Algorithms, searching

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

The algorithm searches during a GA run for the fittest possible string. The fitness function defines a surface across which this search takes place (Figure 5.9) the surface is usually of considerable complexity because it is a function of all the variables that comprise the GA string. 

A. Jin, F. Leung, and D. F. Weaver, ]. Comput. Chem., 18, 1971 (1997). Development of a Genetic Algorithm Search Method (GAP1.0) for Exploring Peptide Conformational Space. 

The approach of Chaudhury el al,131 can in principle be combined with any of the search methods we have discussed in Section 2 (as long as the Hessian can be calculated relatively easy — this seems to be the critical point of the approach), but Chaudhury et a/.131 combined it with a genetic-algorithm search. Subsequently they demonstrated its validity for clusters of Lennard-Jones atoms. 

Mathematically, EFA provides initial estimates of the time profiles, often quite rough and of poor quality. More frequently, algorithms searching for the purest variables of D (e.g., SIMPLISMA [SIMPLe-to-use Interactive Selfmodeling Mixture Analysis]), applied either to the spectral or time domains, are used for finding the most characteristic profiles of the data set (47). 

Once an accurate wavefunction has been obtained in ab initio calculations, the forces on all the atoms in a cluster can be computed exactly and analytically using well-developed quantum-mechanical techniques. This ability enables us to carry out a full ab initio minimization of the cluster geometry and extract the optimal equilibrium geometry. In general, the optimization algorithm searches for a stationary point , that is, a molecular structure such that for all atomic coordinates the force is zero. Mathematically, this means that... 

The predominant approach to sequence motif discovery is the focused approach, which searches for novel motifs in a set of unaligned DNA or protein sequences suspected to contain a common motif. We discuss how the sequences can be selected in the next section. RE-based motif discovery algorithms for the focused approach search the space of all possible REs either exhaustively or heuristically (incompletely). Their objective is usually to identify the REs whose matches are most over-represented in the input sequences (relative to a background sequence model, randomly generated background sequences, or a set of negative control sequences). PWM-based motif discovery algorithms search the space of PWMs for motifs that maximize an objective function that is usually equal to (or related to) log likelihood ratio of the PWM ... 

In the classification setting, every example is assumed to be independent of every other example. However, there are cases where dependencies exist between examples and the label corresponding to such dependent examples forms a complex object. The structured-prediction problem attempts to predict a complex object such as a protein interaction network, phylogenetic tree, a binding site on a protein, etc. In short, a structured-prediction problem D is a classification problem where y e Y (the space of fhe label on an example) has a structure. For a finite set of data structures, the learning algorithm searches for the structured output that minimizes the expected cost E[c/,(j )] of example x [44] where cosf measures fhe dissimilarify between the example and a proposed structured output. 

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