Search Methods
       Global-Local
                Multistart
                Clustering Methods

These methods are estimating the global minimum by finding local minima. The starting point is Multistart. When applied Multistart will several times end up in the same local minimum. Clustering is normally used to avoid this.

In the first clustering method presented a sample of uniformly distributed points in A is determined. The following steps are performed until some stopping condition is fulfilled [Törn 1972]:

1. The point are concentrated to some local minima by either leaving out points like in the Mode-Seeking algorithm or by performing some steps of a local minimization algorithm.

2. The clusters are identified by using some cluster analysis technique.

3. Retain every m'th point in each cluster and go to step 1.

Finally minima were determined by starting a local minimization algorithm from the best point in each cluster.

Preliminary experiments with the two techniques to concentrate the points to local minima led to the decision to use local minimization steps to concentrate points.

Several modifications of the original method has been developed by many authors. A modification where the cluster center is directly identified without any clustering technique (Topographical Global Optimization) has been developed and applied. [Törn and Viitanen 1994, Ali and Storey 1994].