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Usage Of DACE Toolbox Lien-Chi Lai, Optimization Lab 2009/10/09

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Download DACE Toolbox (1/2) Download DACE ToolboxUsage of DACE Toolbox2 DACE website: http://www2.imm.dtu.dk/~hbn/dace/http://www2.imm.dtu.dk/~hbn/dace/

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Download DACE Toolbox (2/2) Download DACE ToolboxUsage of DACE Toolbox3

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Command and Parameter (1/5) Command and ParameterUsage of DACE Toolbox4 Command >> [dmodel,perf] = dacefit(S,Y,regr,corr,theta0) >> pred = predictor(x, dmodel) Parameter S experimental points (m-by-n) Y responses at S (m-by-1) regr regression function corr correlation function theta0 parameter of correlation function (1-by-1 if all dimensions are identical, or n-by-1) x p trial points with n dimensions (p-by-n) pred predicted responses (p-by-1)

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Command and Parameter (2/5) Command and ParameterUsage of DACE Toolbox5 Command >> [dmodel,perf] =... dacefit(S,Y,regr,corr,theta0,lob,upb) >> pred = predictor(x, dmodel) Parameter lob,upb optional parameter, if present, then should be vectors of the same length as theta0 dim. should be same as the one of theta0

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Command and Parameter (3/5) Command >> [dmodel,perf] =... dacefit(S,Y,regr,corr,theta0,lob,upb) >> pred = predictor(x, dmodel) Parameter dmodel DACE model, struct with regr, corr, theta, beta … perf information about the optimization, struct with nv, … Command and ParameterUsage of DACE Toolbox6

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Command and Parameter (4/5) Regression Models regpoly0 Zero order polynomial regpoly1 First order polynomial regpoly2 Second order polynomial Correlation Models correxp Exponential correxpg Generalized exponential corrgauss Gaussian corrlin Linear corrspherical Spherical corrspline Cubic spline Command and ParameterUsage of DACE Toolbox7

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Command and Parameter (5/5) Command >> x = gridsamp([1 1;3 3], 3) x = 1 1 1 2 1 3 2 1 2 2 2 3 3 1 3 2 3 3 Command and ParameterUsage of DACE Toolbox8

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Example >> [dmodel, perf] = dacefit(S, Y, @regpoly0,... @corrgauss, 10); >> [dmodel, perf] = dacefit(S, Y, @regpoly0,... @corrgauss, 10, 0.1, 20); >> [dmodel, perf] = dacefit(S, Y, @regpoly0,... @corrgauss, [10 10],... [0.1 0.1], [20 20]); >> pred = predictor(x, dmodel); ExampleUsage of DACE Toolbox9

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Example Complete code for Branin function ExampleUsage of DACE Toolbox10

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Appendix – Complete Code (1/2) % S = lhsamp(25,2); load S.mat S = [S(:,1)*15-5, S(:,2)*15]; Y = ft_branin(S(:,1), S(:,2)); x = gridsamp([-5 0;10 15], 25); theta = [10 10]; lob = [1e-1 1e-1]; upb = [20 20]; [dmodel, perf] = dacefit(S, Y, @regpoly0,... @corrgauss, theta, lob, upb); % [dmodel, perf] = dacefit(S, Y, @regpoly0,... @corrgauss, 1); pred = predictor(x, dmodel); Appendix – Complete CodeUsage of DACE Toolbox11

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Appendix – Complete Code (1/2) [x_grid, y_grid] = meshgrid(-5:15/24:10, 0:15/24:15); surf(x_grid, y_grid, reshape(pred, 25, 25)); view(2); xlabel('x'); ylabel('y'); title('Surrogate Surface'); % final_theta = dmodel.theta; % function z = ft_branin(x, y) % z = (y - 5.1*x.^2/(4*pi*pi) + 5*x/pi -6).^2 +... 10*(1-1/(8*pi))*cos(x) + 10; Appendix – Complete CodeUsage of DACE Toolbox12

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