What Is Direct Search?

Direct search is a method for solving optimization problems that does not require any information about the gradient of the objective function. As opposed to more traditional optimization methods that use information about the gradient or higher derivatives to search for an optimal point, a direct search algorithm searches a set of points around the current point, looking for one where the value of the objective function is lower than the value at the current point. You can use direct search to solve problems for which the objective function is not differentiable, or even continuous. The Genetic Algorithm and Direct Search Toolbox implements a special class of direct search algorithms called pattern search algorithms. A pattern search algorithm computes a sequence of points that get closer and closer to the optimal point. At each step, the algorithm searches a set of points, called a mesh, around the current point -- the point computed at the previous step of the algorithm. The algorithm forms the mesh by adding the current point to a scalar multiple of a fixed set of vectors called a pattern. If the algorithm finds a point in the mesh that improves the objective function at the current point, the new point becomes the current point at the next step of the algorithm.


Pattern Search Terminology

This section explains some standard terminology for pattern search, including
Patterns
Meshes
Polling

Patterns
A pattern is a collection of vectors that the algorithm uses to determine which points to search at each iteration