Uniform mapping algorithms

Another possibility to deal with irregularly shaped experimental domains is to use so-called uniform mapping algorithms such as the algorithm of Kennard and Stone. They have the advantage that the number of experiments can be sequentially increased. It ensures that the experiments cover the space as uniformly as possible and that they are situated as far as possible from each other. It consists of maximizing the minimal distance between a newly selected point and those previously selected. The distance is the Euclidean distance, given by... 

FIGURE 2.11. Selected experimental points by the uniform mapping algorithm of Kennard and Stone (a) without requirements and (b) with the requirement that the center point was the first selected point. 

We thus advocate a more disciplined approach to algorithm synthesis rather than use a uniform method for instantiating all variables of a given schema (possibly without any awareness of such a schema), one should deploy for each variable the best-suited method. We thus propose to view research on program synthesis as (1) the search for adequate schemas (2) the development of useful methods of predicate-variable instantiation and (3) the discovery of interesting mappings between these methods and the variables of these schemas. 

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