Recent advances in ALAMO

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1 Recent advances in ALAMO Nick Sahinidis 1,2 Acknowledgements: Alison Cozad 1,2 and David Miller 1 1 National Energy Technology Laboratory, Pittsburgh, PA,USA 2 Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute orimply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

2 ALAMO METHODOLOGY Model i Sample Points Model i+1 Surrogate model Data points Model error New surrogate model Black box function New sample point Derivative free optimization In low dimensions Mixed integer programming for best simple model Carnegie Mellon University 2

3 ALAMO SOFTWARE Version lines of Matlab code Written in Used GAMS to solve algebraic optimization subproblems Demonstrated advantages vs. least squares and lasso Carnegie Mellon University 3

4 ALAMO SOFTWARE Version lines of Matlab code Written in Used GAMS to solve algebraic optimization subproblems Demonstrated advantages vs. least squares and lasso Version lines of Fortran code Written in 2013 Carnegie Mellon University 4

5 ALAMO SOFTWARE Version lines of Matlab code Written in Used GAMS to solve algebraic optimization subproblems Demonstrated advantages vs. least squares and lasso Version lines of Fortran code Written in 2013 Current version 7000 lines of Fortran code Uses GAMS to solve algebraic optimization subproblems Carnegie Mellon University 5

6 BASIC ALAMO FUNCTIONS Curve fitting Given a collection of points in an input output space, find a function that relates inputs to outputs ALAMO considers potential functions and automatically identifies a simple function that fits the data Carnegie Mellon University 6

7 BASIC ALAMO FUNCTIONS Curve fitting Given a collection of points in an input output space, find a function that relates inputs to outputs ALAMO considers potential functions and automatically identifies a simple function that fits the data Design of experiments ALAMO can interface to a simulator (or experimental system) to guide collection of data with the aim to Build a model entirely from scratch Validate quality of model built based on a pre existing data set Supplement existing experimental data Carnegie Mellon University 7

8 EXAMPLE ALAMO INPUT FILE Input output data used to fit model Carnegie Mellon University 8

9 ALAMO OUTPUT Carnegie Mellon University 9

10 A DATA AND THEORY DRIVEN APPROACH Empirical data System knowledge output bounds + = boundary conditions derivative bounds mass balances Richer models consistent with sampled data and theoretical insights Apply system knowledge beyond sampled data to build regression models First principles derivation Engineering insight Output and derivative bounds Insights that are generally available free of charge Carnegie Mellon University 10

11 CONSTRAINED REGRESSION Extrapolation zone Fits the true function better Fits the data better Problem Space Safe Extrapolation velocity profile model Add no slip Boundary values Convexity Carnegie Mellon University 11

12 IMPLEMENTATION Enforced everywhere Ordinary least squares regression objective Carnegie Mellon University 12

13 IMPLEMENTATION Enforced everywhere Ordinary least squares regression objective Semi infinite program Carnegie Mellon University 13

14 IMPLEMENTATION Enforced everywhere Bounding set Semi infinite program Simple linear constraints Carnegie Mellon University 14

15 CONCLUSIONS Expanding the scope of MINLP algorithms Using low complexity surrogate models to strike a balance between optimal decision making and model fidelity Enforcing theoretical insights to datadriven experimental science Iteratively use implicit regression constraints to ensure limits on models ALAMO site: archimedes.cheme.cmu.edu/?q=alamo Carnegie Mellon University 15

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