# Global Optimization Toolbox

## Solve multiple maxima, multiple minima, and nonsmooth optimization problems

### Define and Solve Optimization Problems

Define your optimization problem, apply a solver, and set options for algorithm behavior, tolerances, stopping criteria, visualizations, and customizations.

### GlobalSearch and MultiStart

Apply gradient-based solvers to find local minima from multiple starting points in search of global minima. Other local or global minima are returned. Solve unconstrained and constrained problems that are smooth.

### Surrogate Optimization

Search for global minima on problems with time-consuming objective functions, which can be nonsmooth. The solver builds an approximation to the function that can be quickly evaluated and minimized.

### Pattern Search

Start from the current point and add a set of vectors to get new trial points. Evaluate the objective function on the trial points and use that information to update the current point. Repeat until the current point is an optimum.

### Genetic Algorithm

Search for global minima by mimicking the principles of biological evolution, repeatedly modifying a population of individual points using rules modeled on gene combinations in biological reproduction.

### Particle Swarm

Search for global minima using an algorithm inspired by the behavior of insects swarming. Each particle moves with a velocity and direction influenced by the best location it has found so far and the best location the swarm has found.

### Simulated Annealing

Search for global minima with a probabilistic search algorithm that mimics the physical process of annealing, in which a material is heated and then the temperature is slowly lowered to decrease defects, thus minimizing the system energy.

### Multiobjective Optimization

Identify the Pareto front—the set of nondominated solutions—for problems with multiple objectives and bound, linear, or nonlinear constraints. Use either the pattern search or genetic algorithm solvers.

#### Product Resources:

"I...applied a pattern search algorithm in Global Optimization Toolbox to optimize for factors such as throughput, required production equipment, manpower, and waste. It would take thousands of experiments to assess all possible model variants. I could achieve the same results with a fraction of this number using the pattern search algorithm."

Marius Gemeinhardt, Daimler AG

## Get a Free Trial

30 days of exploration at your fingertips.