Genetic Algorithm Optimization of Point Charges in Force Field Development: Challenges and Insights

Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields

Constrained Nonlinear Model Predictive Control of an MMA Polymerization Process via Evolutionary Optimization

In this work, a nonlinear model predictive controller is developed for a batch polymerization process. The physical model of the process is parameterized along a desired trajectory resulting in a trajectory linearized piecewise model (a multiple linear model bank) and the parameters are identified for an experimental polymerization reactor. Then, a multiple model adaptive predictive controller is designed for thermal trajectory tracking of the MMA polymerization. The input control signal to the process is constrained by the maximum thermal power provided by the heaters. The constrained optimization in the model predictive controller is solved via genetic algorithms to minimize a DMC cost function in each sampling interval.Comment: 12 pages, 9 figures, 28 reference

Quaternionic representation of the genetic code

A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick on the origin and evolution of the code as well as with the chronological order of appearence of the amino acids along the evolution as inferred from work that mixtures known experimental results with theoretical speculations. Suggested by the diagram we propose a Hamilton quaternions based mathematical representation of the code as it stands now-a-days. The central object in the description is a codon function that assigns to each amino acid an integer quaternion in such a way that the observed code degeneration is preserved. We emphasize the advantages of a quaternionic representation of amino acids taking as an example the folding of proteins. With this aim we propose an algorithm to go from the quaternions sequence to the protein three dimensional structure which can be compared with the corresponding experimental one stored at the Protein Data Bank. In our criterion the mathematical representation of the genetic code in terms of quaternions merits to be taken into account because it describes not only most of the known properties of the genetic code but also opens new perspectives that are mainly derived from the close relationship between quaternions and rotations.Comment: 19 pages, 11 figure

The structural optimization of atomic and molecular microclusters using a genetic algorithm in real-valued space-fixed coordinates

This dissertation documents the development and application of the space-fixed modified genetic algorithm, SFMGA. The SFMGA is shown to be both portable and fast for the structural optimization of Lennard-Jones, silicon, water, benzene, naphthalene, and anthracene microclusters. We introduce the SFMGA and apply it to LJ atomic clusters. CPU times needed to obtain the global minimum are compared with similar methods. We then investigate a complicated potential representing silicon atoms. The results show that SFMGA is applicable to non-pairwise additive potentials. We demonstrate the use of SFMGA for clusters where the monomers are molecules. Water clusters are optimized and the relative performance of the genetic operators, for both LJ and H\sb2O clusters, is explored. Finally, we investigate benzene, naphthalene, and anthracene clusters. In these clusters the size and potential surface complexity can be varied independently