Update ARMOEA and add CA-MOEA

PlatEMO/Algorithms/AR-MOEA/ARMOEA.m

@@ -21,7 +21,7 @@ function ARMOEA(Global)
     W          = UniformPoint(Global.N,Global.M);
     [Archive,RefPoint,Range] = UpdateRefPoint(Population(all(Population.cons<=0,2)).objs,W,[]);
 
-    %% Start the interations
+    %% Optimization
     while Global.NotTermination(Population)
         MatingPool = MatingSelection(Population,RefPoint,Range);
         Offspring  = GA(Population(MatingPool));

PlatEMO/Algorithms/CA-MOEA/CAMOEA.m

@@ -0,0 +1,58 @@
+function CAMOEA(Global)
+% <algorithm> <C>
+% Clustering based adaptive multi-objective evolutionary algorithm
+
+%------------------------------- Reference --------------------------------
+% Y. Hua, Y. Jin, K. Hao, A clustering-based adaptive eEvolutionary
+% algorithm for multiobjective optimization with irregular Pareto fronts,
+% IEEE Transactions on Cybernetics, 2018.
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2018-2019 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 is written by Yicun Hua
+
+    %% Generate random population
+    Population = Global.Initialization();
+
+    %% Optimization
+    while Global.NotTermination(Population)
+        % Generate offspring randomly
+        MatingPool = randperm(Global.N);
+        Offspring  = GA(Population(MatingPool));
+
+        % Elitism strategy
+        UniPop = [Population,Offspring];
+        PopObj = UniPop.objs;
+        [FrontNo,MaxFNo] = NDSort(PopObj,Global.N);
+
+        % The number of individuals to be selected in the last
+        % non-dominated front
+        K = Global.N-sum(FrontNo<MaxFNo);
+
+        if K~= 0
+            % Normalization
+            pareto_population = find(FrontNo<MaxFNo);
+            last_population = find(FrontNo == MaxFNo);
+            Zmin = min(PopObj(FrontNo == MaxFNo,:));
+            Zmax = max(PopObj(FrontNo == MaxFNo,:));
+            S = sum(FrontNo == MaxFNo);
+            MaxFnorm = (PopObj(last_population,:)-repmat(Zmin,S,1))./repmat(Zmax-Zmin,S,1);
+
+            % Clustering-based reference points generation
+            [Ref] = Reference_Generation( MaxFnorm,Global.M,K);
+
+            % Clustering-based environmental selection
+            [reference_population] = Reference_Point_Selection(MaxFnorm,last_population,Ref,K,Global.M);
+        else
+            pareto_population = find(FrontNo<=MaxFNo);
+            reference_population = [];
+        end
+        Population = UniPop([pareto_population,reference_population]);
+    end
+end

PlatEMO/Algorithms/CA-MOEA/Reference_Generation.m

@@ -0,0 +1,62 @@
+function [Ref] = Reference_Generation(MaxFnorm, M, K)
+% Clustering-based reference points generation
+
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2018-2019 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 is written by Yicun Hua
+
+    % Calculate boundary individuals: extreme
+    [~,maxobj] = max(MaxFnorm,[],1);
+    [~,minobj] = min(MaxFnorm,[],1);
+    ex = unique([maxobj,minobj]);
+    extreme = unique(MaxFnorm(ex,:),'rows');
+
+    E = size(extreme,1);    
+    Nc = K-E;
+
+    if Nc>0
+        % Clustering
+        T = clusterdata(MaxFnorm,'maxclust',Nc,'distance','euclidean','linkage','ward');
+
+        % Calculate cluster centers
+        for i = 1:Nc
+
+            p = find(T == i);
+            pn = length(p);
+
+            Ref(i,1:M) = sum(MaxFnorm(p,:),1)/pn;
+
+            Ref(i,M+1) = i;   
+
+        end
+
+        Ref = unique(Ref,'rows');
+        rpr = size(Ref,1);
+
+        % If cluster centers are not enough, 
+        % randomly select some individuals as reference points
+        if rpr < Nc
+            Ncrp = Nc-rpr;
+            Ref(rpr+1:Nc,:) = MaxFnorm(randperm(size(MaxFnorm,1),Ncrp),:);
+        end
+
+        Ref(:,M+1) = [];
+
+        % Use boundary individuals as reference points
+        for er = 1:E
+            Ref(Nc+er,1:M) = extreme(er,1:M);
+        end
+    else
+        % Use boundary individuals as reference points
+        for er = 1:K
+            Ref(er,:) = extreme(er,:);
+        end
+    end
+end

PlatEMO/Algorithms/CA-MOEA/Reference_Point_Selection.m

@@ -0,0 +1,80 @@
+function  [reference_population]=Reference_Point_Selection(MaxFnorm,last_population,Ref,K,M)
+% Clustering-based environmental selection
+
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2018-2019 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 is written by Yicun Hua
+
+    last_Num = size(MaxFnorm,1);
+    Ref_Num = size(Ref,1);
+    dis = pdist2(MaxFnorm,Ref);
+
+    for i = 1:last_Num
+        [~,dmin_p] = min(dis(i,:),[],2);
+
+        % Individual i assigned to Ref(dmin_p,:)
+        MaxFnorm(i,(M+1)) = dmin_p; 
+
+        % Distance between individual i and Ref(dmin_p,:)
+        MaxFnorm(i,(M+2)) = dis(i,dmin_p);
+    end
+
+    % Individuals are labeled 3(to distinguish from 1 and 2)
+    MaxFnorm(:,(M+3)) = 3;
+    for i = 1:Ref_Num
+        if sum(MaxFnorm(:,(M+1)) == i) ~= 0
+            a = find(MaxFnorm(:,(M+1)) == i);
+            a = a';
+            [~,b] = sort(MaxFnorm(a,(M+2)));
+
+            % Individuals closest to reference points are labeled 1
+            MaxFnorm(a(b(1)),(M+3)) = 1;   
+
+            % Individuals in crowd area are labeled 2
+            if sum(MaxFnorm(:,(M+1)) == i) > 3
+                a(b(1)) = [];
+                MaxFnorm(a,(M+3)) = 2; 
+            end
+        end
+    end
+
+    t1 = sum(MaxFnorm(:,(M+3)) == 1);
+    t2 = sum(MaxFnorm(:,(M+3)) == 2); 
+
+    if t1 <= K
+        % If individuals labeled 1 are not enough, we choose some 2, then 3
+        d = find(MaxFnorm(:,(M+3))==1);
+        d = d';
+        reference_population(1:t1) = d;
+        if t2 >= (K-t1)
+            % If individuals labeled 2 are enough
+            d = find(MaxFnorm(:,(M+3))==2);
+            d = d';
+            y = randperm(length(d));
+            reference_population((t1+1):K) = d(y(1:(K-t1)));
+        else
+            % If individuals labeled 2 are not enough, we choose some 3
+            d = find(MaxFnorm(:,(M+3)) == 2);
+            d = d';
+            reference_population((t1+1):(t1+t2)) = d;
+            d = find(MaxFnorm(:,(M+3)) == 3);
+            d = d';
+            y = randperm(length(d));
+            reference_population((t1+t2+1):K) = d(y(1:(K-t1-t2)));
+        end
+    else
+        % If individuals labeled 1 are enough
+        d = find(MaxFnorm(:,(M+3)) == 1);
+        d = d';
+        y = randperm(length(d));
+        reference_population(1:K) = d(y(1:K));
+    end
+    reference_population = last_population(reference_population);
+end