Optimization algorithms and methods
MCS algorithm
For mathematical optimization, Multilevel Coordinate Search (MCS) is an efficient 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 its neighbours) 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 (multi-dimensional) quadratic interpolant of the function and line searches can be used to augment performance of the algorithm (MCS with local search); in this case the plain MCS is used to provide the starting (initial) points. The information provided by local searches (local minima of the objective function) is then fed back to the optimizer and affects the splitting criteria, resulting in reduced sample clustering around local minima, faster convergence and higher precision. (Wikipedia).
