Global Optimization Toolbox

Pattern Search Solver

Global Optimization Toolbox contains three direct search algorithms: generalized pattern search (GPS), generating set search (GSS), and mesh adaptive search (MADS). While more traditional optimization algorithms use exact or approximate information about the gradient or higher derivatives to search for an optimal point, these algorithms use a pattern search method that implements a minimal and maximal positive basis pattern. The pattern search method handles optimization problems with nonlinear, linear, and bound constraints, and does not require functions to be differentiable or continuous.

The following table shows the pattern search algorithm options provided by Global Optimization Toolbox. You can change any of the options from the command line or the Optimization Tool.

Pattern Search OptionDescription
Polling methodsDecide how to generate and evaluate the points in a pattern and the maximum number of points generated at each step. You can also control the polling order of the points to improve efficiency.
Search methodsChoose an optional search step that may be more efficient than a poll step. You can perform a search in a pattern or in the entire search space. Global search methods, like the genetic algorithm, can be used to obtain a good starting point.
MeshControl how the pattern changes over iterations and adjusts the mesh for problems that vary in scale across dimensions. You can choose the initial mesh size, mesh refining factor, or mesh contrac­tion factor. The mesh accelerator speeds up convergence when it is near a minimum.
CacheStore points evaluated during optimization of computationally expensive objective functions. You can specify the size and tolerance of the cache that the pattern search algorithm uses and vary the cache tolerance as the algorithm proceeds, improving opti­mization speed and efficiency.
Nonlinear constraint algorithm settingsSpecify a penalty parameter for the nonlinear constraints as well as a penalty update factor.

Using the Optimization Tool (top) to find the peak, or global optima, of the White Mountains (middle and bottom) using pattern search.

Using the Optimization app (top) to find the peak, or global optima, of the White Mountains (middle and bottom) using pattern search.

Next: Simulated Annealing Solver

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