PlatEMO4.2

PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/CTSEA.m

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+classdef CTSEA < ALGORITHM
+% <multi/many> <real/integer/label/binary/permutation> <constrained>
+% Constrained two-stage evolutionary algorithm
+
+%------------------------------- Reference --------------------------------
+% F. Ming, W. Gong, H. Zhen, S. Li, L. Wang, and Z. Liao, A simple
+% two-stage evolutionary algorithm for constrained multi-objective
+% optimization, Knowledge-Based Systems, 2021, 228: 107263.
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2023 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 Fei Ming
+
+    methods
+        function main(Algorithm,Problem)
+            %% Generate the sampling points and random population
+            Population = Problem.Initialization();
+            W = UniformPoint(Problem.N,Problem.M);
+            [ARMOEA_Archive,RefPoint,Range] = UpdateRefPoint(Population.objs,W,[]);
+            CV = sum(max(0,Population.cons),2);
+            Archive = Population(CV==0);
+            stage_conver = 0;
+
+            %% Optimization
+            while Algorithm.NotTerminated(Population)
+                if Problem.FE<0.5*Problem.maxFE
+                    % evolve population to PF by ARMOEA
+                    MatingPool = MatingSelection1(Population,RefPoint,Range);
+                    Offspring = OperatorGA(Problem,Population(MatingPool));
+                    [ARMOEA_Archive,RefPoint,Range] = UpdateRefPoint([ARMOEA_Archive;Offspring.objs],W,Range);
+                    Archive = UpdateArchive(Archive,[Population,Offspring],Problem.N);
+                    [Population,Range] = EnvironmentalSelection1([Population,Offspring],RefPoint,Range,Problem.N);
+                else
+                    if stage_conver==0
+                        % exchange archive and population
+                        temp = Population;
+                        Population = Archive;
+                        Archive = temp;
+                        stage_conver = 1;
+                    end
+                    % evolve population to CPF by modified SPEA2
+                    MatingPool = MatingSelection2(Population,Archive,Problem.N);
+                    Offspring = OperatorGA(Problem,MatingPool);
+                    Population = EnvironmentalSelection2([Population,Offspring],Problem.N);
+                end
+            end
+        end
+    end
+end

PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/CalDistance.m

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+function Distance = CalDistance(PopObj,RefPoint)
+% Calculate the distance between each solution to each adjusted reference point
+
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2023 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 Fei Ming
+
+    N  = size(PopObj,1);
+    NR = size(RefPoint,1);
+    PopObj   = max(PopObj,1e-6);
+    RefPoint = max(RefPoint,1e-6);
+
+    %% Adjust the location of each reference point
+    Cosine = 1 - pdist2(PopObj,RefPoint,'cosine');
+    NormR  = sqrt(sum(RefPoint.^2,2));
+    NormP  = sqrt(sum(PopObj.^2,2));
+    d1     = repmat(NormP,1,NR).*Cosine;
+    d2     = repmat(NormP,1,NR).*sqrt(1-Cosine.^2);
+    [~,nearest] = min(d2,[],1);
+    RefPoint    = RefPoint.*repmat(d1(N.*(0:NR-1)+nearest)'./NormR,1,size(RefPoint,2));
+
+    %% Calculate the distance between each solution to each point
+    Distance = pdist2(PopObj,RefPoint);
+end

PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/CalFitness.m

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+function Fitness = CalFitness(PopObj,PopCon)
+% Calculate the fitness of each solution
+
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2023 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 Fei Ming
+
+    N = size(PopObj,1);
+    if nargin == 1
+        CV = zeros(N,1);
+    else
+        CV = sum(max(0,PopCon),2);
+    end
+    %% Detect the dominance relation between each two solutions
+    Dominate = false(N);
+    for i = 1 : N-1
+        for j = i+1 : N
+            if CV(i) < CV(j)
+                Dominate(i,j) = true;
+            elseif CV(i) > CV(j)
+                Dominate(j,i) = true;
+            else
+                k = any(PopObj(i,:)<PopObj(j,:)) - any(PopObj(i,:)>PopObj(j,:));
+                if k == 1
+                    Dominate(i,j) = true;
+                elseif k == -1
+                    Dominate(j,i) = true;
+                end
+            end
+        end
+    end
+
+    %% Calculate S(i)
+    S = sum(Dominate,2);
+
+    %% Calculate R(i)
+    R = zeros(1,N);
+    for i = 1 : N
+        R(i) = sum(S(Dominate(:,i)));
+    end
+
+    %% Calculate D(i)
+    Distance = pdist2(PopObj,PopObj);
+    Distance(logical(eye(length(Distance)))) = inf;
+    Distance = sort(Distance,2);
+    D = 1./(Distance(:,floor(sqrt(N)))+2);
+
+    %% Calculate the fitnesses
+    Fitness = R + D';
+end

PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/EnvironmentalSelection1.m

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+function [Population,Range] = EnvironmentalSelection1(Population,RefPoint,Range,N)
+% The environmental selection of AR-MOEA
+
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2023 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".
+%--------------------------------------------------------------------------
+
+    %% Selection among feasible solutions
+    % Non-dominated sorting
+    [FrontNo,MaxFNo] = NDSort(Population.objs,N);
+    Next = FrontNo < MaxFNo;
+    % Select the solutions in the last front
+    Last   = find(FrontNo==MaxFNo);
+    Choose = LastSelection(Population(Last).objs,RefPoint,Range,N-sum(Next));
+    Next(Last(Choose)) = true;
+    Population = Population(Next);
+    % Update the range for normalization
+    Range(2,:) = max(Population.objs,[],1);
+    Range(2,Range(2,:)-Range(1,:)<1e-6) = 1;
+end
+
+function Remain = LastSelection(PopObj,RefPoint,Range,K)
+% Select part of the solutions in the last front
+
+    N  = size(PopObj,1);
+    NR = size(RefPoint,1);
+
+    %% Calculate the distance between each solution and point
+    Distance    = CalDistance(PopObj-repmat(Range(1,:),N,1),RefPoint);
+    Convergence = min(Distance,[],2);
+
+    %% Delete the solution which has the smallest metric contribution one by one
+    [dis,rank] = sort(Distance,1);
+    Remain     = true(1,N);
+    while sum(Remain) > K
+        % Calculate the fitness of noncontributing solutions
+        Noncontributing = Remain;
+        Noncontributing(rank(1,:)) = false;
+        METRIC = sum(dis(1,:)) + sum(Convergence(Noncontributing));
+        Metric = inf(1,N);
+        Metric(Noncontributing) = METRIC - Convergence(Noncontributing);
+        % Calculate the fitness of contributing solutions
+        for p = find(Remain & ~Noncontributing)
+            temp = rank(1,:) == p;
+            noncontributing = false(1,N);
+            noncontributing(rank(2,temp)) = true;
+            noncontributing = noncontributing & Noncontributing;
+            Metric(p) = METRIC - sum(dis(1,temp)) + sum(dis(2,temp)) - sum(Convergence(noncontributing));
+        end
+        % Delete the worst solution and update the variables
+        [~,del] = min(Metric);
+        temp    = rank ~= del;
+        dis     = reshape(dis(temp),sum(Remain)-1,NR);
+        rank    = reshape(rank(temp),sum(Remain)-1,NR);
+        Remain(del) = false;
+    end
+end

PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/EnvironmentalSelection2.m

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+function [Population,Fitness] = EnvironmentalSelection2(Population,N)
+% The environmental selection of SPEA2
+
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2023 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".
+%--------------------------------------------------------------------------
+
+    %% Calculate the fitness of each solution
+    Fitness = CalFitness(Population.objs,Population.cons);
+
+    %% Environmental selection
+    Next = Fitness < 1;
+    if sum(Next) < N
+        [~,Rank] = sort(Fitness);
+        Next(Rank(1:N)) = true;
+    elseif sum(Next) > N
+        Del  = Truncation(Population(Next).objs,sum(Next)-N);
+        Temp = find(Next);
+        Next(Temp(Del)) = false;
+    end
+    % Population for next generation
+    Population = Population(Next);
+    Fitness    = Fitness(Next);
+    % Sort the population
+    [Fitness,rank] = sort(Fitness);
+    Population = Population(rank);
+end
+
+function Del = Truncation(PopObj,K)
+% Select part of the solutions by truncation
+
+    %% Truncation
+    Distance = pdist2(PopObj,PopObj);
+    Distance(logical(eye(length(Distance)))) = inf;
+    Del = false(1,size(PopObj,1));
+    while sum(Del) < K
+        Remain   = find(~Del);
+        Temp     = sort(Distance(Remain,Remain),2);
+        [~,Rank] = sortrows(Temp);
+        Del(Remain(Rank(1))) = true;
+    end
+end

PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/MatingSelection1.m

@@ -0,0 +1,39 @@
+function MatingPool = MatingSelection1(Population,RefPoint,Range)
+% The mating selection of AR-MOEA
+
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2023 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".
+%--------------------------------------------------------------------------
+
+    %% Calculate the fitness of each feasible solution based on IGD-NS
+    % Calculate the distance between each solution and point
+    N = length(Population);
+    Distance    = CalDistance(Population.objs-repmat(Range(1,:),N,1),RefPoint);
+    Convergence = min(Distance,[],2);
+    [dis,rank]  = sort(Distance,1);
+    % Calculate the fitness of noncontributing solutions
+    Noncontributing = true(1,N);
+    Noncontributing(rank(1,:)) = false;
+    METRIC   = sum(dis(1,:)) + sum(Convergence(Noncontributing));
+    fitness  = inf(1,N);
+    fitness(Noncontributing) = METRIC - Convergence(Noncontributing);
+    % Calculate the fitness of contributing solutions
+    for p = find(~Noncontributing)
+        temp = rank(1,:) == p;
+        noncontributing = false(1,N);
+        noncontributing(rank(2,temp)) = true;
+        noncontributing = noncontributing & Noncontributing;
+        fitness(p) = METRIC - sum(dis(1,temp)) + sum(dis(2,temp)) - sum(Convergence(noncontributing));
+    end
+
+    %% Combine the fitness of feasible solutions with the fitness of infeasible solutions
+    Fitness = -inf(1,length(Population));
+
+    %% Binary tournament selection
+    MatingPool = TournamentSelection(2,length(Population),-Fitness);
+end

PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/MatingSelection2.m

@@ -0,0 +1,18 @@
+function MatingPool = MatingSelection2(Population,Archive,N)
+% The mating selection of stage 2
+
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2023 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 Fei Ming
+
+    Fitness1    = CalFitness(Population.objs,Population.cons);
+    MatingPool1 = TournamentSelection(2,N,Fitness1);
+    MatingPool  = Population(MatingPool1);
+end

PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/UpdateArchive.m

@@ -0,0 +1,55 @@
+function UpdatedArchive=UpdateArchive(Archive,Population,N)
+% Update Archive
+
+%------------------------------- Copyright --------------------------------
+% Copyright (c) 2023 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 Fei Ming
+
+        CV = sum(max(0,Population.cons),2);
+        Archive=[Archive,Population(CV==0)];
+        if length(Archive)==N
+            UpdatedArchive=Archive;
+        elseif length(Archive)<N
+            Population=setdiff(Population,Archive);
+            CV = sum(max(0,Population.cons),2);
+            [~,index]=sort(CV,'ascend');
+            remain_size=N-length(Archive);
+            Remain=Population(index(1:remain_size));
+            UpdatedArchive=[Archive,Remain];
+        else
+            Fitness=CalFitness(Archive.objs,Archive.cons);
+            Next = Fitness < 1;
+            if sum(Next) < N
+                [~,Rank] = sort(Fitness);
+                Next(Rank(1:N)) = true;
+            elseif sum(Next) > N
+                Del  = Truncation(Archive(Next).objs,sum(Next)-N);
+                Temp = find(Next);
+                Next(Temp(Del)) = false;
+            end
+            % Archive for next generation
+            UpdatedArchive = Archive(Next);
+        end
+end
+
+function Del = Truncation(PopObj,K)
+% Select part of the solutions by truncation
+
+    %% Truncation
+    Distance = pdist2(PopObj,PopObj);
+    Distance(logical(eye(length(Distance)))) = inf;
+    Del = false(1,size(PopObj,1));
+    while sum(Del) < K
+        Remain   = find(~Del);
+        Temp     = sort(Distance(Remain,Remain),2);
+        [~,Rank] = sortrows(Temp);
+        Del(Remain(Rank(1))) = true;
+    end
+end