Nuclear Magnetic Resonance (NMR) Spectroscopy is a widely used technique to predict the native structure of proteins. However, NMR machines are only able to report approximate and partial distances between pair of atoms. To build the protein structure one has to solve the Euclidean distance geometry problem given the incomplete interval distance data produced by NMR machines. In this paper, we propose a new genetic algorithm for solving the Euclidean distance geometry problem for protein structure prediction given sparse NMR data. Our genetic algorithm uses a greedy mutation operator to intensify the search, a twin removal technique for diversification in the population and a random restart method to recover stagnation. On a standard set of benchmark dataset, our algorithm significantly outperforms standard genetic algorithms.
Euclidean distance geometry problem and its variants are applied to many problems in various fields including wireless sensor network localization @cite_8 , inverse kinematic problem @cite_16 , multi dimensional scaling @cite_9 , protein structure determination @cite_2 etc. The variant of the MDGP problem, when we know distances for all pairs @math and @math has a polynomial algorithm to produce exact solution @cite_10 . Even when some of the pairwise distances are unknown, the problem is solvable by a linear time algorithm @cite_17 . However, the variant of MDGP with sparse and inaccurate data is shown to be NP-hard by More and Wu @cite_5 . A recent survey of computational methods applied to solve this variant of MDGP can be found in @cite_6 .
@cite_8 @cite_9 @cite_6 @cite_2 @cite_5 @cite_16 @cite_10 @cite_17
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We discuss the geometrical interpretation of a well-known smoothing operator applied to the Molecular Distance Geometry Problem (MDGP), and we then describe a heuristic approach based on Variable Neighbourhood Search on the smoothed and original problem. This algorithm often manages to find solutions having higher accuracy than other methods. This is important as small differences in the objective function value may point to completely different 3D molecular structures. We consider the non-metric multidimensional scaling problem: given a set of dissimilarities ∆, find an embedding whose inter-point Euclidean distances have the same ordering as ∆. In this paper, we look at a generalization of this problem in which only a set of order relations of the form dij < dkl are provided. Unlike the original problem, these order relations can be contradictory and need not be specified for all pairs of dissimilarities. We argue that this setting is more natural in some experimental settings and propose an algorithm based on convex optimization techniques to solve this problem. We apply this algorithm to human subject data from a psychophysics experiment concerning how reflectance properties are perceived. We also look at the standard NMDS problem, where a dissimilarity matrix ∆ is provided as input, and show that we can always find an orderrespecting embedding of ∆. This paper describes a distributed, linear-time algorithm for localizing sensor network nodes in the presence of range measurement noise and demonstrates the algorithm on a physical network. We introduce the probabilistic notion of robust quadrilaterals as a way to avoid flip ambiguities that otherwise corrupt localization computations. We formulate the localization problem as a two-dimensional graph realization problem: given a planar graph with approximately known edge lengths, recover the Euclidean position of each vertex up to a global rotation and translation. This formulation is applicable to the localization of sensor networks in which each node can estimate the distance to each of its neighbors, but no absolute position reference such as GPS or fixed anchor nodes is available. We implemented the algorithm on a physical sensor network and empirically assessed its accuracy and performance. Also, in simulation, we demonstrate that the algorithm scales to large networks and handles real-world deployment geometries. Finally, we show how the algorithm supports localization of mobile nodes. Distance geometry problems arise in the determination of protein structure. We consider the case where only a subset of the distances between atoms is given and formulate this distance geometry problem as a global minimization problem with special structure. We show that global smoothing techniques and a continuation approach for global optimization can be used to determine global solutions of this problem reliably and efficiently. The global continuation approach determines a global solution with less computational effort than is required by a standard multistart algorithm. Moreover, the continuation approach usually finds the global solution from any given starting point, while the multistart algorithm tends to fail.