Maxmin approach

Dissimilarity-based compound selection (DECS) methods involve selecting a subset of compounds directly based on pairwise dissimilarities [37]. The first compound is selected, either at random or as the one that is most dissimilar to all others in the database, and is placed in the subset. The subset is then built up stepwise by selecting one compound at a time until it is of the required size. In each iteration, the next compound to be selected is the one that is most dissimilar to those already in the subset, with the dissimilarity normally being computed by the MaxMin approach [38]. Here, each database compound is compared with each compound in the subset and its nearest neighbor is identified the database compound that is selected is the one that has the maximum dissimilarity to its nearest neighbor in the subset. 

The maxmin approach (23c) uses the shortest nearest-neighbor distance as a measure of diversity in the sample ... 

The behaviour of some of these methods is illustrated using a two-dimensional example in Figure 12.30. If the most dissimilar compound is chosen as the first molecule in the maximum-dissimilarity cases then the MaxSum method tends to select compounds at the extremities of the distribution. Hiis is also the initial behaviour of the MaxMin approach, but it then starts to sample from the middle. The sphere exclusion methods typically start somewhere in the middle of the distribution and work outwards. 

This approach is particularly efficient when combined with the Cosine coefficient (69) and was used by Pickett et al. in combination with pharmacophore descriptors (70). In lower dimensional spaces the maxsum measure tends to force selection from the comers of diversity space (6b, 71) and hence maxmin is the preferred function in these cases. A similar conclusion was drawn from a comparison of algorithms for dissimilarity-based compound selection (72). 

For an optimal control problem, the complementary maxmin problem is equivalent to the controller having perfect knowledge of the plant parameters and disturbances, including future disturbances. This formulation could be termed the crystal ball approach to control. For many problems, the crystal ball control will be successful, but this says very little about whether any realizable control system exists that can meet the performance specification. 

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