Minimization optimization Genetic algorithm

algorithms/Genetic-Algorithm/Minimization of polynomial function/Crossover.m

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+function [y1, y2] = Crossover(x1,x2)
+    m=randi([1,3]);
+    switch m
+        case 1
+            [y1, y2] = SinglePointCrossover(x1,x2);
+        case 2
+            [y1, y2] = DoublePointCrossover(x1,x2);
+        otherwise
+            [y1, y2] = UniformCrossover(x1,x2);
+    end
+end

algorithms/Genetic-Algorithm/Minimization of polynomial function/DoublePointCrossover.m

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+function [y1,y2] = DoublePointCrossover(x1,x2)
+    nVar = numel(x1);
+
+    q = randperm(nVar);
+    j1 = min(q(1),q(2));
+    j2 = max(q(1),q(2));
+
+    y1 = [x1(1:j1) x2(j1+1:j2) x1(j2+1:end)];
+    y2 = [x2(1:j1) x1(j1+1:j2) x2(j2+1:end)];
+
+end

algorithms/Genetic-Algorithm/Minimization of polynomial function/Mutate.m

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+function y = Mutate(x,mu)
+    flag = rand(size(x)) < mu;
+    y=x;
+    y(flag) = 1-x(flag);
+end

algorithms/Genetic-Algorithm/Minimization of polynomial function/RouletteWheelSelection.m

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+function i = RouletteWheelSelection(p)
+    r= rand*sum(p);
+    c=cumsum(p);
+    i=find(r<=c,1,'first');
+end

algorithms/Genetic-Algorithm/Minimization of polynomial function/Run_GA.m

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+function out = RunGA(problem, params)
+
+    % Problem
+    CostFunction = problem.CostFunction;
+    nVar = problem.nVar;
+
+    % Params
+    MaxIt = params.MaxIt;
+    nPop = params.nPop;
+    beta = params.beta;
+    pC = params.pC;
+    nC = round(pC*nPop/2)*2;
+    mu = params.mu;
+
+    % Template for Empty Individuals
+    empty_individual.Position = [];
+    empty_individual.Cost = [];
+
+    % Best Solution Ever Found
+    bestsol.Cost = inf;
+
+    % Initialization
+    pop = repmat(empty_individual, nPop, 1);
+    for i = 1:nPop
+
+        % Generate Random Solution
+        pop(i).Position = randi([0, 1], 1, nVar);
+
+        % Evaluate Solution
+        pop(i).Cost = CostFunction(pop(i).Position);
+
+        % Compare Solution to Best Solution Ever Found
+        if pop(i).Cost < bestsol.Cost
+            bestsol = pop(i);
+        end
+
+    end
+
+    % Best Cost of Iterations
+    bestcost = nan(MaxIt, 1);
+
+    % Main Loop
+    for it = 1:MaxIt
+
+        % Selection Probabilities
+        c = [pop.Cost];
+        avgc = mean(c);
+        if avgc ~= 0
+            c = c/avgc;
+        end
+        probs = exp(-beta*c);
+
+        % Initialize Offsprings Population
+        popc = repmat(empty_individual, nC/2, 2);
+
+        % Crossover
+        for k = 1:nC/2
+
+            % Select Parents
+            p1 = pop(RouletteWheelSelection(probs));
+            p2 = pop(RouletteWheelSelection(probs));
+
+            % Perform Crossover
+            [popc(k, 1).Position, popc(k, 2).Position] = ...
+                Crossover(p1.Position, p2.Position);
+
+        end
+
+        % Convert popc to Single-Column Matrix
+        popc = popc(:);
+
+        % Mutation
+        for l = 1:nC
+
+            % Perform Mutation
+            popc(l).Position = Mutate(popc(l).Position, mu);
+
+            % Evaluation
+            popc(l).Cost = CostFunction(popc(l).Position);
+
+            % Compare Solution to Best Solution Ever Found
+            if popc(l).Cost < bestsol.Cost
+                bestsol = popc(l);
+            end
+
+        end
+
+        % Merge and Sort Populations
+        pop = SortPopulation([pop; popc]);
+
+        % Remove Extra Individuals
+        pop = pop(1:nPop);
+
+        % Update Best Cost of Iteration
+        bestcost(it) = bestsol.Cost;
+
+        % Display Itertion Information
+        disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(bestcost(it))]);
+
+    end
+
+
+    % Results
+    out.pop = pop;
+    out.bestsol = bestsol;
+    out.bestcost = bestcost;
+
+end

algorithms/Genetic-Algorithm/Minimization of polynomial function/SinglePointCrossover.m

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+function [y1, y2] = SinglePointCrossover(x1,x2)
+    nVar = numel(x1);
+    j = randi([1, nVar-1]);
+    y1 = [x1(1:j) x2(j+1:end)];
+    y2 = [x2(1:j) x1(j+1:end)];
+end

algorithms/Genetic-Algorithm/Minimization of polynomial function/SortPopulation.m

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+function pop =SortPopulation(pop)
+    [~,so] = sort([pop.Cost]);
+        pop = pop(so);
+end

algorithms/Genetic-Algorithm/Minimization of polynomial function/UniformCrossover.m

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+function [y1 , y2] = UniformCrossover(x1,x2)
+    alpha  =randi([0,1], size(x1));
+
+    y1 = alpha.*x1 + (1-alpha).*x2;
+    y2 = alpha.*x2 + (1-alpha).*x1;
+
+end

algorithms/Genetic-Algorithm/Minimization of polynomial function/main.m

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+clc;
+clear;
+close all;
+
+%% Problem Definition
+
+problem.CostFunction = @(x) minone(x);
+problem.nVar = 100;
+
+
+%% GA Parameters
+
+params.MaxIt = 150;
+params.nPop = 100;
+
+params.beta = 1;
+params.pC = 1;
+params.mu = 0.02;
+
+%% Run GA
+
+out = Run_GA(problem, params);
+
+
+%% Results
+
+figure;
+plot(out.bestcost, 'LineWidth', 2);
+xlabel('Iterations');
+ylabel('Best Cost');
+grid on;
+
+
+
+
+

algorithms/Genetic-Algorithm/Minimization of polynomial function/minone.m

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+function z= minone(x)
+    z = sum(x.^2);
+end

algorithms/Genetic-Algorithm/Minimization of polynomial function/readme.txt

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+this is a minimization agorithm for a single variable function using genetic algorithm