Random search method

A random search is, in many ways, the antithesis of a systematic search A systematic search explores the energy surface of the molecule in a predictable fashion, whereas it is not 

The Cartesian and dihedral versions of the random search differ in the way in which each new structure is generated. The Cartesian method adds a random amount to the x, y and z coordinates of all the atoms in the molecule [Saunders 1987 Ferguson and Raber 1989] 

In a systematic search there is a defined endpoint to the procedure, which is reached when all possible combinations of bond rotations have been considered. In a random search, there is no natural endpoint one can never be absolutely sure that all of the minimum energy conformations have been found. The usual strategy is to generate conformations until no new structures can be obtained. This usually requires each structure to be generated many times and so the random methods inevitably explore each region of the conformational space a large number of times. 

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More or less automatic ways of finding an optimum are described in Appendix 6. The simplest of these by far is the random search method. It can be used for any number of optimization variables. It is extremely inefficient from the viewpoint of the computer but is joyously simple to implement. The following program fragment illustrates the method. 

Banga et al. [in State of the Art in Global Optimization, C. Floudas and P. Pardalos (eds.), Kluwer, Dordrecht, p. 563 (1996)]. All these methods require only objective function values for unconstrained minimization. Associated with these methods are numerous studies on a wide range of process problems. Moreover, many of these methods include heuristics that prevent premature termination (e.g., directional flexibility in the complex search as well as random restarts and direction generation). To illustrate these methods, Fig. 3-58 illustrates the performance of a pattern search method as well as a random search method on an unconstrained problem. 

FIG. 3-58 Examples of optimization methods without derivatives, (a) Pattern search method. (b) Random search method. O, first phase A, second phase , third phase. 

Scanning of a potential energy surface. Only deterministic methods (that is point by point searches) are fully reliable. However, these are in practice, due to the enormous computational effort, hardly ever possible. The methods currently used include random search methods (stochastic search, for example Monte Carlo methods) and mo-... 

Conformational analysis of substituted 1,3,2-dioxaphosphorinanes has been achieved using a topological approach (429) rather than the more elaborate random search method. This simplified approach only considers chemically and physically accessible positions for the lanthanide. Using this approach the LIS calculations are found to predict the conformational equilibrium for complexed cis conformers which is in good agreement with that based on the response of the coupling constants J(H-H) and J(P-H) to lanthanide addition. For the trans conformers the two approaches are not in agreement. 

Willett S. D. (1997) Inverse modeling of annealing of fission tracks in apatite 1 a controlled random search method. Am. 

Cartesian and Internal Coordinate Random Search Methods... 

Two important considerations with a random search method are how to determine the number of iterations necessary and how to choose the starting structure for each iteration. There is no simple method for deciding when to... 

Further Uses of the Metropolis Algorithm in Random Searching Methods... 

The random-search method will always go to a local optimum. If the size of the random changes are large enough, the search algorithm will eventually go to the global optimum. 

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