Stochastic searche

GROWMOL [70] fragment-based, sequential growth, stochastic search ... 

The stored output of a stochastic search, STOCHASTIC.MEM, for the various local minima of n-pentane using Program MM3 is accessed by the following four lines... 

File 5-3 Output From a Stochastic Search of the n-Pentane Molecule in MM3. The input structure was subjected to 50 kicks. ... 

Can y out the same stochastic search over the conformational space of the trails isomer. The result of this search may surprise you at lirst, but there is a simple explanation, wfiich you should include in your report. 

Systematic searches exhaustively sample conformational space by sequentially incrementing the torsional angles of aU of the rotatable bonds in a given molecule. This conceptually simple approach is straightforward to implement, but scales exponentially with respect to the number of rotatable bonds. To control the exponential increase in the number of potential conformers obtained, systematic searches are usually combined with tree-based search techniques taken from computer science. Even the best implementations of systematic searches become impractical beyond several rotatable bonds (typically greater than 10). Stochastic searches are based on probabiHstic theories and are better suited to calculations... 

Stochastic search methods. In all of the optimization methods discussed so far, the algorithm searches the objec-... 

Various search strategies can be used to locate the optimum. Indirect search strategies do not use information on gradients, whereas direct search strategies require this information. These methods always seek to improve the objective function in each step in a search. On the other hand, stochastic search methods, such as simulated annealing and genetic algorithms, allow some deterioration... 

This criterion requires a search through a nonconvex multidimensional conformation space that contains an immense number of minima. Optimization techniques that have been applied to the problem include Monte Carlo methods, simulated annealing, genetic methods, and stochastic search, among others. For reviews of the application of various optimization methods refer to Pardalos et al. (1996), Vasquez et al. (1994), or Schlick et al. (1999). 

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. 

The second problem can be overcome by using a stochastic search. Thus Corana s simulating annealing SA [89], a sophisticated global search method arising from the Metropolis algorithm [90] was employed. A synthetic seven species problem was constructed and the elements in T-jx were correctly determined using SA. The recovered spectra are essentially identical to the synthetic 7 pure component spectra. [91]... 

Scanning of a potential energy surface (see potential energy surface). The methods currently used include random search (stochastic search, e. g., Monte Carlo methods) and molecular dynamics (see deterministic search, Monte Carlo search, stochastic search, molecular dynamics, scanning an energy surface). 

Random search of configurational space followed by calculation of probabilities based on a Boltzmann distribution (see energy surface, conformational search, stochastic search). 

The data are from Ref. 31. The objective for optimization is the maximization of the effluent concentration of component B. The performance limit of the system is identihed with each stochastic run requiring an average of only 120 CPU sec on an HP 9000-C100 workstation. Numerous designs are obtained from the stochastic search that perform close to the performance target, mostly variations of series arrangements of PFRs and CSTRs. A detailed discussion of this and other studies is given in Ref. 31. 

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]. 

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