1% STK_EXAMPLE_MISC04 Pareto front simulation 2% 3% DESCRIPTION 4% 5% We consider a bi-objective optimization problem, where the objective 6% functions are modeled as a pair of independent stationary Gaussian 7% processes with a Matern 5/2 anisotropic covariance function. 8% 9% Figure (a): represent unconditional realizations of the Pareto front and 10% and estimate of the probability of being non-dominated at each point 11% of the objective space. 12% 13% Figure (b): represent conditional realizations of the Pareto front and 14% and estimate of the posteriorior probability of being non-dominated 15% at each point of the objective space. 16% 17% EXPERIMENTAL FUNCTION WARNING 18% 19% This script uses the stk_plot_probdom2d function, which is currently 20% considered an experimental function. Read the help for more information. 21% 22% REFERENCE 23% 24% [1] Michael Binois, David Ginsbourger and Olivier Roustant, Quantifying 25% uncertainty on Pareto fronts with Gaussian Process conditional simu- 26% lations, European J. of Operational Research, 2043(2):386-394, 2015. 27% 28% See also: stk_plot_probdom2d 29 30% Copyright Notice 31% 32% Copyright (C) 2017, 2019 CentraleSupelec 33% Copyright (C) 2014 SUPELEC 34% 35% Author: Julien Bect <julien.bect@centralesupelec.fr> 36 37% Copying Permission Statement 38% 39% This file is part of 40% 41% STK: a Small (Matlab/Octave) Toolbox for Kriging 42% (http://sourceforge.net/projects/kriging) 43% 44% STK is free software: you can redistribute it and/or modify it under 45% the terms of the GNU General Public License as published by the Free 46% Software Foundation, either version 3 of the License, or (at your 47% option) any later version. 48% 49% STK is distributed in the hope that it will be useful, but WITHOUT 50% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 51% or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public 52% License for more details. 53% 54% You should have received a copy of the GNU General Public License 55% along with STK. If not, see <http://www.gnu.org/licenses/>. 56 57stk_disp_examplewelcome; 58 59 60%% Objective functions 61 62DIM = 2; 63BOX = [[0; 5] [0; 3]]; 64 65f1 = @(x) 4 * x(:,1) .^ 2 + 4 * x(:,2) .^ 2; 66f2 = @(x) (x(:,1) - 5) .^ 2 + (x(:,2) - 5) .^ 2; 67 68 69%% Data 70 71n_obs = 10; 72 73x_obs = stk_sampling_maximinlhs (n_obs, [], BOX); 74 75z_obs = zeros (n_obs, 2); 76z_obs(:, 1) = f1 (x_obs.data); % Remark: f1 (x_obs) should be OK... 77z_obs(:, 2) = f2 (x_obs.data); % ... but see Octave bug #49267 78 79 80%% Stationary GP models 81 82model1 = stk_model ('stk_materncov52_aniso', DIM); 83model1.param = stk_param_estim (model1, x_obs, z_obs(:, 1)); 84 85model2 = stk_model ('stk_materncov52_aniso', DIM); 86model2.param = stk_param_estim (model2, x_obs, z_obs(:, 2)); 87 88stk_figure ('stk_example_misc04 (a)'); 89 90stk_plot_probdom2d (model1, model2, BOX); 91 92 93%% Conditionned GP models 94 95stk_figure ('stk_example_misc04 (b)'); 96 97stk_plot_probdom2d ( ... 98 stk_model_gpposterior (model1, x_obs, z_obs(:, 1)), ... 99 stk_model_gpposterior (model2, x_obs, z_obs(:, 2)), BOX); 100 101 102%!test stk_example_misc04; close all; 103