Empirical rule-based algorithm

Note that so-called heuristics does not mean necessarily empirical-based rules. Most heuristics are the results of fundamental studies or extensive computer simulation, but may be formulated rather as simple decisional rules than by means of mathematical algorithms. 

Overall, it seems electronegativity may be used in modeling compactness of atoms-in-molecules aromaticity - basically without counting on the exchange or correlation effects, or at best within the HF algorithm, while semi-empirical methods seems not well adequate. Yet, for all aromaticity rules formulated, there exists at least one quantum computational environment for which the electronegativity based compactness aromaticity is in agree with each of them. 

The use of soft rules to estimate ideal solvent blend composition and the empirical Casteel-Amis-equation can be helpful to reduce the number of measurements [433]. Another more general approach is the use of the well-established simplex algorithm, which is applied in optimization of technical and economic processes. The most important advantage is that no theoretical assumption has to be made because it is based only on a simple geometric approach (the relation of the control variables to the response variables is unimportant). A second advantage is its efficiency, when many control variables have to be scanned. 

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