ø No Algorithm Can Guarantee to Locate Global Optimum for Multimodal Functions. Ø Gradient Based Algorithms Can Guarantee to Locate Local Optimum. Ø Zero Order Methods Can only Locate a Good Solution which may not even be a Local Optimum.

Multidisciplinary Design Optimization Group, UNSW@ADFA Terminologies F 2(x) Rank =1 ( Nondominated Solutions ) Rank =2 Rank =3 Concept Behind Nondominated Sorting F 1(x) 6 Ø In a Multiobjective Problem, One aims to Find the Set of Nondominated Solutions. Ø A Solution is termed Nondominated is there Does not Exist any other Solution in the Given Set which can Improve the Performance in All Objectives without Degrading atleast one. © Tapabrata Ray, 2005

Multidisciplinary Design Optimization Group, UNSW@ADFA F 2(x) Terminologies F 2(x) F 1(x) 7 Ø The Algorithm Should be Able to Generate Well Spread Nondominated Solutions. Ø It Should also be Capable of Locating Multiple Optima. © Tapabrata Ray, 2005

Multidisciplinary Design Optimization Group, UNSW@ADFA Surrogate Assisted Optimization: Current State l l Initialize (p) Evaluate (p) Repeat – cp = Evolve (p) – Evaluate (cp) – Sort (p + cp) – p = Reduce (p + cp) Stop Underlying Optimization Algorithm: Evolutionary Algorithm, Particle Swarms, Differential Evolution etc. Different types of Surrogates: Quadratic Response Surface Methods, Multilayer Perceptron, Radial Basis Function Networks, Kriging, Co-Kriging etc. Training: One shot or Periodic. Underlying Optimization Algorithm f x Surrogate 8 System model to be approximated Data for Training: Random, DOE based Sampling of Initial Population. Global or Local Surrogates: One single surrogate for the entire variable space or individual surrogates for different regions.

Multidisciplinary Design Optimization Group, UNSW@ADFA Fundamental Questions : Part A 1. Underlying Optimization Algorithm • • 9 How efficient is it ? Can we improve its convergence ? They inherently rank a feasible solution better than an infeasible solution. Underlying recombination operators are fairly dumb. Faces serious problem (lack of convergence for problems with many objectives significantly more than four).

Multidisciplinary Design Optimization Group, UNSW@ADFA Fundamental Questions : Part B 2. Surrogate Model Management • • 10 Do we know which surrogate model to use ? How frequently should we train the surrogate model ? Should we use a single global surrogate or use multiple local ones ? If we want multiple surrogate models, how many should we have ? Should we use multiple surrogate models of one type or should we use multiple surrogate models of multiple types ? Should we rely on our surrogate model to predict performance of a solution even if its neighborhood is under-sampled ? Should we use a surrogate model even though its prediction accuracy is poor ? Should we always approximate a constraint or an objective function using one type of surrogate ?

Multidisciplinary Design Optimization Group, UNSW@ADFA Proposals for Improved Rate of Convergence: IDEA Infeasibility Driven Evolutionary Algorithm (IDEA): Solutions to real life problems are likely to lie on constraint boundaries and hence an Infeasible solution close to the constraint boundary is better than a Feasible solution far away from the constraint boundary. IDEA demonstrated improved rate of convergence for Constrained (Single Objective, Bi-Objective, Many Objective) and Constrained Dynamic Optimization Problems. 11 Performance of an EA (Left) and IDEA (Right)

Multidisciplinary Design Optimization Group, UNSW@ADFA Proposals for Improved Rate of Convergence: IDEA Performance of an EA (Left) and IDEA (Right) on CTP 4 Ray, T. , Singh, H. K. , Isaacs, A. , and Smith, W. (2009). Infeasibility Driven Evolutionary Algorithm for Constrained Optimization, Constraint-Handling in Evolutionary Optimization, Studies in Computational Intelligence Series 198, Eds, Efrén Mezura-Montes, Springer, pp 145 -166. Singh, H. , Isaacs, A. , Nguyen, T. , Ray, T. and Yao, X. (2009). Performance of Infeasibility Driven Evolutionary Algorithm on Constrained Single Objective Dynamic Optimization Problems, Proceedings of IEEE Congress on Evolutionary Computation, CEC 2009, Norway, pp. 3127 -3134. Singh, H. K. , Isaacs, A. , Ray, T. and Smith, W. (2008). Infeasibility Driven Evolutionary Algorithm (IDEA) for Engineering Design Optimization, 21 st Australasian Joint Conference on Artificial Intelligence (AI-08), December 2008, New Zealand, Lecture Notes in Computer Science, Springer, Vol. 5360/2008, pp. 104 -115. 12

Multidisciplinary Design Optimization Group, UNSW@ADFA Proposals for Improved Rate of Convergence: Recombination Background : Simulated Binary Crossover, Polynomial Mutation, Cauchy and Levy Distribution based Mutations, Parent Centric Crossover, Differential Evolution Based Schemes etc have all suggested in literature and used extensively to solve mathematical benchmarks and engineering design optimization problems. Possible Direction: Estimation of Distribution Algorithms (EDA) based sampling schemes offer the promise of generating good candidate solutions based on Probabilistic Models of variable distributions. 13 Parent Centric Crossover

Multidisciplinary Design Optimization Group, UNSW@ADFA Proposals for Improved Rate of Convergence: Hybrids : Using a gradient based local search in Memetic Algorithms. Important for problems where you need the solutions fast such as dynamic optimization problems. FDA 1 and FDA 2 Functions 14 Performance of Memetic Algorithm vs EA. Isaacs, A. , Ray, T. and Smith, W, (2009). Memetic Algorithm for Dynamic Multiobjective Optimization Problems, Proceedings of IEEE Congress on Evolutionary Computation, CEC 2009, Norway, pp. 1707 -1713.

Multidisciplinary Design Optimization Group, UNSW@ADFA Proposals for Improved Rate of Convergence: Many Objectives Many Objective Optimization : The process of Nondominated sorting does not work. Figure below indicates that for 15 objectives, all solutions would be nondominated from the start. • • • Possible Direction: For Constrained Many Objective Problems, use IDEA. For Unconstrained Many Objective Optimization Problems, use Modified Ranking Schemes Use Preference Ranking Schemes/Interactive EMOs. Saxena, D. , Ray, T, Deb, K and Tiwari, A. (2009). Constrained Many Objective Optimization: A Way Forward, Proceedings of IEEE Congress on Evolutionary Computation, CEC 2009, Norway, pp. 545 -552. 15 Singh, H. K. , Isaacs, A. , Ray, T. and Smith, W. (2008) A Study on the Performance of Substitute Distance Based Approaches for Evolutionary Many Objective Optimization, Simulated Evolution and Learning (SEAL 2008), December 2008, Melbourne, Lecture Notes in Computer Science, Springer, Vol. 5361/2008. pp 401 -410.

Multidisciplinary Design Optimization Group, UNSW@ADFA Many Objective Optimization: Interesting Cycle Multiobjective Optimization Problems solved as Single Objective Optimization Problems (Weighted Aggregation). Multiobjective (Biobjective and Tri-objective) Optimization Problems solved using Nondominated Sorting. Many Objective Optimization Problems being attempted using Reference Direction Based Schemes. 16 What is the point in generating huge number of solutions ? Do we have adequate population size to handle huge number of solutions ? Identify important areas of interest through preferences and deliver solutions around those.

Multidisciplinary Design Optimization Group, UNSW@ADFA Proposals for Improved Rate of Convergence: Elite Embedding Elite embedding: Inserting elite individuals can significantly improve the rate of convergence. EA Population on the Left and Embedded EA on the Right. Convergence Plots for the Schemes. 17

Multidisciplinary Design Optimization Group, UNSW@ADFA Surrogate Modeling and Management f x Surrogate System model to be approximated 18

Multidisciplinary Design Optimization Group, UNSW@ADFA Surrogate Modeling and Management f x Surrogate Different types of Surrogate Models 19 System model to be approximated

Multidisciplinary Design Optimization Group, UNSW@ADFA Surrogate Modeling and Management f x Surrogate Different types of Surrogate Models 20 Different number of Surrogate Models System model to be approximated

Multidisciplinary Design Optimization Group, UNSW@ADFA Surrogate Modeling and Management f x Surrogate Different types of Surrogate Models System model to be approximated • Single Surrogate § Multiple Models • Spatially Distributed Surrogates § Fixed § Multiple Adaptive 21 • Surrogate Ensembles Different number of Surrogate Models

Multidisciplinary Design Optimization Group, UNSW@ADFA Surrogate Modeling and Management Surrogate Models need to be trained regularly to capture the function behavior in the regions of interest. (Training) If the prediction accuracy is less than allowable threshold, actual evaluations should be invoked to avoid misguided search. (Accuracy Check) Apart from prediction accuracy, threshold on “adequate sampling” should be incorporated to avoid prediction in under sampled regions. (Neighborhood Check) Presence of multiple types of surrogates allows the flexibility to approximate different functions. (Multiple Surrogates) 22 Cost of Training Various Models

Multidisciplinary Design Optimization Group, UNSW@ADFA Surrogate Assisted Memetic Recombination In an attempt to evaluate “potentially good solutions” only, a selected number of individuals undergo a gradient search/pattern search via a surrogate model. 20 D Sphere Function 20 D Step Function Airfoil Design Problem Figure illustrating that the use of memetic recombination improves the rate of convergence. Isaacs, A. , Ray, T. and Smith, W. (2009). Solving Computationally Expensive Optimization Problems with a Limited Evaluation Budget. Submitted. 23

Multidisciplinary Design Optimization Group, UNSW@ADFA One Surrogate or Multiple Spatially Distributed Surrogates Performance of different types of surrogates on a test function (G 1). SS refers to a Single Surrogate Model (RBF or RSM) within an EA. MSDS refers to Multiple Spatially Distributed Surrogate (RBF and RSM). A max limit on number of clusters is imposed and the model with the minimum error is selected. Figure illustrating that the use of multiple spatially distributed surrogates perform better than a single global surrogate. Ray, T. , Isaacs, A. , and Smith, W. (2009). Surrogate Assisted Evolutionary Algorithm for Multi-objective Optimization, Multi-Objective Techniques and Applications in Chemical Engineering, Eds. Rangaiah, G. P. World Scientific, Singapore, pp. 131 -150. Isaacs, A. , Ray, T. and Smith W. (2009). Multi-objective Design Optimization With Multiple Adaptive Spatially Distributed Surrogates, International Journal of Product Development. Accepted 15 -07 -2008. 24 Isaacs, A. , Ray, T. , and Smith W. , (2007). An Evolutionary Algorithm With Spatially Distributed Surrogates For Multi-objective Optimization, Proceedings of Artificial Life Gold Coast, Australia, Dec. 2007, Lecture Notes in Computer Science, Springer, Vol. 4828, pp. 257 -268.

Multidisciplinary Design Optimization Group, UNSW@ADFA Multiple Spatially Distributed Surrogates of Multiple Types Our Latest Surrogate Assisted Optimization Framework üArchive of solutions are maintained. Archive contains solutions that have been evaluated using actual evaluations. üMultiple Types of Surrogates Coexist. Multiple Spatially Distributed Models can exist if a Single Surrogate fails the Accuracy Check. üSolutions will be evaluated using actual analysis if under sampling is noticed. üIDEA is implemented. üMemetic Recombination Scheme is implemented. üSurrogate Models are trained whenever new solutions are added to archive or periodically. 25

Multidisciplinary Design Optimization Group, UNSW@ADFA Constrained Robust Design Best Performance Design Performance Robust Design Constraint Design Variable Performance Constraint 26 Ray, T. and Smith, W. (2006). A Surrogate Assisted Parallel Multi-objective Evolutionary Algorithm for Robust Engineering Design, Engineering Optimization, Vol. 38, No. 9, 2006, pp. 9971011.

Multidisciplinary Design Optimization Group, UNSW@ADFA Further Challenges: Trans-dimensional Optimization : Problems where one needs to find the number of variables and their values simultaneously. Trans-dimensional Simulated Annealing 1. Runs SA for multiple models in parallel. 2. Searches Model and Variable space simultaneously. 3. Explores each model based on its global fitness with respect to all competing models. 4. In the process, the promising models are explored thoroughly, where as the models with low fitness are discarded. Top: Pareto Fronts for Each Model, Middle: Front Identified by TDSA (across Multiple Runs), Bottom: Fronts Identified using EA (across Multiple Runs) 27 Singh, H. K. , Isaacs, A. , Ray, T. and Smith, W. (2008), A Simulated Annealing Algorithm for Single Objective Trans-Dimensional Optimization Problems, Hybrid Intelligent Systems (HIS) , Proceedings of the 8 th International Conference on Hybrid Intelligent Systems, IEEE Computer Society, September 2008, Barcelona, pp. 19 -24.

Multidisciplinary Design Optimization Group, UNSW@ADFA Further Challenges: Spatial Approximation and Cellular Neural Networks: Instead of a scalar, there is a need to predict the entire field. Prediction of temperature distribution on a plate with given boundary temperatures using ANSYS and CNN. 28 Inverse prediction of boundary temperatures given the temperature distribution within a view section through inverse fitting.

Multidisciplinary Design Optimization Group, UNSW@ADFA Speeding up Multiobjective Optimization Schemes to deal with multiobjective optimization faster Nondominated sorting and computation of hypervolume is significantly expensive as compared to the other parts of an optimization algorithm. Do we need such an elaborate scheme from the beginning ? Simpler schemes are expected to emerge in next two years. 29

Multidisciplinary Design Optimization Group, UNSW@ADFA Many Objective Optimization: Quantum Jump in Capability Until Jan 2009, approaches were unable to solve DTLZ(5, 10), DTLZ(5, 15) even with a population size of 600 running over 10000 generations resulting in 6 million function evaluations. Feb, 2009: DTLZ(5, 10), DTLZ(5, 20), DTLZ(5, 30) solved with a population size of 100 evolving over 5000 generations resulting in 0. 5 million function evaluations. (Dhish, Ray, Deb and Tiwari, IEEE CEC 2009). June 29, 2009: All the above problems solved with a population size of 100 evolving over 100 generations resulting in 10, 000 function evaluations. (Forthcoming) The recent approach developed by our group will enable solutions to many objective optimization problems with much greater confidence and far less computational cost. m 30

Multidisciplinary Design Optimization Group, UNSW@ADFA Conclusions üOur Next Generation Surrogate Assisted Optimization Framework Offers the Possibility of Rationally Approaching and Solving Real Life Computationally Expensive Optimization Problems. üThe Framework has been developed within a MATLAB Environment. üIt is Easy to Integrate any Commercial or in-house Analysis Tools with it. üIt has been tested on Numerous Mathematical Benchmarks, Engineering Design Optimization Problems and Different Variants have been used by a Number of Research Groups. 31

Multidisciplinary Design Optimization Group, UNSW@ADFA Application Snapshots y 1 5 5 1 2 6 6 2 3 7 7 3 4 8 8 4 x Thank You 32

Multidisciplinary Design Optimization Group, UNSW@ADFA Topology Optimization of Compliant Mechanisms Aim: Evolve the Topology of Compliant Mechanisms Generate a Topology of the Mechanism such that the tip in the right follows the desired path. EA coupled with ABAQUS. Kang, T. , Guang, Y. C. and Ray, T. (2002). Design Synthesis of Path Generating Compliant Mechanisms by Evolutionary Optimization of Topology and Shape, ASME Transactions, Journal of Mechanical Design, Vol. 124, September 2002, pp. 492 -500. 33

Multidisciplinary Design Optimization Group, UNSW@ADFA Shape Design with CEM and CFD Considerations 1 d. B Reduction in Bistatic RCS as compared to NACA 64 A 410 Venkatarayalu, N. and Ray, T. Application of Multiobjective Optimization in Electromagnetic Design, Real World Multi-objective Systems Engineering: Methodology and Applications, Eds. Nedjah, N. , Nova Science, NY, 2005. 34

Multidisciplinary Design Optimization Group, UNSW@ADFA Dielectric Filter Design Aim: Identify the Layer Properties and Thickness Bandpass Filter Design: Lower cutoff at 28 GHz and Upper cutoff at 32 GHZ. Reflection coefficient is greater tha -5 d. B in stopband less than -10 d. B in the passband. & layered dielectric. Lowpass Filter Design: Cutoff frequency of 30 GHZ. Maximum of 15000 Design Evaluations. Venkatarayalu, N. , Ray, T. and Gan, Y. B. , (2005). Multilayer Dielectric Filter Design Using a Multi-objective Evolutionary Algorithm, IEEE Trans. On Antennas and Propagation, Vol. 53, No. 11, pp. 3625 -3632, 2005. 35

Multidisciplinary Design Optimization Group, UNSW@ADFA Yagi-Uda Antenna Design Aim: Identify the Element Lengths and their Spacing for Maximum Gain More than 1 d. Bi improvement Venkatarayalu, N. and Ray, T. (2004). Optimum Design of Yagi-Uda Antennas Using Computational Intelligence, IEEE Trans. On Antennas and Propagation, Vol. 52, No. 7, pp. 1811 - 1818, 2004. 36

Multidisciplinary Design Optimization Group, UNSW@ADFA Design of Piezoelectric Patches Aim: Identify the Gains of Piezoelectric Patches y 1 2 3 4 5 6 7 8 1 2 3 4 x Liew, K. M. , He, X. Q, and Ray, T. (2004). Computational Intelligence in Optimal Shape Control of Functionally Graded Smart Plates, Computer Methods in Applied Mechanics and Engineering, Vol. 193, Issues 42 -44, pp. 4475 -4492, 2004. 37

Multidisciplinary Design Optimization Group, UNSW@ADFA Nose Cone Design Aim: Minimization of Total Drag Approach: With and without surrogates Base Design Without Surrogate With Surrogate Computational Saving M = 3. 02 M = 8. 04 0. 2601 0. 3001 0. 2565 (1. 39%) 0. 2942 (1. 96%) 0. 2569 (1. 21%) 0. 2977 (0. 80%) 18% 11% Deepak, R. , Ray. T. and Boyce, R. Evolutionary Algorithm Shape Optimization of a Hypersonic Flight Experiment Nose Cone, Journal of Spacecrafts and Rockets, 45 (3), pp. 428 -437, 2008. 38

Multidisciplinary Design Optimization Group, UNSW@ADFA Optimal Gas Injection Volume for Oil Extraction Aim: Identify Optimal Gas injection Volumes to the Oil Wells for Maximum Extraction An Increase of 243 Barrels per Day for 56 Oil Well Problem (Benchmark Problem) Ray, T. and Sarker, R. Genetic Algorithm for Solving a Gas Lift Optimization Problem, Journal of Petroleum Science and Engineering, Vol. 59, pp. 84 -96, 2007. Ray, T. and Sarker, R. , Evolutionary Algorithms Deliver Promising Results to Gas Lift Optimization Problems, World Oil, April 229 (4), pp. 141 -142, 2008. 39

Multidisciplinary Design Optimization Group, UNSW@ADFA Optimal Stage Masses for a Launch Vehicle Aim: Identify Stage Masses of a Launch Vehicle 47 Kg Reduction in Total Stage Masses Briggs, G. P. , Ray, T. and Milthorpe, J. (2007). Optimal Design of an Australian Medium Launch Vehicle, Innovations in Systems and Software Engineering, (A NASA Journal), Springer. Vol. 3, pp. 105 -116, 2007. 40

Multidisciplinary Design Optimization Group, UNSW@ADFA UAV Path Planning Aim: Identify Optimal Paths for Minimal Threat and Distance Traveled 41 Sanders, G. and Ray, T. Optimal Offline Path Planning of a Fixed Wing Unmanned Aerial Vehicle (UAV) using an Evolutionary Algorithm, IEEE Congress on Evolutionary Computation CEC-2007, Singapore, September, pp. 4410 -4416, 2007.

Multidisciplinary Design Optimization Group, UNSW@ADFA Optimal Parameters for Flapping Aim: Find wing parameters (frequency & amplitude) to Maximize Thrust and Efficiency K*h = 1. 5 42 DOE based sampling Non-dominated solutions in x-space and f-space Transformation to parameter space Surrogate models for f 1 and f 2 as function of parameters

Multidisciplinary Design Optimization Group, UNSW@ADFA Optimal Parameters for Flapping Aim: Find wing parameters (frequency & amplitude) to Maximize Thrust and Efficiency Non-dominated solutions in x-space and f-space Parameters 43 Predicted Calculated Frequency Amplitude Thrust Efficiency 3. 545 0. 4321 0. 7896 0. 0997 0. 7538 0. 0972 3. 034 0. 1403 0. 0863 0. 305 0. 0845 0. 287 3. 2728 0. 1484 0. 1176 0. 2971 0. 1171 0. 2963