Search Methods
       Global
                Random Search
                Mode-Seeking

In Random Search points are just sampled uniformly in A and the best point found is given as an estimate of the global minimum. This algorithm is seldom used on its own but mostly as part of a more sophisticated algorithm.

Mode-Seeking is the first global optimization method using clustering [Becker and Lago 1970]. Only uniform sampling is used and no local optimization is applied. Instead the algorithm aims at partitioning the region into subregions containing a single minimum. A similar idea is presented in [Tsuda and Kiyono 1964].

A is covered by a uniform sample of points. Then the best p % (eg. p=0.1) are retained. These are expected to cluster around some or the best minima in A.

The clusters are recognized by using some clustering technique and rated based on their best point.

In each of highest rated clusters (eg. the 3 best) the points defines a subregion of A (a box) for which the same procedure is applied. Possibly a third iteration is made.

For the problems considered the global minimum value was zero so it was possible to evaluate the goodness of the solution.