Global or Multiple Starting Point Search

Multiple starting point solvers for gradient-based optimization, constrained or unconstrained

These solvers apply to problems with smooth objective functions and constraints. They run Optimization Toolbox™ solvers repeatedly to try to locate a global solution or multiple local solutions.

Functions

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Problem-Based Solution

`optimvalues`	Create values for optimization problem
`solve`	Solve optimization problem or equation problem

Solver-Based Solution

`createOptimProblem`	Create optimization problem structure
`list`	List start points
`run`	Run multiple-start solver

Objects

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Solvers

`GlobalSearch`	Find global minimum
`MultiStart`	Find multiple local minima

Supporting Objects

`CustomStartPointSet`	Custom start points
`GlobalOptimSolution`	Optimization solution
`RandomStartPointSet`	Random start points

Topics

Problem-Based Multiple Start

Minimize Nonlinear Function Using Multiple-Start Solver, Problem-Based
Find a better solution to a nonlinear problem using a multiple-start solver.
Specify Start Points for MultiStart, Problem-Based
Specify start points for MultiStart in the problem-based approach.
Find Multiple Local Solutions Using MultiStart or GlobalSearch, Problem-Based
Use the local field of the output structure to examine the points where GlobalSearch and MultiStart start.
MultiStart with lsqnonlin, Problem-Based
Fit a function to data using MultiStart and lsqnonlin.

GlobalSearch and MultiStart Optimization Basics

Find Global or Multiple Local Minima
Example showing that GlobalSearch returns fewer solutions than MultiStart, often with higher quality.
Maximizing Monochromatic Polarized Light Interference Patterns Using GlobalSearch and MultiStart
Find a global minimum in a problem having multiple local minima.
Optimize Using Only Feasible Start Points
Example showing how to avoid starting from infeasible points.
MultiStart Using lsqcurvefit or lsqnonlin
Shows how to use MultiStart to help find a global minimum to a least-squares problem.

Optimization Workflow

Workflow for GlobalSearch and MultiStart
How to set up and run the solvers.
Create Problem Structure
Provides detailed steps for creating a problem structure.
Create Solver Object
Describes what a solver object is, and how to set its properties.
Set Start Points for MultiStart
Provides details on the ways to set the start points.
Run the Solver
Provides basic examples of the complete workflow for both GlobalSearch and MultiStart.

Techniques for Effective Search

Parallel MultiStart
Shows how to compute in parallel for faster searches.
Isolated Global Minimum
An extended example showing ways to search for a global minimum.
Refine Start Points
Examples of how to search your space effectively and efficiently.
Change Options
Considerations in setting local solver options and global solver properties.
Reproduce Results
How to set random seeds to reproduce results.

Examine Results

Iterative Display
Describes the two types of iterative display for monitoring solver progress.
Global Output Structures
Describes the types of output structures that GlobalSearch and MultiStart can return.
Visualize the Basins of Attraction
Example showing how to plot multiple initial and final points in a 2-D problem.
Output Functions for GlobalSearch and MultiStart
Provides details and an example of monitoring and halting solvers by using output functions.
Plot Functions for GlobalSearch and MultiStart
How to use both built-in and custom plot functions for monitoring solution progress.

Multiple Start Solver Background

Problems That GlobalSearch and MultiStart Can Solve
GlobalSearch and MultiStart apply to smooth problems where there are multiple local solutions.
How GlobalSearch and MultiStart Work
Describes the solver algorithms.
Single Solution
Describes the first four outputs, usually called x, fval, exitflag, and output, from both GlobalSearch and MultiStart.
Multiple Solutions
Describes how to obtain multiple solutions from GlobalSearch and MultiStart, and how to change the definition of distinct solutions.
GlobalSearch and MultiStart Properties (Options)
Describes properties of GlobalSearch and MultiStart objects.