AGEA

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

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+classdef AGEA < ALGORITHM
+% <multi> <real/binary/permutation>
+% Adaptive grid based evolutionary algorithm
+% limit --- 1 --- limit output solutions number to N (1. limit  0. no limit)
+% div --- 10 --- initial number of grid divisions
+
+%------------------------------- Reference --------------------------------
+% Z. Liu, F. Han, Q. Ling, H. Han, J. Jiang, and Q. Liu, A multi-objective
+% evolutionary algorithm based on a grid with adaptive divisions for
+% multi-objective optimization with irregular Pareto fronts, Applied Soft 
+% Computing, 2025, 176: 113106.
+%------------------------------- 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 is written by Zhe Liu
+
+    methods
+        function main(Algorithm,Problem)
+            %% Parameter setting
+            [limit, div]= Algorithm.ParameterSet(1, 10);
+            %% Generate random population
+            Population = Problem.Initialization(); 
+            Grid   = Population;  
+            zmin = min(Population.objs,[],1);
+            zmax = max(max(Population.objs, [], 1), zmin + 1e-10);
+            gmax = zmax;            
+            while Algorithm.NotTerminated(Grid)
+            %% Optimization
+                MatingPool = randperm(length(Population));
+                Offspring = OperatorGA(Problem, Population(MatingPool));
+                Population = [Grid, Offspring];
+                [FrontNo, ~] = NDSort(roundn(Population.objs, -10), Problem.N);              
+                Grid = Population(FrontNo ~= inf);
+                NDPop = Population(FrontNo == 1);
+                zmin = min(zmin, min(Grid.objs,[],1));
+                gmax = GridStabilization(NDPop, zmin, gmax, div);               
+                [Grid, GridIndex, div] = GridAdaptiveAdjustment(Grid, zmin, gmax, div, Problem.N);              
+                Population = PopulationReselection(Grid, GridIndex, Problem.N);                                    
+              %% limit output solutions number to N
+                if limit ~= 0 && length(Grid) > Problem.N
+                    if Problem.FE >= Problem.maxFE
+                        Grid = EnvironmentalSelection_SPEA2(Grid, Problem.N);
+                    end
+                end
+            end
+        end
+    end
+end
+
+

PlatEMO/Algorithms/Multi-objective optimization/AGEA/EnvironmentalSelection_AGEA.m

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+function [Grid, GridIndex] = EnvironmentalSelection_AGEA(Grid, zmin, gmax, div)
+PopObj = Grid.objs;
+[N, M] = size(PopObj);
+GridIndex = zeros(N, M);
+GridCorner = zeros(N, M);
+delta = ones(N, M);    % The blow-up factor
+side_length    = (gmax - zmin) / (div - 1);
+lower_boundary    = zmin - 0.5 * side_length;
+for i = 1: N
+    for j = 1: M
+        GridIndex(i, j) = floor((PopObj(i, j) - lower_boundary(j)) / side_length(j));
+        GridCorner(i, j) = lower_boundary(j) + side_length(j) *  GridIndex(i, j);
+        if GridIndex(i, j) == 0
+            delta(i, j) = 1e+6;
+        end
+    end
+end    
+normalized_obj = (PopObj - zmin) ./ (gmax - zmin);
+normalized_GridCorner = (GridCorner - zmin) ./ (gmax - zmin);
+Loser = false(N, 1);
+fitness = sum(((normalized_obj - normalized_GridCorner) .* delta) .^ 2, 2);
+for i = 1: N - 1
+    for j = i + 1: N
+        if GridIndex(i,:) == GridIndex(j,:)
+            if fitness(i) <= fitness(j)
+                Loser(j) = true;
+            else
+                Loser(i) = true;
+            end
+        end
+    end
+end
+Grid = Grid(~Loser);
+GridIndex = GridIndex(~Loser, :);
+end

PlatEMO/Algorithms/Multi-objective optimization/AGEA/EnvironmentalSelection_SPEA2.m

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+function Archive = EnvironmentalSelection_SPEA2(Archive, N)
+    ArchiveObj = Archive.objs;
+    [ArchiveSize, ~] = size(Archive.objs);
+    ideal_point      = min(ArchiveObj,[],1);
+    worst_point      = max(ArchiveObj,[],1);   
+    nf               = worst_point - ideal_point;
+    nf(nf < 1e-100)  = 1e-100;
+    normalized_obj   = ArchiveObj ./ nf;  
+    Distance         = pdist2(normalized_obj, normalized_obj);
+    Distance(logical(eye(length(Distance)))) = inf;
+    Del = false(1,ArchiveSize);
+    while sum(Del) < ArchiveSize - N
+        Remain   = find(~Del);
+        Temp     = sort(Distance(Remain,Remain),2);
+        [~,Rank] = sortrows(Temp);
+        Del(Remain(Rank(1))) = true;
+    end
+    Archive = Archive(~Del);
+end

PlatEMO/Algorithms/Multi-objective optimization/AGEA/GridAdaptiveAdjustment.m

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+function [Grid, Grid_index, div] = GridAdaptiveAdjustment(Grid, zmin, gmax, div, N) 
+    [Grid, Grid_index] = EnvironmentalSelection_AGEA(Grid, zmin, gmax, div); 
+    if length(Grid) > N && div > 2
+        div = div - 1;
+        [Grid_temp, Grid_index_temp] = EnvironmentalSelection_AGEA(Grid, zmin, gmax, div);
+        if length(Grid_temp) > N  && div >= 2
+            Grid = Grid_temp;
+            Grid_index = Grid_index_temp;
+        else
+            div = div + 1;
+        end
+    end
+    if length(Grid) < N && div < 200
+        div = div + 1;
+    end
+end

PlatEMO/Algorithms/Multi-objective optimization/AGEA/GridStabilization.m

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+function gmax = GridStabilization(NDPop, zmin, gmax, div)
+    [~, M] = size(NDPop.objs);
+    zmax = max(max(NDPop.objs, [], 1), zmin + 1e-10);
+    side_length = (gmax - zmin) / (div - 1);
+    for i = 1: M
+        if abs(zmax(i) - gmax(i)) > 0.5*side_length(i)
+            gmax(i) = zmax(i);
+        end
+    end       
+end

PlatEMO/Algorithms/Multi-objective optimization/AGEA/PopulationReselection.m

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+function Population = PopulationReselection(Grid, GridIndex, N)
+    [FrontNo, ~] = NDSort(roundn(Grid.objs, -10), N);
+    [~, M] = size(Grid.objs);
+    D = pdist2(GridIndex, GridIndex, 'chebychev');
+    D(D>1) = 0;
+    crowding = sum(D, 2).^(1/M);
+    fitness = crowding / max(max(crowding), 1e-10) * (N-1) + 1;
+    fitness(FrontNo > 1) = fitness(FrontNo > 1) + max(fitness);
+    Population = Grid(RouletteWheelSelection(N, fitness));   
+end