MCS algorithm
Encyclopedia
Multilevel Coordinate Search (MSC) is an algorithm
for bound constrained global optimization
using function
values only.
To do so, the n-dimensional search space
is represented by a set of non-intersecting hypercubes (boxes). The boxes are then iteratively split along an axis plane according to the value of the function at a representative point of the box and the box's size. These two splitting criteria combine to form a global search by splitting large boxes and a local search by splitting areas for which the function value is good.
Additionally a local search combining a quadratic interpolant of the function and line searches can be used to augment performance of the algorithm.
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
for bound constrained global optimization
Global optimization
Global optimization is a branch of applied mathematics and numerical analysis that deals with the optimization of a function or a set of functions to some criteria.- General :The most common form is the minimization of one real-valued function...
using function
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
values only.
To do so, the n-dimensional search space
Search space
Search space may refer to one of the following.*In optimization, the domain of the function to be optimized*In search algorithms of computer science, the set of all possible solutions...
is represented by a set of non-intersecting hypercubes (boxes). The boxes are then iteratively split along an axis plane according to the value of the function at a representative point of the box and the box's size. These two splitting criteria combine to form a global search by splitting large boxes and a local search by splitting areas for which the function value is good.
Additionally a local search combining a quadratic interpolant of the function and line searches can be used to augment performance of the algorithm.