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GlobalSearch-rs

Comparison with MATLAB

MATLAB provides a function called GlobalSearch. This function is part of the Global Optimization Toolbox and is used to solve global optimization problems 1. The GlobalSearch algorithm is similar to the algorithm used in globalsearch-rs. However, there are some key differences between the two algorithms.

Local solvers

MATLAB uses the fmincon function to solve the local optimization problems. The fmincon function is a constrained nonlinear programming solver that finds the minimum of a multivariable function. This function supports using five different algorithms to solve the optimization problem 2:

  • interior-point (default)
  • trust-region-reflective
  • sqp
  • sqp-legacy
  • active-set

However, globalsearch-rs uses the cobyla and the argmin crate to solve the local optimization problems.

COBYLA is the only algorithm that supports constraints and bounds, while the other algorithms are unconstrained.

However, we also provide support for the unconstrained nonlinear programming solvers from the argmin crate to solve the local optimization problems. We currently support the following local solvers:

  • COBYLA (default)
  • LBFGS
  • NelderMead
  • SteepestDescent
  • TrustRegion
  • NewtonCG

Support for more constrained solvers is planned when the argmin crate supports it. See argmin’s issue #137 for more information.

Since unconstrained solvers can return solutions outside of variables bounds, we provide a function exclude_out_of_bounds to filter solutions out of bounds.

Evaluation of the reference set

In MATLAB’s GlobalSearch, the reference set contains NumTrialPoints points. However, the number of evaluations of the objective function is limited to NumStageOnePoints.

In globalsearch-rs, the reference set contains population_size points, and we evaluate the objective function for all points in the reference set.

Variable bounds

In MATLAB’s GlobalSearch, the variable bounds are specified using the lb and ub parameters. However, unbounded components have artificial bounds imposed, where lb = -1e4 + 1 and ub = 1e4 + 1 3.

In globalsearch-rs, the variable bounds are specified using the variable_bounds argument. The bounds are specified as an Array2 of f64, where each row contains the lower and upper bounds of each variable. Not specifying bounds for a variable is not supported, so the user must specify bounds for all the variables. This is to ensure that the user is aware of the bounds of the variables and selects them appropriately.

Additional features

globalsearch-rs provides additional features, including checkpointing and parallel execution. For more information, see the feature flags documentation.

Checkpointing is not available in the Python bindings.

References

Footnotes

  1. GlobalSearch. The MathWorks, Inc. Available at: https://www.mathworks.com/help/gads/globalsearch.html (Accessed: 27 January 2025) ↩

  2. Choosing the Algorithm, fmincon Algorithms. The MathWorks, Inc. Available at: https://www.mathworks.com/help/optim/ug/choosing-the-algorithm.html (Accessed: 18 March 2025) ↩

  3. How GlobalSearch and MultiStart Work. The MathWorks, Inc. Available at: https://www.mathworks.com/help/gads/how-globalsearch-and-multistart-work.html (Accessed: 15 February 2025) ↩