Explosion combinatorial

The basic scheme of this algorithm is similar to cell-to-cell mapping techniques [14] but differs substantially In one important aspect If applied to larger problems, a direct cell-to-cell approach quickly leads to tremendous computational effort. Only a proper exploitation of the multi-level structure of the subdivision algorithm (also for the eigenvalue problem) may allow for application to molecules of real chemical interest. But even this more sophisticated approach suffers from combinatorial explosion already for moderate size molecules. In a next stage of development [19] this restriction will be circumvented using certain hybrid Monte-Carlo methods. 

To identify this set of final feasible solutions, X e 1, with low scores, we developed a greedy search procedure, S (Saraiva and Stephanopoulos, 1992c), that has resulted, within an acceptable computation time, in almost-optimal solutions for all the cases studied so far, while avoiding the combinatorial explosion with the number of (x, y) pairs of an exhaustive enumeration/evaluation of all feasible alternatives. The algorithm starts by partitioning the decision space into a number of isovolu-... 

Only one stereotype can be attached to an element. UML permits a stereotype to be defined as a combination of several others. This arrangement causes problems with combinatorial explosion as well as lack of semantics. 

In this case, systematic methods for generation of feasible molecular and mixture candidates have been reported for the design of functional chemical products [see Achenie et al (2003)]. Methods based on database search, total enumeration of feasible candidates (rule-based techniques that avoid a combinatorial explosion), mathematical programming, genetic algorithm, and,... 

By default, Permute would generate all possible combinations of protonation states at all of these functional groups when contained in a molecule. A number of additional rules are used to prevent unreasonable combinations and combinatorial explosion ... 

This covers the most common tautomer pairs including, for example, imidazole and tetrazole. No other tautomerism is considered, for example, keto-enol. Two additional rules prevent combinatorial explosion ... 

It is obvious that the simultaneous inclusion of all possible reactor-reactive separation-separator design options into an automated design framework quickly leads to combinatorial explosion. In combination with the nonlinear models used to describe the reaction, mass, and heat transfer phenomena that occur in the processing units, the resulting synthesis problem is beyond the scope of existing optimization technology, even for relatively small problems. This has led to the... 

Burello, E., Farrusseng, D. and Rothenberg, G. (2004) Combinatorial explosion in homogeneous catalysis screening 60 000 cross-coupling reactions. Adv. Synth. Catal., 346, 1844. 

Leland, B.A., Christie, B.D., Nourse, J.G., Grier, D.L. and Smith, D.H., Managing the combinatorial explosion, presented at the 4th International Conference on Chemical Structures, Noordwijkerhout, The Netherlands, 2-6 June 1996. 

The set of all transformed reaction centres is generated by a straightforward implementation of the usual combinatorial algorithm (cf. Sect. 4.2.3), and the transformed reaction centers are checked to fulfill several restrictive conditions which allow one to suppress the possibility of combinatorial explosion at the very beginning of the SPS generation. The generation of transformed reaction centers is very fast (it usually takes no more then 10-15% of the overall execution time when the reaction center has no more then 4 atoms in a molecule with more then 10-15 atoms). Only non-isomorphic transformed reaction centers are processed by the second step. 

In principle, it is possible to use the GENFIS algorithm for the generation of the SPS of any synthon. In practice, as was explained in the preceeding sections, this must lead to a combinatorial explosion for all but trivial tasks. The stabilization permits us to generate directly the synthetic precursors/successors of any given synthon. The STAB(S(A), S(4), Jf) is used to find all stabilizations S (A) e JT of synthon S(2f) with respect to S(T) (X c A) ... 

Now comes the "combinatorial explosion" for finding all allowed aromatic systems with a re-electron sextet. Just for discussing Yg hetarenes with one ring composed of five carbon atoms and one atom different from carbon, a whole chapter was written that discussed thousands of molecules (09MI2). 

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