Molecular Conformation Problem Research Articles

Unassigned distance geometry and molecular conformation problems

3D protein structures and nanostructures can be obtained by exploiting distance information provided by experimental techniques, such as nuclear magnetic resonance and the pair distribution function method. These are examples of instances of the unassigned distance geometry problem (uDGP), where the aim is to calculate the position of some points using a list of associated distance values not previoulsy assigned to the pair of points. We propose new mathematical programming formulations and a new heuristic to solve the uDGP related to molecular structure calculations. In addition to theoretical results, computational experiments are also provided.

On the estimation of unknown distances for a class of Euclidean distance matrix completion problems with interval data

We consider some Euclidean distance matrix completion problems whose structure is inspired by molecular conformation problems. Some matrix distances are given precisely or in terms of intervals and other values are unknown. We present theoretical results that can be useful in methods to estimate the possible values of the unknown matrix distances.

Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems

Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that effectively leverage the complementary strengths of deterministic algorithms and QC techniques to overcome combinatorial complexity for solving large-scale mixed-integer programming problems. Four applications, namely the molecular conformation problem, job-shop scheduling problem, manufacturing cell formation problem, and the vehicle routing problem, are specifically addressed. Large-scale instances of these application problems across multiple scales ranging from molecular design to logistics optimization are computationally challenging for deterministic optimization algorithms on classical computers. To address the computational challenges, hybrid QC-based algorithms are proposed and extensive computational experimental results are presented to demonstrate their applicability and efficiency. The proposed QC-based solution strategies enjoy high computational efficiency in terms of solution quality and computation time, by utilizing the unique features of both classical and quantum computers.

Testing Different Nonsmooth Formulations of the Lennard–Jones Potential in Atomic Clustering Problems

A cluster is a group of identical molecules or atoms loosely bound by inter-atomic forces. The optimal geometry minimises the potential energy--usually modelled as the Lennard---Jones potential--of the cluster. The minimisation of the Lennard---Jones potential is a very difficult global optimisation problem with extremely many local minima. In addition to cluster problems, the Lennard---Jones potential represents an important component in many of the potential energy models used, for example, in protein folding, protein---peptide docking, and complex molecular conformation problems. In this paper, we study different modifications of the Lennard---Jones potential in order to improve the success rate of finding the global minimum of the original potential. The main interest of the paper is in nonsmooth penalised form of the Lennard---Jones potential. The preliminary numerical experiments confirm that the success rate of finding the global minimum is clearly improved when using the new formulae.

One-step organic phosphating

We consider some Euclidean distance matrix completion problems whose structure is inspired by molecular conformation problems. Some matrix distances are given precisely or in terms of intervals and other values are unknown. We present theoretical results that can be useful in methods to estimate the possible values of the unknown matrix distances.

Multi-scale global optimization of all-atom molecular models of n-alkanes

All-atom potential energy models of solid n-alkanes are important in understanding wax formation. Numerical results for molecular conformation computations using the multi-scale terrain/funneling method of Lucia and co-workers [Lucia, A., DiMaggio, P. A., & Depa, P. (2004a). A geometric terrain methodology for global optimization. Journal of Global Optimization, 29, 297; Lucia, A., DiMaggio, P. A., & Depa, P. (2004b). Funneling algorithms for multi-scale optimization on rugged terrains. Industrial & Engineering Chemistry Research, 43, 3770; Gattupalli, R. R., & Lucia, A. (2007). Molecular conformation of n-alkanes using terrain/funneling methods. Journal of Global Optimization, doi:10.1007/s10898-007-9206-5] are reported for all-atom potential energy models of the solid n-alkanes: dodecane, hexadecane, tetracosane, and triacontane, and compared with the basin hopping method of Wales and Doye [Wales, D. J., & Doye, J. P. K. (1997). Global optimization by basin hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. Journal of Physical Chemistry A, 101, 5111]. It is shown that the terrain/funneling method is capable of finding the global minimum energy molecular conformation for all examples in a reliable and efficient manner while basin hopping often fails. These numerical results provide strong evidence demonstrating that the multi-scale terrain/funneling method is a powerful global optimization method for solving molecular conformation problems.

Disk Packing in a Square: A New Global Optimization Approach

We present a new computational approach to the problem of placing n identical nonoverlapping disks in the unit square in such a way that their radii are maximized. The problem has been studied in a large number of papers, from both a theoretical and a computational point of view. In this paper, we conjecture that the problem possesses a so-called funneling landscape, a feature that is commonly found in molecular conformation problems. Based on this conjecture, we develop a stochastic search algorithm that displays excellent numerical performance. Thanks to this algorithm, we could improve over previously known putative optima in the range n ≤ 130 in as many as 32 instances, the smallest of which is n = 53.

PANMIN: sequential and parallel global optimization procedures with a variety of options for the local search strategy

We present two sequential and one parallel global optimization codes, that belong to the stochastic class, and an interface routine that enables the use of the Merlin/MCL environment as a non-interactive local optimizer. This interface proved extremely important, since it provides flexibility, effectiveness and robustness to the local search task that is in turn employed by the global procedures. We demonstrate the use of the parallel code to a molecular conformation problem. Program summary Title of program: PANMIN Catalogue identifier: ADSU Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADSU Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: PANMIN is designed for UNIX machines. The parallel code runs on either shared memory architectures or on a distributed system. The code has been tested on a SUN Microsystems ENTERPRISE 450 with four CPUs, and on a 48-node cluster under Linux, with both the GNU g77 and the Portland group compilers. The parallel implementation is based on MPI and has been tested with LAM MPI and MPICH Installation: University of Ioannina, Greece Programming language used: Fortran-77 Memory required to execute with typical data: Approximately O( n 2) words, where n is the number of variables No. of bits in a word: 64 No. of processors used: 1 or many Has the code been vectorised or parallelized?: Parallelized using MPI No. of bytes in distributed program, including test data, etc.: 147163 No. of lines in distributed program, including the test data, etc.: 14366 Distribution format: gzipped tar file Nature of physical problem: A multitude of problems in science and engineering are often reduced to minimizing a function of many variables. There are instances that a local optimum does not correspond to the desired physical solution and hence the search for a better solution is required. Local optimization techniques can be trapped in any local minimum. Global Optimization is then the appropriate tool. For example, solving a non-linear system of equations via optimization, one may encounter many local minima that do not correspond to solutions, i.e. they are far from zero Method of solution: PANMIN is a suite of programs for Global Optimization that take advantage of the Merlin/MCL optimization environment [1,2]. We offer implementations of two algorithms that belong to the stochastic class and use local searches either as intermediate steps or as solution refinement Restrictions on the complexity of the problem: The only restriction is set by the available memory of the hardware configuration. The software can handle bound constrained problems. The Merlin Optimization environment must be installed. Availability of an MPI installation is necessary for executing the parallel code Typical running time: Depending on the objective function

Predicting molecular structures: an application of the cutting angle method

The ability to predict molecular geometries has important applications in chemistry. Specific examples include the areas of protein space structure elucidation, the investigation of host–guest interactions, the understanding of properties of superconductors and of zeolites. This prediction of molecular geometries often depends on finding the global minimum or maximum of a function such as the potential energy. In this paper, we consider several well-known molecular conformation problems to which we apply a new method of deterministic global optimization called the cutting angle method. We demonstrate that this method is competitive with other global optimization techniques for these molecular conformation problems.

Global Optimization on Funneling Landscapes

Molecular conformation problems arising in computational chemistry require the global minimization of a non-convex potential energy function representing the interactions of, for example, the compo...

Genetic operators for the atomic cluster problem

This paper investigates the recent advances in applying genetic algorithms to non-bonded molecular conformation problems. Through the use of deterministic local optimisation to reduce the search domain and innovative phenotype genetic crossover operators, genetic algorithms are now able to efficiently solve problems such as determining the minimum energy configurations of pure atomic clusters ( N =2, …,100), mixed atomic clusters ( N = 2,…,20) and molecular clusters ( N = 2,…,32). A comparison of the more conventional genotype crossover operators with the more recently developed phenotype operators is presented.

Global Optima of Lennard-Jones Clusters

This paper summarizes the current state of knowledge concerning putative global minima of the potential energy function for Lennard-Jones clusters, an intensely studied molecular conformation problem. Almost all known exceptions to global optimality of the well-known Northby multilayer icosahedral conformations for microclusters are shown to be minor variants of that geometry. The truly exceptional case of face-centered cubic lattice conformations is examined and connections are made with the macrocluster problem. Several types of algorithms and their limitations are explored, and a new variation on the growth sequence idea is presented and shown to be effective for both small and large clusters.

The Effective Energy Transformation Scheme as a Special Continuation Approach to Global Optimization with Application to Molecular Conformation

This paper discusses a generalization of the function transformation scheme used in Coleman, Shalloway, and Wu [Comput. Optim. Appl., 2 (1993), pp. 145--170; J. Global Optim., 4 (1994), pp. 171--185] and Shalloway [Global Optimization, C. Floudas and P. Pardalos, eds., Princeton University Press, 1992, pp. 433--477; Global Optim., 2 (1992), pp. 281--311] for global energy minimization applied to the molecular conformation problem. A mathematical theory for the method as a special continuation approach to global optimization is established. We show that the method can transform a nonlinear objective function into a class of gradually deformed, but ``smoother'' or ``easier'' functions. An optimization procedure can then be successively applied to the new functions to trace their solutions back to the original function. Two types of transformation are defined: isotropic and anisotropic. We show that both transformations can be applied to a large class of nonlinear partially separable functions, including energy functions for molecular conformation. Methods to compute the transformation for these functions are given.

The Euclidian Distance Matrix Completion Problem

Motivated by the molecular conformation problem, completions of partial Euclidian distance matrices are studied. It is proved that any partial distance matrix with a chordal graph can be completed to a distance matrix. Given any nonchordal graph G, it is shown that there is a partial distance matrix A with graph G such that A does not admit any distance matrix completions. Finally, the connection between distance matrix completions and positive semidefinite completions is outlined.

Direct search methods for the molecular conformation problem

AbstractAn important area of research in computational biochemistry is the design of molecules for specific applications. The design of these molecules, which depends on the accurate determination of their three‐dimensional structure, can be formulated as a global optimization problem. In this article, we present results from the application of a new conformation searching method based on direct search methods. We compare these results to some earlier results using genetic algorithms and simulated annealing. © 1994 by John Wiley & Sons, Inc.

A quadratic assignment formulation of the molecular conformation problem

The molecular conformation problem is discussed, and a concave quadratic global minimization approach for solving it is described. This approach is based on a quadratic assignment formulation of a discrete approximation to the original problem.

Molecular conformation on the CM-5 by parallel two-level simulated annealing

In this paper, we propose a new kind of simulated annealing algorithm calledtwo-level simulated annealing for solving certain class of hard combinatorial optimization problems. This two-level simulated annealing algorithm is less likely to get stuck at a non-global minimizer than conventional simulated annealing algorithms. We also propose a parallel version of our two-level simulated annealing algorithm and discuss its efficiency. This new technique is then applied to the Molecular Conformation problem in 3 dimensional Euclidean space. Extensive computational results on Thinking Machines CM-5 are presented. With the full Lennard-Jones potential function, we were able to get satisfactory results for problems for cluster sizes as large as 100,000. A peak rate of over 0.8 giga flop per second in 64-bit operations was sustained on a partition with 512 processing elements. To the best of our knowledge, ground states of Lennard-Jones clusters of size as large as these have never been reported before.

Global optimization for molecular conformation problems

A primal-relaxed dual global optimization algorithm is presented along with an extensive review for finding the global minimum energy configurations of microclusters composed by particles interacting with any type of two-body central forces. First, the original nonconvex expression for the total potential energy is transformed to the difference of two convex functions (DC transformation) via an eigenvalue analysis performed for each pair potential that constitutes the total potential energy function. Then, a decomposition strategy based on the GOP algorithm [1–4] is designed to provide tight upper and lower bounds on the global minimum through the solutions of a sequence of relaxed dual subproblems. A number of theoretical results are included which expedite the computational effort by exploiting the special mathematical structure of the problem. The proposed approach attainse-convergence to the global minimum in a finite number of iterations. Based on this procedure global optimum solutions are generated for small Lennard-Jones and Morse (a=3) microclustersn≤7. For larger clusters (8≤N≤24 for Lennard-Jones and 8≤N≤30 for Morse), tight lower and upper bounds on the global solution are provided which serve as excellent initial points for local optimization approaches.