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% STK_EXAMPLE_MISC04 Pareto front simulation
%
% DESCRIPTION
%
% We consider a bi-objective optimization problem, where the objective
% functions are modeled as a pair of independent stationary Gaussian
% processes with a Matern 5/2 anisotropic covariance function.
%
% Figure (a): represent unconditional realizations of the Pareto front and
% and estimate of the probability of being non-dominated at each point
% of the objective space.
%
% Figure (b): represent conditional realizations of the Pareto front and
% and estimate of the posteriorior probability of being non-dominated
% at each point of the objective space.
%
% EXPERIMENTAL FUNCTION WARNING
%
% This script uses the stk_plot_probdom2d function, which is currently
% considered an experimental function. Read the help for more information.
%
% REFERENCE
%
% [1] Michael Binois, David Ginsbourger and Olivier Roustant, Quantifying
% uncertainty on Pareto fronts with Gaussian Process conditional simu-
% lations, European J. of Operational Research, 2043(2):386-394, 2015.
%
% See also: stk_plot_probdom2d
% Copyright Notice
%
% Copyright (C) 2017, 2019 CentraleSupelec
% Copyright (C) 2014 SUPELEC
%
% Author: Julien Bect <julien.bect@centralesupelec.fr>
% Copying Permission Statement
%
% This file is part of
%
% STK: a Small (Matlab/Octave) Toolbox for Kriging
% (https://github.com/stk-kriging/stk/)
%
% STK is free software: you can redistribute it and/or modify it under
% the terms of the GNU General Public License as published by the Free
% Software Foundation, either version 3 of the License, or (at your
% option) any later version.
%
% STK is distributed in the hope that it will be useful, but WITHOUT
% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
% or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
% License for more details.
%
% You should have received a copy of the GNU General Public License
% along with STK. If not, see <http://www.gnu.org/licenses/>.
stk_disp_examplewelcome;
%% Objective functions
DIM = 2;
BOX = [[0; 5] [0; 3]];
f1 = @(x) 4 * x(:,1) .^ 2 + 4 * x(:,2) .^ 2;
f2 = @(x) (x(:,1) - 5) .^ 2 + (x(:,2) - 5) .^ 2;
%% Data
n_obs = 10;
x_obs = stk_sampling_maximinlhs (n_obs, [], BOX);
z_obs = zeros (n_obs, 2);
z_obs(:, 1) = f1 (x_obs.data); % Remark: f1 (x_obs) should be OK...
z_obs(:, 2) = f2 (x_obs.data); % ... but see Octave bug #49267
%% Stationary GP models
model1 = stk_model (@stk_materncov52_aniso, DIM);
model1.param = stk_param_estim (model1, x_obs, z_obs(:, 1));
model2 = stk_model (@stk_materncov52_aniso, DIM);
model2.param = stk_param_estim (model2, x_obs, z_obs(:, 2));
stk_figure ('stk_example_misc04 (a)');
stk_plot_probdom2d (model1, model2, BOX);
%% Conditionned GP models
stk_figure ('stk_example_misc04 (b)');
stk_plot_probdom2d ( ...
stk_model_gpposterior (model1, x_obs, z_obs(:, 1)), ...
stk_model_gpposterior (model2, x_obs, z_obs(:, 2)), BOX);
%!test stk_example_misc04; close all;
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