The Handbook of DACE in Tomlab E-Fan Li, Department of Mathematics, National Taiwan University 2009/09/18

The Handbook of DACE in Tomlab

E-Fan Li, Department of Mathematics, National Taiwan University2009/09/18

Contribution Lien-Chi Lai - made a revision

ContributionThe Handbook of DACE in Tomlab2

Outline Setup Function and Parameter Experiment

SetupThe Handbook of DACE in Tomlab4

Setup

Pre-Procedure

The Handbook of DACE in Tomlab5

Go to your own directory and start the Matlab.

Pre-Procedure

Pre-Procedure


Go to /opt/tomlab/ directory and start the Tomlab. >> cd /opt/tomlab >> startup

Pre-Procedure

Pre-Procedure


Back to work in your own directory.

Pre-Procedure

Pre-Procedure


Back to work in your own directory.

Pre-Procedure

Function and ParameterThe Handbook of DACE in Tomlab9

Function and Parameter



The Fundamental Setting of Experience Function

>> Prob = glcAssign(ft_Name, LowerBound, UpperBound,

ft_Name, [], [], [], [], [], [], [], [],

[], [], [], [], [], [], [], []);

>> Prob.MIP.nLocal = [];

>> Prob.MIP.nGlobal = [];

>> Prob.WarmStart = 1; Get initial points from cgoSave.mat

>> Prob.XGrid = OXgrid; % size(OXgrid) = dim-by-N To construct surrogate surface size(OXgrid)=dim-by-N, N = OXgrid is the coordinate in unit space

dimgrid

10 The Handbook of DACE in Tomlab



Save the information of initial points as cgoSave.mat

>> cul_initial(O, F, X, ft_Name); O： the coordinate of initial point in original space F： the function value of initial point X： the coordinate of initial point in unit space

Execute rbfSolve_test

>> Result = rbfSolve_test(Prob); Surrogate surface will be saved as Result.surrogate_surface

11 The Handbook of DACE in Tomlab

ExperimentThe Handbook of DACE in Tomlab12

Experiment

Experiment


>> ft_name = 'Ackley';

>> x_L = [-1.5; -1.5];

>> x_U = [ 1.5; 1.5];

>> Prob = glcAssign(ft_name, x_L, x_U, ft_name, [],

[], [], [], [], [], [], [], [], [], [],

[], [], [], [], []);

>> Prob.MIP.nLocal = [];

>> Prob.MIP.nGlobal = [];

>> Prob.WarmStart = 1;

>> Xgrid = gridsamp([x_L';x_U'], 25);

>> OXgrid = (Xgrid -repmat(x_L', size(Xgrid, 1), 1))

./ repmat((x_U -x_L)‘ ,size(Xgrid,1),1);

>> Prob.XGrid = OXgrid';

13 The Handbook of DACE in Tomlab Experiment

Experiment


>> init_pts = [-1.5000 -1.1250 15.2662;-1.3750 1.2500 15.4227;-1.2500 0.5000 14.0989;

-1.1250 -0.1250 11.6858;-1.0000 1.3750 14.4187;-0.8750 0.6250 12.7996;

-0.7500 0.2500 11.9174;-0.6250 1.5000 15.1234;-0.5000 -0.2500 11.6650;

-0.3750 1.0000 12.5803;-0.2500 -1.0000 11.8531;-0.1250 -1.3750 13.7073;

0 -0.7500 10.9778; 0.1250 0.8750 10.9253; 0.2500 1.1250 12.5025;

0.3750 -0.8750 12.4219; 0.5000 -1.5000 15.0723; 0.6250 0 11.1906;

0.7500 -0.5000 12.7568; 0.8750 0.3750 12.4219; 1.0000 -0.6250 12.9159;

1.1250 -1.2500 14.0343; 1.2500 -0.3750 13.8584; 1.3750 0.7500 14.6122;

1.5000 0.1250 14.2366];

>> O = init_pts(:,1:2);

>> F = init_pts(:,3);

>> X = (O - repmat(x_L', size(init_pts,1),1)) ./

repmat((x_U-x_L)', size(init_pts,1),1);

>> cul_initial(O, F, X, ft_name);

>> Result = rbfSolve_test(Prob,0);

>> sur_vec = Result.surrogate_surface;


Experiment


>> [x_grid, y_grid] = meshgrid(-1.5:3/24:1.5, -1.5:3/24:1.5);

>> surf(x_grid, y_grid, reshape(sur_vec, 25, 25));


Reference


http://tomopt.com/tomlab/ http://tomopt.com/docs/TOMLAB_CGO.pdf

Reference

AppendixThe Handbook of DACE in Tomlab17

Appendix

Appendix – Ackley.m


function [f,error,icount] = Ackely(X, Prob)

global FT_EVAL

FT_EVAL = FT_EVAL + 1;

error=0; icount=1;

a = 20; b = 0.2; c = 2*pi; d = 5.7;z = 0.8;n = 2;

if size(X, 1) == 2

x=X(1);

y=X(2);

f = (1./z).*( -a .* exp(-b.*sqrt((1./n).*(x.^2 + y.^2))) -...

exp((1./n).*(cos(c.*x) + cos(c.*y))) + a + exp(1) + d );

else

x = X(:,1); y = X(:,2);

f = (1./z).*( -a .* exp(-b.*sqrt((1./n).*(x.^2 + y.^2))) -...

exp((1./n).*(cos(c.*x) + cos(c.*y))) + a + exp(1) + d );

end

Appendix

Appendix – cul_initial.m


function cul_initial(O,F,X,Name)

O = O'; X = X';

F_m = min(median(F),F);

Fpen = F; F00 = F;

Cc = [];

nCon = 0;

nInit = length(F);

nFunc = length(F);

n = length(F);

nSample = length(F);

ExDText = 'initial points is design by myself';

rngState = rand('state');

fMinIdx = [];

save cgoSave.mat

Appendix

Appendix – gridsamp.m (1/3)


function S = gridsamp(range, q)

%GRIDSAMP n-dimensional grid over given range

% Call: S = gridsamp(range, q)

%

% range : 2*n matrix with lower and upper limits

% q : n-vector, q(j) is the number of points

% in the j'th direction.

% If q is a scalar, then all q(j) = q

% S : m*n array with points, m = prod(q)

% [email protected]

% Last update June 25, 2002

[mr n] = size(range); dr = diff(range);

if mr ~= 2 | any(dr < 0)

error(‘range must be an array with two rows and range(1,:) <= range(2,:)')

end

Appendix



sq = size(q);

if min(sq) > 1 | any(q <= 0)

error('q must be a vector with non-negative elements')

end

p = length(q);

if p == 1, q = repmat(q,1,n);

elseif p ~= n

error(sprintf('length of q must be either 1 or %d',n))

end

% Check for degenerate intervals

i = find(dr == 0);

if ~isempty(i), q(i) = 0*q(i); end

Appendix



% Recursive computation

if n > 1

A = gridsamp(range(:,2:end), q(2:end)); % Recursive call

[m p] = size(A); q = q(1);

S = [zeros(m*q,1) repmat(A,q,1)];

y = linspace(range(1,1),range(2,1), q);

k = 1:m;

for i = 1 : q

S(k,1) = repmat(y(i),m,1); k = k + m;

end

else

S = linspace(range(1,1),range(2,1), q).';

end

Appendix

Appendix – All m-files

The Handbook of DACE in Tomlab23 Appendix

Ackley.m cul_initial.m gridsamp.m

rbfSolve_test.m sample.m

Documents

The Handbook of DACE in Tomlab E-Fan Li, Department of Mathematics, National Taiwan University 2009/09/18