It looks like the error you are encountering is related to matrix operations in your PSO function. Specifically, the “^” operator in MATLAB is used for matrix exponentiation, and it requires the matrix to be square if used for non-elementwise operations. In your case, you need element-wise operations because “x” and “y” are scalars, but MATLAB interprets them as vectors or matrices when you use the “^” operator.
To resolve this issue, you should use element-wise operators for power and multiplication. Here’s some corrections I’ve made in your code:
- PSO function : I’ve used “.*” operation instead of “*” operation for element-wiser operations.
function z = PSO(x, y)
z = (4 - 2.1 * x.^2 + (x.^4) / 3) .* x.^2 + x .* y + (-4 + 4 * y.^2) .* y.^2;
end
I have also made corrections to other sections of your code, which I have detailed below:
- “nvar” and “VarSize”: You have defined “nvar” as 2, but you are using “nVar” (with an uppercase “V”) in “VarSize”. It is important to maintain consistency in variable names.
Correct “VarSize” initialization to use the correct variable name:
nVar = 2; % Number of Decision Variables
VarSize = [1 nVar]; % Matrix Size of Decision Variables
2. Undefined variables: I have utilized some placeholder values for these variables to ensure code executes correctly.
MinVelocity = -0.1; % Example value for minimum velocity
MaxVelocity = 0.1; % Example value for maximum velocity
ShowIterInfo = true; % Set to true if you want to display iteration information
params.wdamp = 0.99; % Example damping ratio
Here’s the corrected code:
function z = PSO(x, y)
z = (4 - 2.1 * x.^2 + (x.^4) / 3) .* x.^2 + x .* y + (-4 + 4 * y.^2) .* y.^2;
end
clc;
clear;
close all;
% Problem
CostFunction = @(x, y) PSO(x, y);
nVar = 2; % Number of Decision Variables
VarSize = [1 nVar]; % Matrix Size of Decision Variables
VarMin = -10; % Lower Bound of Decision Variables
VarMax = 10;
% Parameters
MaxIt = 50;
nPop = 25; % Population Size (Swarm Size)
w = 1; % Inertia Coefficient
wdamp = 0.99; % Damping Ratio of Inertia Coefficient
c1 = 2; % Personal Acceleration Coefficient
c2 = 2; % Global Acceleration Coefficient
% Initialization
empty_particle.Position = [];
empty_particle.Velocity = [];
empty_particle.Cost = [];
empty_particle.Best.Position = [];
empty_particle.Best.Cost = [];
% Create Population Array
particle = repmat(empty_particle, nPop, 1);
% Initialize Global Best
GlobalBest.Cost = inf;
% Initialize Population Members
for i = 1:nPop
% Generate Random Solution
particle(i).Position = unifrnd(VarMin, VarMax, VarSize);
% Initialize Velocity
particle(i).Velocity = zeros(VarSize);
% Evaluation
particle(i).Cost = CostFunction(particle(i).Position(1), particle(i).Position(2));
% Update the Personal Best
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
BestCosts = zeros(MaxIt, 1);
% Main Loop
for it = 1:MaxIt
for i = 1:nPop
% Update Velocity
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);
% Apply Velocity Limits
particle(i).Velocity = max(particle(i).Velocity, -0.1);
particle(i).Velocity = min(particle(i).Velocity, 0.1);
% Update Position
particle(i).Position = particle(i).Position + particle(i).Velocity;
% Apply Lower and Upper Bound Limits
particle(i).Position = max(particle(i).Position, VarMin);
particle(i).Position = min(particle(i).Position, VarMax);
% Evaluation
particle(i).Cost = CostFunction(particle(i).Position(1), particle(i).Position(2));
% Update Personal Best
if particle(i).Cost < particle(i).Best.Cost
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
end
% Store the Best Cost Value
BestCosts(it) = GlobalBest.Cost;
% Display Iteration Information
if ShowIterInfo
disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestCosts(it))]);
end
% Damping Inertia Coefficient
w = w * wdamp;
end
out.pop = particle;
out.BestSol = GlobalBest;
out.BestCosts = BestCosts;
For futher information, you can refer to the following documentation:
MATLAB operations and special characters: https://in.mathworks.com/help/matlab/matlab_prog/matlab-operators-and-special-characters.html#bvg3oy_-2
If you encounter any further issues, please feel free to leave a comment below.
Hope it helps!
