Request for Updating MOEA/D-EGO Implementation in PlatEMO

PlatEMO/Algorithms/Multi-objective optimization/MOEA-D-EGO/GPmodelFCM.m

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+function [model,centers] = GPmodelFCM(train_x,train_y,L1,L2)
+% Fuzzy clustering-based method for modeling c_size* M models, where c_size
+% is the number of clusters and M the number of objectives.
+
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2024 BIMK Group. You are free to use the PlatEMO for
+% research purposes. All publications which use this platform or any code
+% in the platform should acknowledge the use of "PlatEMO" and reference "Ye
+% Tian, Ran Cheng, Xingyi Zhang, and Yaochu Jin, PlatEMO: A MATLAB platform
+% for evolutionary multi-objective optimization [educational forum], IEEE
+% Computational Intelligence Magazine, 2017, 12(4): 73-87".
+%--------------------------------------------------------------------------
+
+% This function was written by Liang Zhao ([email protected]).
+
+    [K,M] = size(train_y);
+    D     = size(train_x,2);
+    if K <= L1
+        % all the K evaluated points are directly used for building GP model
+        csize = 1;
+        [centers,~] = FCM(train_x,csize,[2 NaN 0.05 false]);
+        model = cell(1,M);
+        theta = (K ^ (-1 ./ K)) .* ones(1, D);
+        for j = 1 : M
+            model{1,j}= Dacefit(train_x,train_y(:,j),'regpoly0','corrgauss',theta,1e-6*ones(1,D),20*ones(1,D));
+        end 
+    else
+        % FuzzyCM
+        csize       = 1 + ceil((K-L1)/L2);
+        [centers,~] = FCM(train_x,csize,[2 NaN 0.05 false]);
+        dis         = pdist2(train_x,centers);
+        [~,index]   = sort(dis);
+        theta       = (L1 ^ (-1 ./ L1)) .* ones(1, D);
+
+        %% Build GP model of each objective for each cluster 
+        model   = cell(csize, M);
+        for i   = 1 : csize
+            for j = 1 :  M
+                temp_index = index(1:L1,i);
+                model{i,j} = Dacefit(train_x(temp_index,:),train_y(temp_index,j), 'regpoly0','corrgauss', theta, 1e-6.*ones(1,D), 20.*ones(1,D));
+            end
+        end
+    end
+
+end
+% >>>>>>>>>>>>>>>>   Auxiliary functions  ==================== 
+function [center, U, obj_fcn] = FCM(data, cluster_n, options)
+    %FCM Data set clustering using fuzzy c-means clustering.
+    %
+    %   [CENTER, U, OBJ_FCN] = FCM(DATA, N_CLUSTER) finds N_CLUSTER number of
+    %   clusters in the data set DATA. DATA is size M-by-N, where M is the number of
+    %   data points and N is the number of coordinates for each data point. The
+    %   coordinates for each cluster center are returned in the rows of the matrix
+    %   CENTER. The membership function matrix U contains the grade of membership of
+    %   each DATA point in each cluster. The values 0 and 1 indicate no membership
+    %   and full membership respectively. Grades between 0 and 1 indicate that the
+    %   data point has partial membership in a cluster. At each iteration, an
+    %   objective function is minimized to find the best location for the clusters
+    %   and its values are returned in OBJ_FCN.
+    %
+    %   [CENTER, ...] = FCM(DATA,N_CLUSTER,OPTIONS) specifies a vector of options
+    %   for the clustering process:
+    %       OPTIONS(1): exponent for the matrix U             (default: 2.0)
+    %       OPTIONS(2): maximum number of iterations          (default: 100)
+    %       OPTIONS(3): minimum amount of improvement         (default: 1e-5)
+    %       OPTIONS(4): info display during iteration         (default: 1)
+    %   The clustering process stops when the maximum number of iterations
+    %   is reached, or when the objective function improvement between two
+    %   consecutive iterations is less than the minimum amount of improvement
+    %   specified. Use NaN to select the default value.
+    %
+    %   Example
+    %       data = rand(100,2);
+    %       [center,U,obj_fcn] = fcm(data,2);
+    %       plot(data(:,1), data(:,2),'o');
+    %       hold on;
+    %       maxU = max(U);
+    %       % Find the data points with highest grade of membership in cluster 1
+    %       index1 = find(U(1,:) == maxU);
+    %       % Find the data points with highest grade of membership in cluster 2
+    %       index2 = find(U(2,:) == maxU);
+    %       line(data(index1,1),data(index1,2),'marker','*','color','g');
+    %       line(data(index2,1),data(index2,2),'marker','*','color','r');
+    %       % Plot the cluster centers
+    %       plot([center([1 2],1)],[center([1 2],2)],'*','color','k')
+    %       hold off;
+    %
+    %   See also FCMDEMO, INITFCM, IRISFCM, DISTFCM, STEPFCM.
+
+    %   Roger Jang, 12-13-94, N. Hickey 04-16-01
+    %   Copyright 1994-2018 The MathWorks, Inc. 
+
+    if nargin ~= 2 && nargin ~= 3
+	    error(message("fuzzy:general:errFLT_incorrectNumInputArguments"))
+    end
+
+    data_n = size(data, 1);
+
+    % Change the following to set default options
+    default_options = [2;	% exponent for the partition matrix U
+		    100;	% max. number of iteration
+		    1e-5;	% min. amount of improvement
+		    1];	% info display during iteration 
+
+    if nargin == 2
+	    options = default_options;
+    else
+	    % If "options" is not fully specified, pad it with default values.
+	    if length(options) < 4
+		    tmp = default_options;
+		    tmp(1:length(options)) = options;
+		    options = tmp;
+	    end
+	    % If some entries of "options" are nan's, replace them with defaults.
+	    nan_index = find(isnan(options)==1);
+	    options(nan_index) = default_options(nan_index);
+	    if options(1) <= 1
+		    error(message("fuzzy:general:errFcm_expMustBeGtOne"))
+	    end
+    end
+
+    expo = options(1);		% Exponent for U
+    max_iter = options(2);		% Max. iteration
+    min_impro = options(3);		% Min. improvement
+    display = options(4);		% Display info or not
+
+    obj_fcn = zeros(max_iter, 1);	% Array for objective function
+
+    U = initfcm(cluster_n, data_n);			% Initial fuzzy partition
+    % Main loop
+    for i = 1:max_iter
+	    [U, center, obj_fcn(i)] = stepfcm(data, U, cluster_n, expo);
+	    if display
+		    fprintf('Iteration count = %d, obj. fcn = %f\n', i, obj_fcn(i));
+	    end
+	    % check termination condition
+	    if i > 1
+		    if abs(obj_fcn(i) - obj_fcn(i-1)) < min_impro, break; end
+	    end
+    end
+
+    iter_n = i;	% Actual number of iterations 
+    obj_fcn(iter_n+1:max_iter) = [];
+end
+
+function out = distfcm(center, data)
+    %DISTFCM Distance measure in fuzzy c-mean clustering.
+    %	OUT = DISTFCM(CENTER, DATA) calculates the Euclidean distance
+    %	between each row in CENTER and each row in DATA, and returns a
+    %	distance matrix OUT of size M by N, where M and N are row
+    %	dimensions of CENTER and DATA, respectively, and OUT(I, J) is
+    %	the distance between CENTER(I,:) and DATA(J,:).
+    %
+    %       See also FCMDEMO, INITFCM, IRISFCM, STEPFCM, and FCM.
+
+    %	Roger Jang, 11-22-94, 6-27-95.
+    %       Copyright 1994-2016 The MathWorks, Inc. 
+
+    out = zeros(size(center, 1), size(data, 1));
+
+    % fill the output matrix
+
+    if size(center, 2) > 1
+        for k = 1:size(center, 1)
+	    out(k, :) = sqrt(sum(((data-ones(size(data, 1), 1)*center(k, :)).^2), 2));
+        end
+    else	% 1-D data
+        for k = 1:size(center, 1)
+	    out(k, :) = abs(center(k)-data)';
+        end
+    end
+end
+function U = initfcm(cluster_n, data_n)
+    %INITFCM Generate initial fuzzy partition matrix for fuzzy c-means clustering.
+    %   U = INITFCM(CLUSTER_N, DATA_N) randomly generates a fuzzy partition
+    %   matrix U that is CLUSTER_N by DATA_N, where CLUSTER_N is number of
+    %   clusters and DATA_N is number of data points. The summation of each
+    %   column of the generated U is equal to unity, as required by fuzzy
+    %   c-means clustering.
+    %
+    %       See also DISTFCM, FCMDEMO, IRISFCM, STEPFCM, FCM.
+
+    %   Roger Jang, 12-1-94.
+    %   Copyright 1994-2002 The MathWorks, Inc. 
+
+    U = rand(cluster_n, data_n);
+    col_sum = sum(U);
+    U = U./col_sum(ones(cluster_n, 1), :);
+end
+
+function [U_new, center, obj_fcn] = stepfcm(data, U, cluster_n, expo)
+    %STEPFCM One step in fuzzy c-mean clustering.
+    %   [U_NEW, CENTER, ERR] = STEPFCM(DATA, U, CLUSTER_N, EXPO)
+    %   performs one iteration of fuzzy c-mean clustering, where
+    %
+    %   DATA: matrix of data to be clustered. (Each row is a data point.)
+    %   U: partition matrix. (U(i,j) is the MF value of data j in cluster j.)
+    %   CLUSTER_N: number of clusters.
+    %   EXPO: exponent (> 1) for the partition matrix.
+    %   U_NEW: new partition matrix.
+    %   CENTER: center of clusters. (Each row is a center.)
+    %   ERR: objective function for partition U.
+    %
+    %   Note that the situation of "singularity" (one of the data points is
+    %   exactly the same as one of the cluster centers) is not checked.
+    %   However, it hardly occurs in practice.
+    %
+    %       See also DISTFCM, INITFCM, IRISFCM, FCMDEMO, FCM.
+
+    %   Copyright 1994-2014 The MathWorks, Inc. 
+
+    mf = U.^expo;       % MF matrix after exponential modification
+    center = mf*data./(sum(mf,2)*ones(1,size(data,2))); %new center
+    dist = distfcm(center, data);       % fill the distance matrix
+    obj_fcn = sum(sum((dist.^2).*mf));  % objective function
+    tmp = dist.^(-2/(expo-1));      % calculate new U, suppose expo != 1
+    U_new = tmp./(ones(cluster_n, 1)*sum(tmp));
+end