The discrete gradient evolutionary strategy method for global optimization

Global optimization problems continue to be a challenge in computational mathematics. The field is progressing in two streams: deterministic and heuristic approaches. In this paper, we present a hybrid method that uses the discrete gradient method, which is a derivative free local search method, and evolutionary strategies. We show that the hybridization of the two methods is better than each of them in isolation.E

State Transition Algorithm

In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called rotation, translation, expansion and axesion are designed. Adjusting measures of the transformations are mainly studied to keep the balance of exploration and exploitation. Convergence analysis is also discussed about the algorithm based on random search theory. In the meanwhile, to strengthen the search ability in high dimensional space, communication strategy is introduced into the basic algorithm and intermittent exchange is presented to prevent premature convergence. Finally, experiments are carried out for the algorithms. With 10 common benchmark unconstrained continuous functions used to test the performance, the results show that state transition algorithms are promising algorithms due to their good global search capability and convergence property when compared with some popular algorithms.Comment: 18 pages, 28 figure

Computational Potential Energy Minimization Studies on the Prion AGAAAAGA Amyloid Fibril Molecular Structures

X-ray crystallography, NMR (Nuclear Magnetic Resonance) spectroscopy, and dual polarization interferometry, etc are indeed very powerful tools to determine the 3D structures of proteins (including the membrane proteins), though they are time-consuming and costly. However, for some proteins, due to their unstable, noncrystalline and insoluble nature, these tools cannot work. Under this condition, mathematical and physical theoretical methods and computational approaches allow us to obtain a description of the protein 3D structure at a submicroscopic level. This Chapter presents some practical and useful mathematical optimization computational approaches to produce 3D structures of the Prion AGAAAAGA Amyloid Fibrils, from a potential energy minimization point of view. X-ray crystallography finds the X-ray final structure of a protein, which usually need refinements in order to produce a better structure. The computational methods presented in this Chapter can be also acted as a tool for the refinements.Comment: published in [Recent Advances in Crystallography, ISBN: 978-953-51-0754-5, Editor Jason B. Bendict, InTech Open Access Publisher, 19 Sept 2012, hardcover] Chapter 12, DOI: 10.5772/47733, pp.297-312: http://www.intechopen.com/books/recent-advances-in-crystallography/computational-potential-energy-minimization-studies-on-the-prion-agaaaaga-amyloid-fibril-molecular-

Derivative-free hybrid methods in global optimization and their applications

In recent years large-scale global optimization (GO) problems have drawn considerable attention. These problems have many applications, in particular in data mining and biochemistry. Numerical methods for GO are often very time consuming and could not be applied for high-dimensional non-convex and / or non-smooth optimization problems. The thesis explores reasons why we need to develop and study new algorithms for solving large-scale GO problems .... The thesis presents several derivative-free hybrid methods for large scale GO problems. These methods do not guarantee the calculation of a global solution; however, results of numerical experiments presented in this thesis demonstrate that they, as a rule, calculate a solution which is a global one or close to it. Their applications to data mining problems and the protein folding problem are demonstrated.Doctor of Philosoph