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Some Problems in Need of Sampling-Based Optimization Under Uncertainty Methods

Some Problems in Need of Sampling-Based Optimization Under Uncertainty Methods. Genetha Gray Predictive Simulation R&D Sandia National Laboratories Livermore, CA, USA. Outline and Motivation. Problem Context Problem Characteristics Current Practices Some Wants/Needs Lessons Learned

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Some Problems in Need of Sampling-Based Optimization Under Uncertainty Methods

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  1. Some Problems in Need of Sampling-Based Optimization Under Uncertainty Methods Genetha Gray Predictive Simulation R&D Sandia National Laboratories Livermore, CA, USA

  2. Outline and Motivation • Problem Context • Problem Characteristics • Current Practices • Some Wants/Needs • Lessons Learned NOTE: The purpose of this talk is to inspire you to think about sampling methods in the context of some particular applications. It is meant to generate discussion.

  3. Problem Context • Computational Simulators • Attempt to model some real world scenario • To now, often physics-based description of the behavior of an engineering-based component • Example: model of an electrical circuit • Example: model of mechanical system (i.e. two pieces of metal screwed together) • Moving to models that have heuristic components • Example: model of a reservoir • Example: model of social interactions • Want to make predictive assessments &/or use results to make risk-informed decisions • May represent a full system by coupling models

  4. Optimization Problems • Design • Meet a specified want/need • Minimize cost • Continuous, integer, categorical variables • Examples: Find a well field to contains a contaminant; Create an appropriate waste system; Prevent saltwater intrusion • Calibration • Set the inherent model parameters so that the results best match the real world • Real data for comparison may not be available • Examples: Electrical circuit simulation; Hydrogen economy model • Worst-case Scenario • Generate plausible scenarios for a decision maker • Examples: Change in water supply given climate change; Description of the power supply network given alternative energy sources NEW NEW

  5. simulation outputs(x) temperature x time Traditional Model Calibration or Parameter Estimation Simulation output that depends on x Given data s(x) datad parameters Simulator

  6. Problem Characteristics • Simulator is a black box • Real Data • Often limited (sometimes as small as 2 data points) • May be legacy (and lacking pedigree) • May be dedicated • Contains uncertainties • Usually a significant expense associated with data collection • Parameters • 2 ≤ n ≤ 50 • “Real” parameters (with bounds) and “fudge factors” • Continuous, integer • Computational Costs • Simulator may take as long as 4 days on 800 processors • Usually working to a hard deadline

  7. Other Considerations of the Data • Data components • May be challenging to boil results down to one representative real number • May give more than one result • Examples: behavior over time, thresholds • Two results may be opposed in the objective function • Calibration vs. Validation • Mirrors the training-testing issue in machine learning • Want the calibration set be representative and as small as possible

  8. What We’re Doing Now • Basic sensitivity analysis to reduce problem size or identify “highest importance” parameters • LHS • Need more adaptive approaches for expensive problems • Need cheaper alternative (Xiu n+1 sample) • Derivative-Free Hybrids • APPS-TGP: combines pattern search with Treed Gaussian process • EAGLS: Evolutionary Algorithms Guiding Local Search • Surrogate-based PSO • Data Collection • “Fill out” existing data • DOE for future tests

  9. Accept guess as optimum based on inability to find better guess within decreasing search region. Say, TP1 is found optimum. But, a design at TP1 looks like it is not robust to small design perturbations New algorithms:decision-maker chooses “best” point based on additional criteria Uncertainties Other constraints Incorporate expert opinion Sample Problem: Looking for a Robust Optimum TP1 TP2 TP3 Robustness

  10. Hidden Constraints • The constraints on the domain are not always known • Can be bound, nonlinear, or not in a form that can be written down • Information may be solely feasible or infeasible • No information about the size of the feasibility neighborhood around a feasible point • May be discontinuous • May not be initially expressed by applications expert • Affect choice of optimization method

  11. Some Final Thoughts • There are LOTS of applications needing appropriate sampling-based optimization methods that consider uncertainty • To tackle some of these issues, I am researching “hybrid” methods which combine the benefits of multiple methods • Combining traditional optimization with statistical sampling allows us to address (or at least characterize) uncertainty and provide better information • Methods may need to be tailored to problem characteristics or even to specific application areas

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