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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 |
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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 | ||
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||
%------------------------------- 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". | ||
%-------------------------------------------------------------------------- | ||
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||
% This function is written by Fei Ming | ||
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N = size(PopObj,1); | ||
NR = size(RefPoint,1); | ||
PopObj = max(PopObj,1e-6); | ||
RefPoint = max(RefPoint,1e-6); | ||
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%% 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)); | ||
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%% Calculate the distance between each solution to each point | ||
Distance = pdist2(PopObj,RefPoint); | ||
end |
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PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/CalFitness.m
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function Fitness = CalFitness(PopObj,PopCon) | ||
% Calculate the fitness of each solution | ||
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%------------------------------- 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". | ||
%-------------------------------------------------------------------------- | ||
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% This function is written by Fei Ming | ||
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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 | ||
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%% Calculate S(i) | ||
S = sum(Dominate,2); | ||
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%% Calculate R(i) | ||
R = zeros(1,N); | ||
for i = 1 : N | ||
R(i) = sum(S(Dominate(:,i))); | ||
end | ||
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%% Calculate D(i) | ||
Distance = pdist2(PopObj,PopObj); | ||
Distance(logical(eye(length(Distance)))) = inf; | ||
Distance = sort(Distance,2); | ||
D = 1./(Distance(:,floor(sqrt(N)))+2); | ||
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%% Calculate the fitnesses | ||
Fitness = R + D'; | ||
end |
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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 | ||
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||
%------------------------------- 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". | ||
%-------------------------------------------------------------------------- | ||
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%% 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 | ||
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function Remain = LastSelection(PopObj,RefPoint,Range,K) | ||
% Select part of the solutions in the last front | ||
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N = size(PopObj,1); | ||
NR = size(RefPoint,1); | ||
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%% Calculate the distance between each solution and point | ||
Distance = CalDistance(PopObj-repmat(Range(1,:),N,1),RefPoint); | ||
Convergence = min(Distance,[],2); | ||
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%% 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 |
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PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/EnvironmentalSelection2.m
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function [Population,Fitness] = EnvironmentalSelection2(Population,N) | ||
% The environmental selection of SPEA2 | ||
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||
%------------------------------- 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". | ||
%-------------------------------------------------------------------------- | ||
|
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%% Calculate the fitness of each solution | ||
Fitness = CalFitness(Population.objs,Population.cons); | ||
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%% 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 | ||
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function Del = Truncation(PopObj,K) | ||
% Select part of the solutions by truncation | ||
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%% 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 |
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PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/MatingSelection1.m
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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 | ||
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%% Combine the fitness of feasible solutions with the fitness of infeasible solutions | ||
Fitness = -inf(1,length(Population)); | ||
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%% Binary tournament selection | ||
MatingPool = TournamentSelection(2,length(Population),-Fitness); | ||
end |
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PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/MatingSelection2.m
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function MatingPool = MatingSelection2(Population,Archive,N) | ||
% The mating selection of stage 2 | ||
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%------------------------------- 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". | ||
%-------------------------------------------------------------------------- | ||
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% This function is written by Fei Ming | ||
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Fitness1 = CalFitness(Population.objs,Population.cons); | ||
MatingPool1 = TournamentSelection(2,N,Fitness1); | ||
MatingPool = Population(MatingPool1); | ||
end |
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PlatEMO/Algorithms/Multi-objective optimization/C-TSEA/UpdateArchive.m
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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 | ||
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function Del = Truncation(PopObj,K) | ||
% Select part of the solutions by truncation | ||
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%% 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 |
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