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Author: puneet-pr-arya

algorithms/Particle_Swarm_Optimization/Polynomial Minimization/Parabola.m

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

algorithms/Particle_Swarm_Optimization/Polynomial Minimization/code.m

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+clc;
+clear;
+close all;
+
+%% Problem Definition
+
+
+CostFunction=@(x) Parabola(x);   % Cost Function
+
+nVar = 5;           % 5 dimensional-Number of unknown (Decision Variables)
+
+VarSize = [1 nVar]; % Matrix size of Decision Variables
+
+VarMin = -10;       % Lower bound of Decision Variables
+VarMax =  10;       % Upper bound of Decision Variables
+
+
+%% Parameters of PSO
+
+MaxIt = 1000; % Maximum Numbers of Iterations
+
+nPop = 50;   % Population size (Swarm Size)
+
+w = 1;        % Inertia Coefficient
+wdamp=0.99;     % Damping Ratio of intertia weight
+c1 = 2;       % Personal Acceleration Coefficient
+c2  = 2;      % Social Acceleration Coefficient
+
+
+
+%% Initialization
+
+% The Particle Template
+empty_particle.Position = [];      % position of particle
+empty_particle.Velocity = [];      % velocity of particle
+empty_particle.Cost = [];          % own measurement of particle(cost value)
+empty_particle.Best.Position = []; % personal best with its position
+empty_particle.Best.Cost = [];     % personal best with its cost value
+
+
+particle = repmat(empty_particle, nPop,1); % Create random Population Array
+
+%Initialization Global best
+GlobalBest.Cost=inf; % for minization fun. its infinity before 1st iteration
+
+% Initialize Population Members
+
+    for i=1:nPop
+    
+    % Generate Random Solutions
+    particle(i).Position=unifrnd(VarMin,VarMax,VarSize);
+    
+    % Initialize Velocity
+    particle(i).Velocity=zeros(VarSize); %matrix with all o of varsize
+    
+     % Evaluation at above particle i position
+    particle(i).Cost=CostFunction(particle(i).Position);
+    
+    % Update Personal Best value
+    particle(i).Best.Position=particle(i).Position;
+    particle(i).Best.Cost=particle(i).Cost;
+    
+    % Update Global Best
+    if particle(i).Best.Cost<GlobalBest.Cost
+        
+        GlobalBest=particle(i).Best;
+        
+    end
+    end
+    % Array to hold best cost value on each iteration
+    BestCost=zeros(MaxIt,1);
+    
+    %% Main Loop of PSO
+    for it=1:MaxIt % first iter to last iteration
+    
+      for i=1:nPop % for every particle thisloop is required
+        
+        % Update Velocity    %element wise multiplication is there
+        particle(i).Velocity = w*particle(i).Velocity ...
+            +c1*rand(VarSize).*(particle(i).Best.Position-particle(i).Position) ...
+            +c2*rand(VarSize).*(GlobalBest.Position-particle(i).Position);
+        
+         %Update Position
+        particle(i).Position = particle(i).Position + particle(i).Velocity;
+        
+         % Evaluation
+        particle(i).Cost = CostFunction(particle(i).Position);
+        
+        % Update Personal Best
+        if particle(i).Cost<particle(i).Best.Cost
+            
+            particle(i).Best.Position=particle(i).Position; %best updated with current
+            particle(i).Best.Cost=particle(i).Cost;
+            
+            % Update Global Best
+            if particle(i).Best.Cost<GlobalBest.Cost
+                
+                GlobalBest=particle(i).Best;
+                
+            end
+            
+            
+        end
+        
+      end
+       % store the Best cost value
+    BestCost(it)=GlobalBest.Cost;
+     
+    % Display iteration info.
+    disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestCost(it))]);
+    
+     %Damping Intertia coefficient
+    w=w*wdamp; 
+    end
+    
+    %% Results
+    
+    % Graph converges to origin
+figure;
+%plot(BestCost,'LineWidth',2); % for normal graph
+semilogy(BestCost,'LineWidth',2); %for exponential graph
+xlabel('Iteration');
+ylabel('Best Cost');
+grid on;
+
+        
+        
+        
+        
+