Any ways for 2D surface fit with particle swarm optimization?

https://kr.mathworks.com/help/curvefit/fit.html?lang=en

From webpage above, I found that it is possible to 2D surface fit with local optimization solver.

Is it also possible with global optimization solver such as particle swarm optimization?

Answer 1

[Aditya]

Hi Yunhyeok,

I understand that you are trying to use particle swarm optimisation(PSO).

The fit function itself does not directly support global optimization solvers like Particle Swarm Optimization (PSO), you can use MATLAB's Global Optimization Toolbox to implement a global optimization approach for fitting problems. The Global Optimization Toolbox provides functions such as particleswarm for solving optimization problems using PSO.

To perform a 2D surface fit using PSO, you would need to define the surface fitting problem as an optimization problem where the objective function calculates the error between the surface defined by your model's parameters and the actual data points. Then, you would use the particleswarm function to find the parameters that minimize this error.

Here's a simplified example of how you might set this up:

% Define your data points (xData, yData, zData)
xData = ...; % x-coordinates
yData = ...; % y-coordinates
zData = ...; % z-values

% Define your model function (e.g., a polynomial)
modelFunc = @(params, x, y) params(1) + params(2)*x + params(3)*y + params(4)*x.*y;

% Define the objective function
objectiveFunc = @(params) sum((modelFunc(params, xData, yData) - zData).^2);

% Define the number of parameters in your model
numParams = 4; % For example, a linear model a + bx + cy + dxy

% Set the options for particleswarm (optional)
options = optimoptions('particleswarm', 'Display', 'iter', 'SwarmSize', 50);

% Run the Particle Swarm Optimization
[bestParams, bestError] = particleswarm(objectiveFunc, numParams, [], [], options);

% Use bestParams to evaluate your fitted model
fittedSurface = modelFunc(bestParams, xData, yData);

Hope this helps.