Search algorithms

There are several basic strategies for the improvement of the performance of substructure search algorithms ... 

The next sections deal exclusively with the second and the third approaches to the optimization of substructure search algorithms. 

The depth-first search algorithm the backtracking algorithm, respectively) has an exponential order of computational complexity CC [11] CC = 0(b ). The ex-... 

A substructure search algorithm is usually the first step in the implementation of other important topological procedures for the analysis of chemical structures such as identification of equivalent atoms, determination of maximal common substructure, ring detection, calculation of topological indices, etc. 

Transition stale search algorithms rather climb up the potential energy surface, unlike geometry optimi/.ation routines where an energy minimum is searched for. The characterization of even a simple reaction potential surface may result in location of more than one transition structure, and is likely to require many more individual calculations than are necessary to obtain et nilibrinm geometries for either reactant or product. 

The input to a minimisation program consists of a set of initial coordinates for the system. The initial coordinates may come from a variety of sources. They may be obtained from an experimental technique, such as X-ray crystallography or NMR. In other cases a theoretical method is employed, such as a conformational search algorithm. A combination of experimenfal and theoretical approaches may also be used. For example, to study the behaviour of a protein in water one may take an X-ray structure of the protein and immerse it in a solvent bath, where the coordinates of the solvent molecules have been obtained from a Monte Carlo or molecular dynamics simulation. 

A comparison of fine different conformational searching algorithms. (Data from [Saunders et at 1990].)... 

An effective way to construct loops using a systematic search algorithm is to grow the two ends of the in until they meet. 

Sources, which compare conformation search algorithms are... 

Mountain-climbing analogy to using a searching algorithm to find the optimum response for a response surface. The path on the left leads to the global optimum, and the path on the right leads to a local optimum. 

Example of a false optimum for a one-factor-at-a-time searching algorithm. 

Find the optimum response for the response surface in Figure 14.7 using the fixed-sized simplex searching algorithm. Use (0, 0) for the initial factor levels, and set the step size for each factor to 1.0. 

Tor each of the following equations, determine the optimum response, using the one-factor-at-a-time searching algorithm. Begin the search at (0, 0) with factor A, and use a step size of 1 for both factors. The boundary conditions for each response surface are 0 < A < 10 and 0 < B < 10. Continue the search through as many cycles as necessary until the optimum response is found. Compare your optimum response for each equation with the true optimum. 

The following texts and articles provide an excellent discussion of optimization methods based on searching algorithms and mathematical modeling, including a discussion of the relevant calculations. 

To overcome the limitations of the database search methods, conformational search methods were developed [95,96,109]. There are many such methods, exploiting different protein representations, objective function tenns, and optimization or enumeration algorithms. The search algorithms include the minimum perturbation method [97], molecular dynamics simulations [92,110,111], genetic algorithms [112], Monte Carlo and simulated annealing [113,114], multiple copy simultaneous search [115-117], self-consistent field optimization [118], and an enumeration based on the graph theory [119]. 

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