A Fusion-Based Multi-Information Source Optimization Approach using Knowledge Gradient Policies

Optimization of complex systems often involves evaluation of a quantity several times, which is potentially computationally prohibitive. This can be alleviated by considering information sources representing the original model with lower fidelity and cost. This paper describes an optimization method for the case where the objective function is represented by different information sources with varying fidelities and computational costs. The proposed methodology creates a multi-information source value-of-information framework that defines optimal strategies for querying of information sources. The surrogate Gaussian process model is used for fusion of information sources. Then, the knowledge gradient policy is incorporated by considering the probability of violation of constraints for sequential decision making to identify the next design and information source to evaluate. The high performance of the developed methodology is demonstrated in terms of making balance between cost and information gain of various information sources of a one-dimensional example test problem and an aerodynamic design example.

[1]  P. A. Newman,et al.  Approximation and Model Management in Aerodynamic Optimization with Variable-Fidelity Models , 2001 .

[2]  Warren B. Powell,et al.  Optimal Learning: Powell/Optimal , 2012 .

[3]  Ali Mosleh,et al.  The Assessment of Probability Distributions from Expert Opinions with an Application to Seismic Fragility Curves , 1986 .

[4]  Karen Willcox,et al.  Provably Convergent Multifidelity Optimization Algorithm Not Requiring High-Fidelity Derivatives , 2012 .

[5]  M. Drela.  XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils , 1989 .

[6]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[7]  Douglas Allaire,et al.  Adaptive Uncertainty Propagation for Coupled Multidisciplinary Systems , 2017 .

[8]  S. Gupta,et al.  Bayesian look ahead one-stage sampling allocations for selection of the best population , 1996 .

[9]  Warren B. Powell,et al.  The Correlated Knowledge Gradient for Simulation Optimization of Continuous Parameters using Gaussian Process Regression , 2011, SIAM J. Optim..

[10]  Warren B. Powell,et al.  A Knowledge-Gradient Policy for Sequential Information Collection , 2008, SIAM J. Control. Optim..

[11]  Warren B. Powell,et al.  The Knowledge-Gradient Policy for Correlated Normal Beliefs , 2009, INFORMS J. Comput..

[12]  Karen Willcox,et al.  Multifidelity Optimization using Statistical Surrogate Modeling for Non-Hierarchical Information Sources , 2015 .

[13]  Douglas Allaire,et al.  Quantifying the Impact of Different Model Discrepancy Formulations in Coupled Multidisciplinary Systems , 2017 .

[14]  William J. Welch,et al.  Computer experiments and global optimization , 1997 .

[15]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[16]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[17]  Klaus Hllig,et al.  Approximation and Modeling with B-Splines , 2013 .

[18]  David Draper,et al.  Assessment and Propagation of Model Uncertainty , 2011 .

[19]  R. A. Miller,et al.  Sequential kriging optimization using multiple-fidelity evaluations , 2006 .

[20]  George E. Apostolakis,et al.  Including model uncertainty in risk-informed decision making , 2006 .

[21]  P. A. Newman,et al.  Optimization with variable-fidelity models applied to wing design , 1999 .

[22]  Raphael T. Haftka,et al.  A convex hull approach for the reliability-based design optimization of nonlinear transient dynamic problems , 2007 .

[23]  John Platt,et al.  Probabilistic Outputs for Support vector Machines and Comparisons to Regularized Likelihood Methods , 1999 .

[24]  Douglas Allaire,et al.  Compositional Uncertainty Analysis via Importance Weighted Gibbs Sampling for Coupled Multidisciplinary Systems , 2016 .

[25]  D. Madigan,et al.  Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam's Window , 1994 .

[26]  A. J. Booker,et al.  A rigorous framework for optimization of expensive functions by surrogates , 1998 .

[27]  M. Sasena,et al.  Exploration of Metamodeling Sampling Criteria for Constrained Global Optimization , 2002 .

[28]  Adrian E. Raftery,et al.  Bayesian Model Averaging: A Tutorial , 2016 .

[29]  Ulisses Braga-Neto,et al.  Particle filters for partially-observed Boolean dynamical systems , 2018, Autom..

[30]  Charles A. Ingene,et al.  Specification Searches: Ad Hoc Inference with Nonexperimental Data , 1980 .

[31]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

[32]  Jack P. C. Kleijnen,et al.  Kriging Metamodeling in Simulation: A Review , 2007, Eur. J. Oper. Res..

[33]  Andrew Ning,et al.  Comparison of Airfoil Precomputational Analysis Methods for Optimization of Wind Turbine Blades , 2016, IEEE Transactions on Sustainable Energy.

[34]  Ramana V. Grandhi,et al.  Quantification of Modeling Uncertainty in Aeroelastic Analyses , 2011 .

[35]  Thomas D. Economon,et al.  Stanford University Unstructured (SU 2 ): An open-source integrated computational environment for multi-physics simulation and design , 2013 .

[36]  Karen Willcox,et al.  A Bayesian-Based Approach to Multifidelity Multidisciplinary Design Optimization , 2010 .

[37]  Ulisses Braga-Neto,et al.  ParticleFilters for Partially-ObservedBooleanDynamical Systems , 2017 .

[38]  Seyede Fatemeh Ghoreishi.  Uncertainty Analysis for Coupled Multidisciplinary Systems Using Sequential Importance Resampling , 2016 .

[39]  W. D. Thomison,et al.  A Model Reification Approach to Fusing Information from Multifidelity Information Sources , 2017 .

[40]  Charles Audet,et al.  A surrogate-model-based method for constrained optimization , 2000 .

[41]  N. M. Alexandrov,et al.  A trust-region framework for managing the use of approximation models in optimization , 1997 .

[42]  Samy Missoum,et al.  Reliability assessment using probabilistic support vector machines , 2013 .

[43]  Antonio Harrison Sánchez,et al.  Limit state function identification using Support Vector Machines for discontinuous responses and disjoint failure domains , 2008 .

[44]  Samy Missoum,et al.  Classification-based Quantification of Constraint Violation for Efficient Global Optimization and Failure Probability Confidence Bound Calculation , 2013 .

[45]  R. L. Winkler.  Combining Probability Distributions from Dependent Information Sources , 1981 .

[46]  Mahdi Imani,et al.  Point-Based Methodology to Monitor and Control Gene Regulatory Networks via Noisy Measurements , 2019, IEEE Transactions on Control Systems Technology.

[47]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..