Global Optimization Toolbox
Product Description
- Key Features
- Defining, Solving, and Assessing Optimization Problems
- Global Search and Multistart Solvers
- Genetic Algorithm Solver
- Multiobjective Genetic Algorithm Solver
- Pattern Search Solver
- Simulated Annealing Solver
- Solving Optimization Problems Using Parallel Computing
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 Option | Description |
|---|---|
| Polling methods | Decide 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 methods | Choose 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. |
| Mesh | Control 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. |
| Cache | Store 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 settings | Specify 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.
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