Upload CoDEA

PlatEMO/Algorithms/Multi-objective optimization/CoDEA/CoDEA.m

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+classdef CoDEA < ALGORITHM
+% <2022> <multi/many> <real/integer/label/binary/permutation>
+% collaborative decomposition-based evolutionary algorithm
+
+%------------------------------- Reference --------------------------------
+% Yu Wu, Jianle Wei, Weiqin Ying, Yanqi Lan, Zhen Cui, Zhenyu Wang,
+% A collaborative decomposition-based evolutionary algorithm integrating 
+% normal and penalty-based boundary intersection methods for many-objective 
+% optimization, Information Sciences,Volume 616,2022,Pages 505-525
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2025 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".
+%--------------------------------------------------------------------------
+
+    methods
+        function main(Algorithm,Problem)
+            %% Generate the reference points and random population
+            [W,Problem.N] = UniformPoint(Problem.N,Problem.M);
+            Population   = Problem.Initialization();
+            [z,znad]     = deal(min(Population.objs),max(Population.objs));
+            H1 = 1;
+            while nchoosek(H1+Problem.M,Problem.M-1) <= Problem.N
+                H1 = H1 + 1;
+            end
+            ILid = nchoosek(H1+Problem.M-1,Problem.M-1);
+            r = [];
+            for i = 1 : ILid
+                deta = min(W(i,:));
+                beta = (1 - max(W(i,:)));
+                r(i) = ((2*(1-deta*Problem.M)+(beta/(0.5)))/2);
+            end
+
+            %% Optimization
+            while Algorithm.NotTerminated(Population)
+                MatingPool = randi(Problem.N,1,Problem.N);
+                Offspring  = OperatorGA(Problem,Population(MatingPool));
+                [Population,z,znad] = EnvironmentalSelection([Population,Offspring],W,Problem.N,z,znad,ILid,r );
+            end
+        end
+    end
+end

PlatEMO/Algorithms/Multi-objective optimization/CoDEA/EnvironmentalSelection.m

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+function [Population,z,znad] = EnvironmentalSelection(Population,W,N,z,znad,ILid,r)
+% The environmental selection of CoDEA
+
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2025 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".
+%--------------------------------------------------------------------------
+
+    %% Non-dominated sorting
+    [FrontNo,MaxFNo] = NDSort(Population.objs,N);
+    St = find(FrontNo<=MaxFNo);
+
+    %% Normalization
+    [PopObj,z,znad] = Normalization(Population(St).objs,z,znad);
+
+    %% CoD-non-dominated sorting
+    tFrontNo = CoDSort(PopObj,W,ILid,r);
+
+    %% Selection
+    MaxFNo    = find(cumsum(hist(tFrontNo,1:max(tFrontNo)))>=N,1);
+    LastFront = find(tFrontNo==MaxFNo);
+    LastFront = LastFront(randperm(length(LastFront)));
+    tFrontNo(LastFront(1:sum(tFrontNo<=MaxFNo)-N)) = inf;
+
+    Next      = St(tFrontNo<=MaxFNo);
+    % Population for next generation
+    Population = Population(Next);
+
+
+end
+
+function tFrontNo = CoDSort(PopObj,W,ILid,r)
+    % Do CoD-non-dominated sorting
+
+    N  = size(PopObj,1);
+    [NW,M] = size(W);
+
+    %% Calculate the d1 and d2 values for each solution to each weight
+    normP  = sqrt(sum(PopObj.^2,2));
+    Cosine = 1 - pdist2(PopObj,W,'cosine');
+    d2     = repmat(normP,1,size(W,1)).*sqrt(1-Cosine.^2);
+
+    %% Clustering
+    [~,class] = min(d2,[],2);
+
+    %% Sort
+    tFrontNo = zeros(1,N);
+
+    for i = 1 : NW
+        C = find(class==i);
+        if(size(C,1) == 0)
+            continue;
+        end
+
+        if i <= ILid  
+            d = max(PopObj(C,:)-W(i,:),[],2);       
+            g = ((d+(M)/(1+exp(-1*(M-5.5)*M))*r(i)*((d2(C,i)-min(d2(C,i)))./(max(d2(C,i))-min(d2(C,i))))));
+            [~,rank] = sort(g);
+        else
+             d = 1 - pdist2(PopObj(C,:),ones(1,M)*(1/M),'cosine');
+            [~,rank] = sort(d); 
+        end
+        tFrontNo(C(rank)) = 1 : length(C);
+    end
+
+
+
+

PlatEMO/Algorithms/Multi-objective optimization/CoDEA/Normalization.m

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+function [PopObj,z,znad] = Normalization(PopObj,z,znad)
+% Normalize the population and update the ideal point and the nadir point
+
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2025 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".
+%--------------------------------------------------------------------------
+
+    [N,M] = size(PopObj);
+
+    %% Update the ideal point
+    z = min(z,min(PopObj,[],1));
+
+    %% Update the nadir point
+    % Identify the extreme points
+    W = zeros(M) + 1e-6;
+    W(logical(eye(M))) = 1;
+    ASF = zeros(N,M);
+    for i = 1 : M
+        ASF(:,i) = max(abs((PopObj-repmat(z,N,1))./(repmat(znad-z,N,1)))./repmat(W(i,:),N,1),[],2);
+    end
+    [~,extreme] = min(ASF,[],1);
+    % Calculate the intercepts
+    Hyperplane = (PopObj(extreme,:)-repmat(z,M,1))\ones(M,1);
+    a = (1./Hyperplane)' + z;
+    if any(isnan(a)) || any(a<=z)
+        a = max(PopObj,[],1);
+    end
+    znad = a;
+
+    %% Normalize the population
+    PopObj = (PopObj-repmat(z,N,1))./(repmat(znad-z,N,1));
+end