Aimo Törn: Global Optimization


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Elements of Global Optimization Methods

All methods will evaluate the function f(x) in some points x1,...,xN in A, and they differ only in their choice of these points.

Strategies in choosing points.

Because we do not have any information about where in A to find the global minimum, one strategy that must be used is to spread out some of the points to cover A. We call any realization of this strategy a global technique. A possible global technique is uniform sampling. Any serious GO method must use some global technique.

Given a point x it is normally possible to find a nearby point with a smaller function value. We call any technique realizing this a local technique. A possible local technique is local optimization. Any serious GO method will use local optimization, at least to improve upon the estimates of the global minimum found.

A special local technique is to adapt the probes in the global technique so that more effort is put on sampling in regions where relatively small function values are found. We call this technique adaption. Adaption can range from no adaption, i.e., global technique, to extreme adaption, i.e., local technique. A GO method can be based exclusively on successive adaption.