MATLAB Toolbox for Global Fitting/Optimization

This MATLAB toolbox can be used for the following problems:

• finding global minimum of a function
• fitting a function to a dataset

This toolbox is specially adapted to the following problems:

• non-smooth error function
• non-convex error function
• computationally heavy error function
• error function with local minima
• error function with many input variables

This toolbox provides a common interface for different solvers:

• gradient: fminunc / fmincon
• simplex: fminsearch
• surrogate: surrogateopt
• evolutionary: particleswarm / ga
• the aforementioned solvers can be combined

Customized error function:

• custom weights for the dataset points
• choice of the error metric (norm, average, percentile, etc.)
• recover from undefined values
• vectorized evaluation of the error function
• parallel evaluation of the error function
• caching of the error function

Advanced variable handling:

• abstraction layer for the variables
• initial values
• scalar or vector variables
• variable transformation (linear, quadratic, logarithmic, etc.)
• variable normalization
• constraints (lower and upper bounds)
• sine transformation for handling constraints

Advanced monitoring capabilities:

• compute various error metrics
• compute solver figures of merit
• plot/display the solver progress
• plot/display the final results

Limitations

• All the provided features have a computational cost.
• Therefore, this library is mostly adapted to time-consuming error functions.
• For simple error functions, the overhead is non-negligible.

Examples

• run_example_fitting.m - Simple fitting of a model with respect to a dataset.
• run_example_optim.m - Find the global minimum of a function.

Compatibility

• Tested with MATLAB R2021a.
• The gads_toolbox is required (for the MATLAB solvers).
• The optimization_toolbox is required (for the MATLAB solvers).
• The distrib_computing_toolbox is required (for parfor loops)
• Compatibility with GNU Octave not tested but probably problematic.

Author

Thomas Guillod - GitHub Profile

License

This project is licensed under the BSD License, see LICENSE.md.