Stochastic searching procedures

So far, only techniques, starting from some initial point and searching locally for an optimum, have been discussed. However, most optimization problems of interest will have the complication of multiple local optima. Stochastic search procedures (cf Section 4.4.4.1) attempt to overcome this problem. Deterministic approaches have to rely on rigorous sampling techniques for the initial configuration and repeated application of the local search method to reliably provide solutions that are reasonably close to globally optimal solutions. 

Conformational isomers represent minima on an energy surface, and all structures and the corresponding strain energies can be obtained by a careful analysis. This can be performed manually (such as in Sections 17.3 and 17.4) or automatically. An automatic procedure may involve a systematic search (grid search methods), a stochastic search (e.g., torsional Monte Carlo or cartesian stochastic, i.e., the random kick method) or molecular dynamics (see Chapter 5 and Section 16.5). Implemented in MOMEC is a random kick stochastic search module, and this has been shown to lead to excellent results, not only for conformational equilibria, but also for distributions of configurational isomers[37]. 

Comparisons of a variety of methods were made on cycloheptadecane by Saunders et al. (91) and it was concluded that the stochastic method was most efficient. In one of the few independent comparisons of the effectiveness of these procedures, Boehm et al. (122) studied the sampling properties on the model system caprylolactam, a nine-membered ring, and concluded that systematic search was both inefficient and ineffective at finding the minima found by the other methods when the number of conformers examined was limited. 

The various procedures that address side chain generation as an energy-driven conformational search can be grouped as systematic, combinatorial, and stochastic methods. The CONGEN procedure " includes five different tree-based implementations of the first two approaches. The first methods, named ALL, generates all possible conformations by a series of nested iterations over every side chain, and hence is limited to 7 or 8 residues. The second method, named FIRST, uses... 

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